EXPLORATION 1<\/strong><\/p>\nSeconds to Liftoff
\nWork with a partner. You are listening to a command center before the liftoff of a rocket. You hear the following:
\n\u201cT minus 10 seconds . . . go for main engine start . . . T minus 9 . . . 8 . . . 7 . . . 6 . . . 5 . . . 4 . . . 3 . . . 2 . . . 1 . . . we have liftoff.\u201d
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.2-1.png\")
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.2-2.png\")
\na. Represent these events on a number line.
\nAnswer:
\nRocket clears launchpad tower = +6 = A Event
\nLaunch Verification = -16 = B Event
\nMain Engine Start = -3 = C Event
\nRocket Topping sequence complete = -110 = D Event
\nLaunch control system enabled = -90 = E Event
\nBoosters ignite = 0 = F Event
\n![\"Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers,-Number-Lines-and-the-Coordinate-Plane-Lesson-8.2-Comparing-Ordering-Integers-Exploration-1\"](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-Lesson-8.2-Comparing-Ordering-Integers-Exploration-1.png\")
\nb. List the events in the order they occurred. Explain your reasoning.
\nAnswer:
\n1 – Rocket Topping sequence complete = -110 = D Event
\n2 – Launch control system enabled = -90 = E Event
\n3 – Launch Verification = -16 = B Event
\n4 – Main Engine Start = -3 = C Event
\n5 – Boosters ignite = 0 = F Event
\n6 – Rocket clears launchpad tower = +16 = A Event
\nAs per the above number line the events which take place are ordered from left side to right side<\/p>\n
c. Extend the number line in part(a) to show events in an astronaut\u2019s day. Include at least five events before liftoff and at least five events after liftoff. Use the Internet or another reference source to gather information.
\nAnswer:
\n1 – Rocket Topping sequence complete = -110 = D Event
\n2 – Launch control system enabled = -90 = E Event
\n3 – Launch Verification = -16 = B Event
\n4 – Main Engine Start = -3 = C Event
\n5 – Boosters ignite = 0 = F Event
\n6 – Rocket clears launchpad tower = +6 = A Event
\n7- Stage 1 Burnout = +16 = G Event
\n8 – Fairing Jettison = +25 = H Event
\n9 – Stage 1 Separation = + 30 = I Event
\n10 – Stage 2 Ignition = +35 = J Event
\n11 – Transfer to the launch pad = – 120 = K Event
\n![\"Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers,-Number-Lines-and-the-Coordinate-Plane-Lesson-8.2-Comparing-Ordering-Integers-Exploration-1-C\"](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-Lesson-8.2-Comparing-Ordering-Integers-Exploration-1-C.jpg\")
<\/p>\n
Recall that on a horizontal number line, numbers to the left are less than numbers to the right. Numbers to the right are greater than numbers to the left. On a vertical number line, numbers below are less than numbers above. Numbers above are greater than numbers below.<\/p>\n
Try It<\/strong><\/p>\nCopy and Complete the statement using < or >.<\/strong>
\nQuestion 1.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.2-3.png\")
\nAnswer:
\n0 > -4
\nExplanation:
\nThe Negative Numbers which are near to the 0 are greater .Numbers to the right are greater.With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller. Think what the number represents. Think what the value is.<\/p>\nQuestion 2.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.2-4.png\")
\nAnswer:
\n-5 < 5
\nExplanation:
\nAll Positive Numbers are greater than the Negative numbers .<\/p>\n
Question 3.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.2-5.png\")
\nAnswer:
\n-8 < -7
\nExplanation:
\nThe Negative Numbers which are near to the 0 are greater .Numbers to the right are greater.
\nWith negative numbers, we have to remember that as the digit gets bigger, the number gets smaller. Think what the number represents. Think what the value is.<\/p>\n
Order the integers from least to greatest.<\/strong>
\nQuestion 4.
\n-2, -3, 3, 1, -1
\nAnswer:
\n-3, -2, -1, 1, 3<\/p>\nQuestion 5.
\n4, -7, -8, 6, 1
\nAnswer:
\n-8, -7, 1, 4, 6<\/p>\n
Question 6.
\nIn Example 3, what is the least possible integer value of the number?
\nAnswer:<\/p>\n
Self-Assessment for Concepts & Skills<\/strong><\/p>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.
\nORDERING INTEGERS<\/strong> Order the integers from least to greatest.
\nQuestion 7.
\n6, – 4, – 1, 3, 5
\nAnswer:
\n-4, -1,\u00a0 3, 5, 6<\/p>\nQuestion 8.
\n– 7, – 9, 0, 8, – 2
\nAnswer:
\n-9, -7, -2, 0, 8<\/p>\n
Question 9.
\nWRITING<\/strong>
\nExplain how to determine which of two integers is greater.
\nAnswer:<\/p>\nWe are used to big positive numbers meaning a big value – the bigger the number, the more, or higher, or longer, or expensive, or whatever the number represents.<\/p>\n
With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller. Think what the number represents and what the value is.<\/p>\n
Question 10.
\nREASONING<\/strong>
\nThe positions of four fish are shown.
\na. Use red, blue, yellow, and green dots to graph the positions of the fish on a horizontal number line and a vertical number line.
\nb. Explain how to use the number lines from part(a) to order the positions from least to greatest.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.2-6.1.png\")
\nAnswer a :
\nThe position of red fish = -4
\nThe position of Yellow fish = -6
\nThe position of green fish = 0
\nThe position of Blue fish = 8
\n![\"Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers,-Number-Lines-and-the-Coordinate-Plane-Self-Assessment-for-Concepts-Skills-Question](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-Self-Assessment-for-Concepts-Skills-Question-10-1a.jpg\")
\n![\"Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers,-Number-Lines-and-the-Coordinate-Plane-Self-Assessment-for-Concepts-Skills-Question](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-Self-Assessment-for-Concepts-Skills-Question-10-2a.jpg\")
\nAnswer b:
\nLeast to greatest numbers are
\n-6, -4, 0, 8
\nExplanation:
\nFrom the above horizontal number line we notice that the numbers from left to right of number line\u00a0 represent least to greatest numbers.<\/p>\nQuestion 11.
\nNUMBER SENSE<\/strong>
\na and bare negative integers. Compare a and b. Explain your reasoning.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.2-6.png\")
\nAnswer:<\/p>\nb > a
\nExplanation:
\nwe notice that the numbers from left to right of number line\u00a0 represent least to greatest numbers.The Negative Numbers which are near to the 0 are greater .Numbers to the right are greater.
\nWith negative numbers, we have to remember that as the digit gets bigger, the number gets smaller. Think what the number represents. Think what the value is..<\/p>\n
Question 12.
\nThe freezing temperature of nitrogen is \u2212210\u00b0C, and the freezing temperature of oxygen is \u2212219\u00b0C. A container of nitrogen and a container of oxygen are both cooled to \u2212215\u00b0C. Do the contents of each container freeze? Explain.
\nAnswer:
\nThe temperature of liquid nitrogen can readily be reduced to its freezing point\u00a063 K\u00a0(\u2212210 \u00b0C; \u2212346 \u00b0F) by placing it in a vacuum chamber pumped by a vacuum pump
\nThe temperature at which a substance freezes\u00a0is called the\u00a0freezing\u00a0point. The\u00a0freezing point of oxygen is -219\u00b0C .\u00a0This means that they\u00a0need\u00a0to be cooled to lower temperatures to make them\u00a0freeze.<\/p>\n
Question 13.
\nDIG DEEPER!<\/strong>
\nThe diagram shows the daily high temperatures during a school week. Was a positive Celsius temperature recorded on Tuesday? on Friday? Explain.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.2-7.png\")
\nAnswer:
\nNo
\nExplanation:
\nThe natural numbers 1, 2, 3, 4, 5, \u2026\u2026\u2026 are called\u00a0positive integers.
\nPositive numbers\u00a0are represented to the right of zero on the number line. Positive numbers\u00a0are greater than negative\u00a0numbers\u00a0as well a zero.
\nBecause zero is neither\u00a0positive\u00a0nor\u00a0negative . Zero is a neutral number.
\nTherefore positive Celsius temperature recorded on Monday and Friday .<\/p>\nComparing and Ordering Integers Homework & Practice 8.2<\/h3>\n![\"Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers,-Number-Lines-and-the-Coordinate-Plane-Comparing-Ordering-Integers-Homework-Practice-8.2-Question-34-a\"](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-Comparing-Ordering-Integers-Homework-Practice-8.2-Question-34-a.jpg\")
.2<\/h3>\n
Review & Refresh<\/strong><\/p>\nWrite a positive or negative integer that represents the situation.<\/strong>
\nQuestion 1.
\nYou walk up 83 stairs.
\nAnswer:
\nup indicates + .so it is + 83<\/p>\nQuestion 2.
\nA whale is 17 yards below sea level.
\nAnswer:
\nBelow indicates – . So it is -17<\/p>\n
Question 3.
\nAn organization receives a $75 donation.
\nAnswer:
\nReceives indicates +. So it is +$75<\/p>\n
Question 4.
\nA rock falls 250 feet off a cliff.
\nAnswer:
\nFalls indicates – . So it is -250<\/p>\n
Question 5.
\nWhat is the area of the trapezoid?
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.2-8.png\")
\nA. 6.3 ft2<\/sup>
\nB. 44.1 ft2<\/sup>
\nC. 50.4 ft2<\/sup>
\nD. 88.2 ft2<\/sup>
\nAnswer:
\nHeight of Trapezoid = 4.2ft
\nBase 1 of Trapezoid = 12ft
\nBase 2 of Trapezoid = 9 ft
\nArea of Trapezoid = half-height \u00d7 (base1 + base2) = \\(\\frac{4.2}{2}\\) (12 + 9)
\n=2.1 \u00d7 21 = 44.1 ft2<\/sup><\/p>\nDivide. Write the answer in simplest form.<\/strong>
\nQuestion 6.
\n\\(\\frac{1}{5} \\div \\frac{1}{9}\\)
\nAnswer:
\n\\(\\frac{1}{5}\\)\u00f7latex]\\frac{9}{1}[\/latex]= 9\/5=1.8<\/p>\nQuestion 7.
\n\\(\\frac{2}{5} \\div \\frac{1}{3}\\)
\nAnswer:
\n(2\/5) \/(1\/3) = (2\u00d73) \/5 = 6\/5=1.2<\/p>\n
Question 8.
\n\\(\\frac{1}{4}\\) \u00f7 3
\nAnswer:
\n\\(\\frac{1}{4}\\)\u00d7 \\(\\frac{1}{3}\\)=\\(\\frac{1}{12}\\) = 0.083<\/p>\n
Question 9.
\n\\(\\frac{4}{7}\\) \u00f7 8
\nAnswer:
\n\\(\\frac{4}{7}\\) \u00d7 \\(\\frac{1}{8}\\)=\\(\\frac{1}{14}\\) =0.071<\/p>\n
Concepts, Skills, &Problem Solving<\/strong><\/p>\nOPEN-ENDED<\/strong> Name an event that could occur at the given time (in seconds) in Exploration 1. Describe when the event occurs in the order of events from the exploration. (See Exploration 1, p. 351.)<\/p>\nQuestion 10.
\n– 300
\nAnswer:<\/p>\n
Question 11.
\n– 150
\nAnswer:<\/p>\n
Question 12.
\n10
\nAnswer:<\/p>\n
COMPARING INTEGERS Copy and complete the statement using < or >.
\n<\/strong>Question 13.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.2-9.png\")
\nAnswer:
\n3 > 0
\nExplanation:
\nAll Positive Numbers are greater than the Negative numbers .<\/p>\nQuestion 14.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.2-10.png\")
\nAnswer:
\n-2 < 0
\nExplanation:
\nAll Positive Numbers are greater than the Negative numbers .<\/p>\n
Question 15.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.2-11.png\")
\nAnswer:
\n6 > -6
\nExplanation:
\nAll Positive Numbers are greater than the Negative numbers .<\/p>\n
Question 16.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.2-12.png\")
\nAnswer:
\n3 > -4
\nExplanation:
\nAll Positive Numbers are greater than the Negative numbers .<\/p>\n
Question 17.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.2-13.png\")
\nAnswer:
\n-1 < 4
\nExplanation:
\nAll Positive Numbers are greater than the Negative numbers .<\/p>\n
Question 18.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.2-14.png\")
\nAnswer:
\n-7 > -8
\nExplanation:
\nThe Negative Numbers which are near to the 0 are greater .Numbers to the right are greater.With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.<\/p>\n
Question 19.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.2-15.png\")
\nAnswer:
\n-3 < -2
\nExplanation:
\nThe Negative Numbers which are near to the 0 are greater .Numbers to the right are greater.With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.<\/p>\n
Question 20.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.2-16.png\")
\nAnswer:
\n-5 > – 10
\nExplanation:
\nThe Negative Numbers which are near to the 0 are greater .Numbers to the right are greater.With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.<\/p>\n
YOU BE THE TEACHER<\/strong>
\nYour friend compares two integers. Is your friend correct? Explain your reasoning.
\nQuestion 21.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.2-17.png\")
\nAnswer:
\nNo My friend is wrong.
\nExplanation:
\nThe Negative Numbers which are near to the 0 are greater .Numbers to the right are greater.With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.
\n-1 is nearer to 0 than -3 so -1 is greater
\n-3 < – 1<\/p>\nQuestion 22.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.2-18.png\")
\nAnswer:
\nYes it is True .
\n– 7 < -3<\/p>\n
ORDERING INTEGERS<\/strong> Order the integers from least to greatest.
\nQuestion 23.
\n0, – 1, 2, 3, – 3
\nAnswer:
\n-3, -1, 0, 2, 3
\nExplanation:
\nWith negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.All Positive Numbers are greater than the Negative numbers .<\/p>\nQuestion 24.
\n– 4, – 2, – 3, 2, 1
\nAnswer:
\n-4, -3, -2, 1, 2
\nExplanation:
\nWith negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.All Positive Numbers are greater than the Negative numbers .<\/p>\n
Question 25.
\n– 2, 3, – 3, – 4, 4
\nAnswer:
\n-4, -3, -2, 3, 4
\nExplanation:
\nWith negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.All Positive Numbers are greater than the Negative numbers .<\/p>\n
Question 26.
\n5, – 11, – 9, 3, – 4
\nAnswer:
\n-11, -9, -4. 3, 5
\nExplanation:
\nWith negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.All Positive Numbers are greater than the Negative numbers .<\/p>\n
Question 27.
\n– 3, 8, 4, 0, – 13
\nAnswer:
\n-13, -3, 0, 4, 8
\nExplanation:
\nWith negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.All Positive Numbers are greater than the Negative numbers .<\/p>\n
Question 28.
\n– 7, 2, 6, – 4, 3
\nAnswer:
\n-7, -4, 2, 3, 6
\nExplanation:
\nWith negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.All Positive Numbers are greater than the Negative numbers .<\/p>\n
Question 29.
\n12, – 8, – 16, 7, 1
\nAnswer:
\n-16, -8, 1, 7, 12
\nExplanation:
\nWith negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.All Positive Numbers are greater than the Negative numbers .<\/p>\n
Question 30.
\n10, – 10, 30, – 30, – 50
\nAnswer:
\n-50, -30, -10, 10, 30
\nExplanation:
\nWith negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.All Positive Numbers are greater than the Negative numbers .<\/p>\n
Question 31.
\n– 5, 15, – 10, – 20, 25
\nAnswer:
\n-20, -10, -5, 15, 25
\nExplanation:
\nWith negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.All Positive Numbers are greater than the Negative numbers .<\/p>\n
Question 32.
\nMODELING REAL LIFE<\/strong>
\nAn archaeologist discovers the two artifacts shown.
\na. What integer represents ground level?
\nb. A dinosaur bone is 42 centimeters below ground level. Is it deeper than both of the artifacts? Explain.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.2-19.png\")
\nAnswer a :
\nAn integer represents ground level = 0 (as it is neutral)
\nAnswer b :
\nDinosaur bone is at = – 42cms
\nFirst artifact is at =-38 cms
\nSecond artifact is at = – 44 cms
\nNo it not depper than both the artifacts.
\nExplanation:
\nIt is in between the artifacts. as -42 lies in between -38 and -44<\/p>\nQuestion 33.
\nREASONING<\/strong>
\nA number is between \u22122 and \u221210. What is the least possible integer value of this number? What is the greatest possible integer value of this number?
\nAnswer:
\nThe numbers between -2 and -10 = -3, -4, -5, -6, -7, -8, -9
\nGreatest value = -3
\nLeast Value = – 9
\nExplanation:
\nThe Negative Numbers which are near to the 0 are greater .Numbers to the right are greater.With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.<\/p>\nQuestion 34.
\nNUMBER SENSE<\/strong>
\nDescribe the locations of the integers m and n on a number line for each situation.
\na. m < n
\nb. m > n
\nc. n > m
\nAnswer a :
\nm < n where m = 1 and n = 3
\n
\nAnswer b :
\nm > n where n = -1 and m = 1
\n![\"Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers,-Number-Lines-and-the-Coordinate-Plane-Comparing-Ordering-Integers-Homework-Practice-8.2-Question-34-b\"](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-Comparing-Ordering-Integers-Homework-Practice-8.2-Question-34-b.png\")
\nAnswer c :
\nn > m where n = 5 and m = -5
\n![\"Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers,-Number-Lines-and-the-Coordinate-Plane-Comparing-Ordering-Integers-Homework-Practice-8.2-Question-34-c\"](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-Comparing-Ordering-Integers-Homework-Practice-8.2-Question-34-c.jpg\")
<\/p>\nCRITICAL THINKING<\/strong> Tell whether the statement is always, sometimes, or never true. Explain.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.2-20.png\")
\nQuestion 35.
\nA positive integer is greater than its opposite.
\nAnswer:
\nYES,
\nExplanation:
\nThe opposite number of a positive number is negative numbers. Negative are always lesser than positive numbers.<\/p>\nQuestion 36.
\nAn integer is less than its opposite and greater than 0.
\nAnswer:
\nNo
\nExplanation:
\ninteger = 5
\nThe opposite of 5 is -5
\nHere integer is not less than its oppositeand greater than 0 it is -5 < 5 .<\/p>\n
Question 37.
\nMODELING REAL LIFE<\/strong>
\nThe table shows the highest and lowest elevations for five states.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.2-21.png\")
\na. Order the states by their highest elevations, from least to greatest.
\nb. Order the states by their lowest elevations, from least to greatest.
\nc. What does the lowest elevation for Florida represent?
\nAnswer a :
\nFlorida < Louisiana <Arkansas < Tennessee < California
\n345< 535 < 2753 < 6643 < 14494
\nAnswer b :
\nCalifornia < Louisiana < Florida < Arkansas < Tennessee
\n-282 < -8 < 0 < 55 < 178<\/p>\nQuestion 38.
\nNUMBER SENSE<\/strong>
\nPoint A is on a number line halfway between \u221217 and 5. Point Bis halfway between Point A and 0. What integer does Point B represent?
\nAnswer:
\nPoint A = half way between -17 and 5 = (- 17 + 5) \u00f7 2 = – 12\u00f72 = -6
\nPoint B = halfway between Point A and 0 = (-6 + 0) \u00f7 2= -6 \u00f7 2 = – 3
\nTherefore Point B represent -3 integer<\/p>\nQuestion 39.
\nREASONING<\/strong>
\nEleven Fahrenheit temperatures are shown on a map during a weather report. When the temperatures are ordered from least to greatest, the middle temperature is below off. Do you know exactly how many of the temperatures are represented by negative numbers? Explain.
\nAnswer:<\/p>\nQuestion 40.
\nPUZZLE<\/strong>
\nNine students each choose one integer. Here are seven of them:
\n5, \u2212 8, 10, \u2212 1, \u2212 12, \u2212 20, and 1.
\na. When all nine integers are ordered from least to greatest, the middle integer is 1. Describe the integers chosen by the other two students.
\nb. When all nine integers are ordered from least to greatest, the middle integer is \u22123. Describe the integers chosen by the other two students.<\/p>\nAnswer a :
\nOrder the numbers so that 1 is in the middle:
\n-20, -12, -8, -1,\u00a01<\/strong>, 5, 10, x, x -> The other 2 numbers must be greater than 1, as the range can be 2 < x, x being the number chosen
\nAnswer b .
\nOrder the numbers so that -3 is in the middle:
\nx, -20, -12, -8, (-3), -1, 1, 5, 10 -> The other number must be less than -3, as the range is x < – 3, x being the number chosen<\/p>\nLesson 8.3 Rational Numbers<\/h3>\n
EXPLORATION 1<\/strong><\/p>\nLocating Fractions on a Number Line
\nWork with a partner. Represent the events on a number line using a fraction or a mixed number.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-1.png\")
\nAnswer:<\/p>\n
![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-2.png\")
<\/p>\n
Integers, fractions, and decimals make up the set of rational numbers. A rational number is a number that can be written as a – b, where a and b are integers and b \u2260 0.<\/p>\n
Try It<\/strong><\/p>\nGraph the number and its opposite.<\/strong>
\nQuestion 1.
\n2\\(\\frac{1}{2}\\)
\nAnswer:
\n2 \u00d7 \\(\\frac{1}{2}\\) = \\(\\frac{2}{2}\\) = 1
\nThe opposite of 1 is -1<\/p>\nQuestion 2.
\n–\\(\\frac{4}{5}\\)
\nAnswer:
\n–\\(\\frac{4}{5}\\)= – ( 4 \u00f7 5) = – 0.8
\nThe opposite of – 0.8 is 0.8<\/p>\n
Question 3.
\n– 3.5
\nAnswer:
\nThe opposite of – 3.5 is 3.5<\/p>\n
Question 4.
\n5.25
\nAnswer:
\nThe opposite of 5.25 is -5.25<\/p>\n
Copy and complete the statement using < or >.<\/strong>
\nQuestion 5.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-3.png\")
\nAnswer:
\n–\\(\\frac{4}{7}\\) = -0.57
\n–\\(\\frac{1}{7}\\)= -0.14
\n– 0.57\u00a0 \u00a0<\u00a0 -0.14<\/p>\nQuestion 6.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-4.png\")
\nAnswer:
\n–\\(\\frac{5}{3}\\) = -1.66
\n–\\(\\frac{11}{6}\\) = -1.83
\n-1.66 > – 1.83<\/p>\n
Question 7.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-5.png\")
\nAnswer:
\n– 0.5\u00a0 <\u00a0 0.3<\/p>\n
Question 8.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-6.png\")
\nAnswer:
\n-6.5\u00a0 > – 6.75<\/p>\n
Self-Assessment for Concepts & Skills<\/strong><\/p>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.
\nCOMPARING RATIONAL NUMBERS<\/strong> Copy and complete the statement using < or >.
\nQuestion 9.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-7.png\")
\nAnswer:
\n–\\(\\frac{2}{3}\\) = -0.66
\n–\\(\\frac{5}{9}\\) = -0.55
\n-0.66\u00a0 < -0.55<\/p>\nQuestion 10.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-8.png\")
\nAnswer:
\n–\\(\\frac{9}{4}\\)= – 2.25
\n–\\(\\frac{19}{8}\\)= -2.375
\n-2.25\u00a0 >\u00a0 -2.375<\/p>\n
Question 11.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-9.png\")
\nAnswer:
\n-1.7\u00a0 \u00a0>\u00a0 \u00a0-2.4<\/p>\n
Question 12.
\nNUMBER SENSE<\/strong>
\nWhich statement is not true?
\nA. On a number line, \u22122\\(\\frac{1}{6}\\) is to the left of \u22122\\(\\frac{2}{3}\\).
\nB. \u22122 \\(\\frac{2}{3}\\) is less than \u22122\\(\\frac{1}{6}\\).
\nC. On a number line, \u22122\\(\\frac{2}{3}\\) is to the left of \u22122\\(\\frac{1}{6}\\).
\nAnswer A :
\n\u22122\\(\\frac{1}{6}\\) = \u2212\\(\\frac{1}{3}\\) = – 0.33
\n\u22122\\(\\frac{2}{3}\\) = \u2212\\(\\frac{4}{3}\\) = -1.33
\nExplanation:
\n![\"Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers,-Number-Lines-and-the-Coordinate-Plane-Lesson-8.3-Rational-Numbers-Question-12-a\"](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-Lesson-8.3-Rational-Numbers-Question-12-a.jpg\")
\nAnswer B :
\n\u22122 \\(\\frac{2}{3}\\) = \u2212 \\(\\frac{4}{3}\\) = -1.33
\n\u22122\\(\\frac{1}{6}\\) = \u2212\\(\\frac{1}{3}\\) = – 0.33
\n-1.33\u00a0 <\u00a0 – 0.33
\nExplanation:
\nThe Negative Numbers which are near to the 0 are greater .Numbers to the right are greater.With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.<\/p>\nAnswer C :
\n\u22122 \\(\\frac{2}{3}\\) = \u2212 \\(\\frac{4}{3}\\) = -1.33
\n\u22122\\(\\frac{1}{6}\\) = \u2212\\(\\frac{1}{3}\\) = – 0.33
\nFrom the above number line we notice that -1.33 is left of -0.33<\/p>\n
Question 13.
\nWRITING<\/strong>
\nExplain how to determine whether a number is a rational number.
\nAnswer:
\nThe rational number which is represented in the \\(\\frac{p}{q}\\)form and where q is not equal to zero.
\nExamples :
\n\\(\\frac{2}{3}\\), \\(\\frac{7}{3}\\)<\/p>\nSelf-Assessment for Problem Solving<\/strong><\/p>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.
\nQuestion 14.
\nYou and your friend rappel down a cliff. Your friend descends 0.11 mile and then waits for you to catch up. You descend and your current change in elevation is \u22120.12 mile. Have you reached your friend? Explain.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-10.png\")
\nAnswer:
\nDistance traveled by my friend = 0.11<\/p>\n
Question 15.
\nThe table shows the changes in the value of a stock over a period of three days. On which day does the value of the stock change the most? Explain your reasoning.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-11.png\")
\nAnswer:
\nChange in stock is most in day 3 that is – 0.45
\nExplanation:
\nOn day 1 the stock change is -0.42
\nOn day 2 there is no stock change that is 0
\nOn day 3 the stock change is -0.45
\nFrom 0 to -0.45 change is more<\/p>\n
Rational Numbers Homework & Practice 8.3<\/h3>\n
Review & Refresh<\/strong><\/p>\nCopy and complete the statement using < or >.<\/strong>
\nQuestion 1.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-12.png\")
\nAnswer:
\n5 < 8<\/p>\nQuestion 2.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-13.png\")
\nAnswer:
\n-4 > -7<\/p>\n
Question 3.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-14.png\")
\nAnswer:
\n2 > -5<\/p>\n
Question 4.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-15.png\")
\nAnswer:
\n0 > -3<\/p>\n
Question 5.
\nYou pay $48 for 8 pounds of chicken. Which is an equivalent rate?
\nA. $44 for 4 pounds
\nB. $28 for 4 pounds
\nC. $15 for 3 pounds
\nD. $30 for 5 pounds
\nAnswer:
\n$30 for 5 pounds
\nExplanation:
\nYou pay $48 for 8 pounds of chicken.
\n$48 = 8 Pounds
\n$__ = 5 Ponds.
\nDo Cross Multiplication
\n(48 \u00d7 5)\u00f78 = 6\u00a0 \u00d7 5 = $30<\/p>\n
Find the whole.<\/strong>
\nQuestion 6.
\n40% of what number is 24?
\nAnswer:
\n40 % = 24
\n100 % = ?
\nThe answer is 60.
\nExplanation:
\nDo cross multiplication we get :
\n100 % \u00d7 24 = 40% \u00d7 ?
\n2400 \u00f7 40 = 60.
\nTherefore answer is 60.<\/p>\nQuestion 7.
\n12% of what number is 9?
\nAnswer:
\n12 % = 9
\n100 % = ?
\nThe answer is 75.
\nExplanation:
\nDo cross multiplication we get :
\n100 % \u00d7 9 = 12% \u00d7 ?
\n900 \u00f7 12 = 75.
\nTherefore answer is 75.
\nQuestion 8.
\n48% of what number is 84?
\nAnswer:
\n48 % = 84
\n100 % = ?
\nThe answer is 175.
\nExplanation:
\nDo cross multiplication we get :
\n100 % \u00d7 84 = 48% \u00d7 ?
\n8400 \u00f7 48 = 175.
\nTherefore answer is 175.<\/p>\n
Question 9.
\n140% of what number is 98?
\nAnswer:
\n140 % = 98
\n100 % = ?
\nThe answer is 70.
\nExplanation:
\nDo cross multiplication we get :
\n100 % \u00d7 98 = 140% \u00d7 ?
\n9800 \u00f7 140 = 70.
\nTherefore answer is 70.<\/p>\n
Multiply.<\/strong>
\nQuestion 10
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-16.png\")
\nAnswer:
\n![\"Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers,-Number-Lines-and-the-Coordinate-Plane-Lesson-8.3-Rational-Numbers-Question-10\"](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-Lesson-8.3-Rational-Numbers-Question-10.jpg\")
<\/p>\nQuestion 11.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-17.png\")
\nAnswer:
\n![\"Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers,-Number-Lines-and-the-Coordinate-Plane-Lesson-8.3-Rational-Numbers-Question-11\"](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-Lesson-8.3-Rational-Numbers-Question-11.jpg\")
\nQuestion 12.
\n3.7 \u00d7 4.854
\nAnswer:
\n![\"Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers,-Number-Lines-and-the-Coordinate-Plane-Lesson-8.3-Rational-Numbers-Question-12\"](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-Lesson-8.3-Rational-Numbers-Question-12.jpg\")
<\/p>\n
Question 13.
\n2.9 \u00d7 8.8609
\nAnswer:
\n![\"Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers,-Number-Lines-and-the-Coordinate-Plane-Lesson-8.3-Rational-Numbers-Question-13\"](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-Lesson-8.3-Rational-Numbers-Question-13.jpg\")
<\/p>\n
Concepts, Skills, &Problem Solving<\/strong><\/p>\nUSING TOOLS<\/strong> Use a fraction or a mixed number to represent the time on a number line. Let 0 represent noon. (See Exploration 1, p. 357.)
\nQuestion 14.
\n8:30 A.M.
\nAnswer:<\/p>\nQuestion 15.
\n12:15 P.M.
\nAnswer:<\/p>\n
Question 16.
\n3:12 P.M.
\nAnswer:<\/p>\n
GRAPHING RATIONAL NUMBERS<\/strong>
\nGraph the number and its opposite.
\nQuestion 17.
\n\\(\\frac{2}{3}\\)
\nAnswer:
\n\\(\\frac{2}{3}\\) = 0.6
\nThe opposite of 0.6 = – 0.6
\n![\"Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers,-Number-Lines-and-the-Coordinate-Plane-Lesson-8.3-Rational-Numbers-Graphing-Rational-Numbers-Question-17\"](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-Lesson-8.3-Rational-Numbers-Graphing-Rational-Numbers-Question-17.jpg\")
\nExplanation :
\nFor any given\u00a0integer\u00a0‘a’, the\u00a0opposite integer\u00a0is found at the same distance from 0 on the number line, but on the other side.
\nSo, the opposite integer of integer ‘0.6’, is ‘-0.6’ on the number line, but on the other side of 0.<\/p>\nQuestion 18.
\n– 4.3
\nAnswer:
\nThe opposite of -4.3 = 4.3
\n![\"Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers,-Number-Lines-and-the-Coordinate-Plane-Lesson-8.3-Rational-Numbers-Graphing-Rational-Numbers-Question-18\"](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-Lesson-8.3-Rational-Numbers-Graphing-Rational-Numbers-Question-18.jpg\")
\nExplanation :
\nFor any given\u00a0integer\u00a0‘a’, the\u00a0opposite integer\u00a0is found at the same distance from 0 on the number line, but on the other side.
\nSo, the opposite integer of integer ‘4.3’, is ‘-4.3’ on the number line, but on the other side of 0.<\/p>\n
Question 19.
\n2.15
\nAnswer:
\nThe opposite of 2.15 = -2.15
\n![\"Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers,-Number-Lines-and-the-Coordinate-Plane-Lesson-8.3-Rational-Numbers-Graphing-Rational-Numbers-Question-19\"](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-Lesson-8.3-Rational-Numbers-Graphing-Rational-Numbers-Question-19.jpg\")
\nExplanation :
\nFor any given\u00a0integer\u00a0‘a’, the\u00a0opposite integer\u00a0is found at the same distance from 0 on the number line, but on the other side.
\nSo, the\u00a0opposite integer\u00a0of\u00a0integer ‘a’, is ‘-a’ on the number line, but on the other side of 0.<\/p>\n
Question 20.
\n– \\(\\frac{3}{7}\\)
\nAnswer:
\n–\\(\\frac{3}{7}\\) = -0.4
\nThe opposite of -0.4 = 0.4
\n![\"Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers,-Number-Lines-and-the-Coordinate-Plane-Lesson-8.3-Rational-Numbers-Graphing-Rational-Numbers-Question-20\"](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-Lesson-8.3-Rational-Numbers-Graphing-Rational-Numbers-Question-20.jpg\")
\nExplanation :
\nFor any given\u00a0integer\u00a0‘a’, the\u00a0opposite integer\u00a0is found at the same distance from 0 on the number line, but on the other side.
\nSo, the opposite integer of integer ‘0.4’, is ‘-0.4’ on the number line, but on the other side of 0.<\/p>\n
Question 21.
\n– 0.4
\nAnswer:
\nThe opposite of -0.4 = 0.4
\n![\"Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers,-Number-Lines-and-the-Coordinate-Plane-Lesson-8.3-Rational-Numbers-Graphing-Rational-Numbers-Question-20\"](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-Lesson-8.3-Rational-Numbers-Graphing-Rational-Numbers-Question-20-1.jpg\")
\nExplanation :
\nFor any given\u00a0integer\u00a0‘a’, the\u00a0opposite integer\u00a0is found at the same distance from 0 on the number line, but on the other side.
\nSo, the\u00a0opposite integer\u00a0of\u00a0integer ‘a’, is ‘-a’ on the number line, but on the other side of 0.<\/p>\n
Question 22.
\n5\\(\\frac{1}{3}\\)
\nAnswer:
\n5\\(\\frac{1}{3}\\) = \\(\\frac{16}{3}\\)=5.3
\nThe opposite of 5.3 = -5.3
\n![\"Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers,-Number-Lines-and-the-Coordinate-Plane-Lesson-8.3-Rational-Numbers-Graphing-Rational-Numbers-Question-22\"](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-Lesson-8.3-Rational-Numbers-Graphing-Rational-Numbers-Question-22.jpg\")
\nExplanation :
\nFor any given\u00a0integer\u00a0‘a’, the\u00a0opposite integer\u00a0is found at the same distance from 0 on the number line, but on the other side.
\nSo, the opposite integer of integer ‘5.3’, is ‘-5.3’ on the number line, but on the other side of 0.<\/p>\n
Question 23.
\n– 2\\(\\frac{1}{4}\\)
\nAnswer:
\n– 2\\(\\frac{1}{4}\\)=- \\(\\frac{9}{4}\\)=-2.25
\nThe opposite of -2.25 = 2.25
\n![\"Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers,-Number-Lines-and-the-Coordinate-Plane-Lesson-8.3-Rational-Numbers-Graphing-Rational-Numbers-Question-23\"](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-Lesson-8.3-Rational-Numbers-Graphing-Rational-Numbers-Question-23.jpg\")
\nExplanation :
\nFor any given\u00a0integer\u00a0‘a’, the\u00a0opposite integer\u00a0is found at the same distance from 0 on the number line, but on the other side.
\nSo, the\u00a0opposite integer\u00a0of\u00a0integer ‘a’, is ‘-a’ on the number line, but on the other side of 0.<\/p>\n
Question 24.
\n-5 \\(\\frac{3}{10}\\)
\nAnswer:
\n-5 \\(\\frac{3}{10}\\) =- \\(\\frac{3}{2}\\) = -1.5
\nThe opposite of -1.5 = 1.5
\n![\"Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers,-Number-Lines-and-the-Coordinate-Plane-Lesson-8.3-Rational-Numbers-Graphing-Rational-Numbers-Question-24\"](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-6th-Grade-Answer-Key-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-Lesson-8.3-Rational-Numbers-Graphing-Rational-Numbers-Question-24.jpg\")
\nExplanation :
\nFor any given\u00a0integer\u00a0‘a’, the\u00a0opposite integer\u00a0is found at the same distance from 0 on the number line, but on the other side.
\nSo, the\u00a0opposite integer\u00a0of\u00a0integer ‘a’, is ‘-a’ on the number line, but on the other side of 0.<\/p>\n
COMPARING RATIONAL NUMBERS<\/strong> Copy and complete the statement using < or >.
\nQuestion 25.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-18.png\")
\nAnswer:
\n-3\\(\\frac{1}{3}\\)\u00a0 >\u00a0 -3\\(\\frac{2}{3}\\)<\/p>\nQuestion 26.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-19.png\")
\nAnswer:
\n–\\(\\frac{1}{2}\\) < –\\(\\frac{1}{6}\\)<\/p>\n
Question 27.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-20.png\")
\nAnswer:
\n–\\(\\frac{3}{4}\\)\u00a0 \u00a0< \\(\\frac{5}{8}\\)<\/p>\n
Question 28.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-21.png\")
\nAnswer:
\n-2\\(\\frac{2}{3}\\)\u00a0 <\u00a0 -2\\(\\frac{1}{2}\\)<\/p>\n
Question 29.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-22.png\")
\nAnswer:
\n-1\\(\\frac{5}{6}\\)\u00a0 <\u00a0 -1\\(\\frac{3}{4}\\)<\/p>\n
Question 30.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-23.png\")
\nAnswer:
\n-4.6\u00a0 > – 4.8<\/p>\n
Question 31.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-24.png\")
\nAnswer:
\n-0.12\u00a0 <\u00a0 -0.05<\/p>\n
Question 32.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-25.png\")
\nAnswer:
\n2.41\u00a0 >\u00a0 -3.16<\/p>\n
Question 33.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-26.png\")
\nAnswer:
\n-3.524\u00a0 >\u00a0 -3.542<\/p>\n
ORDERING RATIONAL NUMBERS<\/strong> Order the numbers from least to greatest.
\nQuestion 34.
\n1.3, – 2, – 1.8, 0, – 1.75
\nAnswer:
\n-2, -1.8, -1.75, 0, 1.3
\nExplanation:
\nThe Negative Numbers which are near to the 0 are greater.With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.
\nSo write the numbers which are bigger with negative symbol are smaller arrange all the negative numbers in this order and then follows 0 and positive numbers from least to greatest .<\/p>\nQuestion 35.
\n– 4, – 4.35, – 4.9, – 5, – 4.3
\nAnswer:
\n-5, -4.9, -4.35, – 4.3 , -4
\nExplanation:
\nThe Negative Numbers which are near to the 0 are greater.With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.
\nSo write the numbers which are bigger with negative symbol are smaller arrange all the negative numbers in this order and then follows 0 and positive numbers from least to greatest .<\/p>\n
Question 36.
\n1.6, 1.2, 0, 0.8, – 0.1
\nAnswer:
\n-0.1, 0, 0.8, 1.2, 1.6
\nExplanation:
\nThe Negative Numbers which are near to the 0 are greater.With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.
\nSo write the numbers which are bigger with negative symbol are smaller arrange all the negative numbers in this order and then follows 0 and positive numbers from least to greatest .<\/p>\n
Question 37.
\n\\(-\\frac{1}{2}, \\frac{1}{8}, \\frac{3}{4},-1,-\\frac{1}{4}\\)
\nAnswer:
\n-0.5, 0.125, 0.75, -1, -0.25 above fractions in decimals points
\n-1, -0.5, -0.25, 0.125, 0.75
\nExplanation:
\nThe Negative Numbers which are near to the 0 are greater.With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.
\nSo write the numbers which are bigger with negative symbol are smaller arrange all the negative numbers in this order and then follows 0 and positive numbers from least to greatest .<\/p>\n
Question 38.
\n\\(-2 \\frac{3}{10},-2 \\frac{2}{5},-2,-2 \\frac{1}{2},-3\\)
\nAnswer:
\n-2.3, -0.8, -2, -2.5, -3
\n-3, -2.5, -2.3, -2, -0.8
\nExplanation:
\nThe Negative Numbers which are near to the 0 are greater.With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.
\nSo write the numbers which are bigger with negative symbol are smaller arrange all the negative numbers in this order and then follows 0 and positive numbers from least to greatest .<\/p>\n
Question 39.
\n\\(-\\frac{1}{20},-\\frac{5}{8}, 0,-1,-\\frac{3}{4}\\)
\nAnswer:
\n-0.05, -0.625, 0, -1, -0.75
\n-0.75, -0.625, -0.05, -1, 0
\nExplanation:
\nThe Negative Numbers which are near to the 0 are greater.With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.
\nSo write the numbers which are bigger with negative symbol are smaller arrange all the negative numbers in this order and then follows 0 and positive numbers from least to greatest .<\/p>\n
Question 40.
\nMODELING REAL LIFE<\/strong>
\nIn rough water, a small sand dollar burrows v centimeter into the sand. A larger sand dollar burrows -1 \\(\\frac{1}{4}\\) centimeters into the sand. Which sand dollar burrowed deeper?
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-27.png\")
\nAnswer:
\nsmall sand dollar burrows = – \\(\\frac{1}{2}\\) = -0.5
\nLarger sand dollar burrows = -1 \\(\\frac{1}{4}\\) =- \\(\\frac{5}{4}\\) = -1.25cms
\nThe Larger sand dollar burrows deeper .
\nExplanation:
\nHere don’t consider the negative signs from ground level that is 0 it is Large sand dollar that is burrowed deeper.<\/p>\nQuestion 41.
\nMODELING REAL LIFE<\/strong>
\nTwo golfers calculate their average scores relative to par over several rounds of golf. Golfer A has an average score of \u22121\\(\\frac{1}{4}\\). Golfer B has an average score of \u22121\\(\\frac{3}{8}\\). Who has the lesser average score?
\nAnswer:
\nAverage score of Golfer A = \u22121\\(\\frac{1}{4}\\)=\u2212\\(\\frac{5}{4}\\)=\u22121.25
\nAverage score of Golfer B = \u22121\\(\\frac{3}{8}\\)= \u2212\\(\\frac{11}{8}\\)=\u22121.375
\nThe golfer B has lesser average score.
\nExplanation:
\nThe Negative Numbers which are near to the 0 are greater.With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.<\/p>\nQuestion 42.
\nMODELING REAL LIFE<\/strong>
\nThe apparent magnitude of a star measures how bright the star appears as seen from Earth. The brighter the star, the lesser the number. Which star is the brightest?
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-28.png\")
\nAnswer:
\nThe Deneb is the brightest star = 1.25 (positive number greatest number than all others )
\nSirius < Canopus < Alpha Centauri\u00a0 < Antares < Deneb
\n-1.46 < -0.72 < -0.27 < 0.96 < 1.25
\nExplanation:
\nThe Negative Numbers which are near to the 0 are greater.With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.
\nSo write the numbers which are bigger with negative symbol are smaller arrange all the negative numbers in this order and then follows 0 and positive numbers from least to greatest .<\/p>\nQuestion 43.
\nREPEATED REASONING<\/strong>
\nThe daily water level relative to the pier is recorded for seven straight days at a tide station on the Big Marco River in Florida. On which days is the water level higher than on the previous day? On which days is it lower? Explain.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-29.png\")
\nAnswer:
\nThe water level on Sun =\u2212\\(\\frac{3}{25}\\) =\u22120.12
\nThe water level on Mon=\u2212\\(\\frac{7}{20}\\)= \u22120.35
\nThe water level on Tue= \u2212\\(\\frac{27}{50}\\) =\u22120.54
\nThe water level on Wed=\u2212\\(\\frac{13}{20}\\)=\u22120.65
\nThe water level on Thrus=\u2212\\(\\frac{16}{25}\\)=\u22120.64
\nThe water level on Fri=\u2212\\(\\frac{53}{100}\\)=\u22120.53
\nThe water level on Sat =\u2212\\(\\frac{1}{3}\\)=\u22120.33
\nExplanation:
\nOn Monday The water level is compared to previous day= – 0.12 – ( – 0.35 ) = 0.23
\nOn Tuesday The water level is compared to previous day=-0.35 – ( -0.54) = 0.19
\nOn Wednesday The water level is compared to previous day= -0.54 – ( – 0.65) =0.11
\nOn Thrusday The water level is compared to previous day= – 0.65 – ( – 0.64)=0.01
\nOn Friday The water level is compared to previous day= – 0.64 – ( – 0.53)=0.11
\nOn Saturday The water level is compared to previous day = – 0.53 – ( -0.33 )=0.20
\nOn Monday the water level is more compared to the previous day .
\nExplanation:
\nThe Negative Numbers which are near to the 0 are greater.With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.<\/p>\nQuestion 44.
\nDIG DEEPER!<\/strong>
\nA guitar tuner allows you to tune a guitar string to its correct pitch. The units on a tuner are measured in cents. The units tell you how far the string tone is above or below the correct pitch.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.3-30.png\")
\na. What number on the tuner represents a correctly tuned guitar string?
\nb. Which strings have a pitch below the correct pitch?
\nc. Which string has a pitch closest to its correct pitch?
\nd. Which string has a pitch farthest from its correct pitch?
\ne. The tuner is rated to be accurate to within 0.5 cent of the true pitch. Which string could possibly be correct? Explain your reasoning.
\nAnswer a :
\nThe Number on the tuner represents a correctly tuned guitar string = 0
\nAnswer b :
\nThe string below the correct pitch = 6
\nExplanation:
\nAs The string 6 is only -0.3 distance away from the correctly tuned guitar string other than strings.
\nAnswer c :
\nA pitch closest to its correct pitch = 6
\nExplanation:
\nAs The string 6 is only -0.3 distance away from the correctly tuned guitar string other than strings. which is the least distance between them.
\nAnswer d :
\nString which is pitch farthest from its correct pitch is 1.
\nExplanation:
\nAs The string 1 is only -3.6 distance away from the correctly tuned guitar string other than strings. which is the Farthest distance between them.
\nAnswer e :
\nNo string tuner is rated to be accurate to within 0.5 cent of the true pitch
\nExplanation:
\nCorrect tuner is at 0
\n0.5 cent of the true pitch = 0
\nWhich is not possible<\/p>\nQuestion 45.
\nNUMBER SENSE<\/strong>
\nWhat integer values of x make the statement \u2212 \\(\\frac{3}{x}\\) < \u2212 \\(\\frac{x}{3}\\) true?
\nAnswer:
\n\u2212 \\(\\frac{3}{x}\\) < \u2212 \\(\\frac{x}{3}\\)
\nX\u00a0 should be more than 3 .
\nif x is in the numerator in the fraction form it resultant will be more when divided by 3
\nIf x is in the denominator in the fraction form it resultant will be less when 3 is divided by x
\nExplanation:
\nFor example: take x = 4
\n\u2212 \\(\\frac{3}{4}\\) =\u22120.75
\n\u2212 \\(\\frac{4}{3}\\) = \u22121.33
\n\u22120.75 < \u22121.33<\/p>\nLesson 8.4 Absolute Value<\/h3>\n
EXPLORATION 1<\/strong>
\nComparing Positions of Objects
\nWork with a partner. The diagram shows the positions of several objects.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.4-1.png\")
\na. What integer represents sea level? How can you compare the positions of objects relative to sea level?
\nAnswer:
\nAn integer represents sea level = 0
\nYou can compare the positions of objects relative to sea levels by number of meters above and below as given in the above figure.<\/p>\nb. Which pairs of objects are the same distance from sea level? How do you know?
\nAnswer:
\nWhale and sea plane
\nExplanation:
\nWhale and sea plane are at -1000 and 1000 meters below and above respectively from sea level.
\nBoth are at equidistant from the sea level.<\/p>\n
c. The vesselsKaiko, Alvin, and Jason Jr.move to be the same distance from sea level as the Boeing 747. About how many meters did each vessel travel?
\nAnswer:
\nDistance of Boeing 747 from sea level = 5000 metres.
\nDistance of\u00a0 Kaiko below sea level = – 7000 metres
\nDistance of\u00a0 Alvin below sea level = -4500 metres
\nDistance of\u00a0 Janson Jr.below sea level = 4000 metres
\nExplanation:
\nTo travel same distance as Boeing 747 the Kaiko should travel + 2000 metres towards the sea level so that it comes at 5000 metres below sea level.
\nTo travel same distance as Boeing 747 the Alvin should travel – 500 metres below the sea level so that it comes at 5000 metres below sea level.
\nTo travel same distance as Boeing 747 the Janson Jr should travel -1000 metres below the sea level so that it comes at 5000 metres below sealevel.<\/p>\n
![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.4-2.png\")
<\/p>\n
Try It<\/strong><\/p>\nFind the absolute value.<\/strong>
\nQuestion 1.
\n|8|
\nAnswer:
\n|8| = 8
\nExplanation:
\nThe absolute value\u00a0or modulus of a real number x, denoted |x|, is the non-negative\u00a0value of x without regard to its sign. Namely, |x| = x\u00a0 and |-x| = x .
\nThe\u00a0absolute value\u00a0of a number is its real distance from zero on a number line; therefore, we need to calculate how many spaces the number is tot he left of zero on a number line. This number is a distance from zero and will not be negative. All\u00a0absolute values\u00a0are positive.<\/p>\nQuestion 2.
\n|-6|
\nAnswer:
\n|-6| = 6
\nExplanation:
\nThe absolute value\u00a0or modulus of a real number x, denoted |x|, is the non-negative\u00a0value of x without regard to its sign. Namely, |x| = x\u00a0 and |-x| = x .
\nThe\u00a0absolute value\u00a0of a number is its real distance from zero on a number line; therefore, we need to calculate how many spaces the number is tot he left of zero on a number line. This number is a distance from zero and will not be negative. All\u00a0absolute values\u00a0are positive.<\/p>\n
Question 3.
\n|0|
\nAnswer:
\n|0| = 0
\nExplanation:
\nThe absolute value\u00a0or modulus of a real number x, denoted |x|, is the non-negative\u00a0value of x without regard to its sign. Namely, |x| = x\u00a0 and |-x| = x .
\nThe\u00a0absolute value\u00a0of a number is its real distance from zero on a number line; therefore, we need to calculate how many spaces the number is tot he left of zero on a number line. This number is a distance from zero and will not be negative. All\u00a0absolute values\u00a0are positive.<\/p>\n
Question 4.
\n\\(\\left| \\frac { 1 }{ 4 } \\right| \\)
\nAnswer:
\n\\(\\left| \\frac { 1 }{ 4 } \\right| \\) = 0.25
\n|0.25| = 0.25
\nExplanation:
\nThe absolute value\u00a0or modulus of a real number x, denoted |x|, is the non-negative\u00a0value of x without regard to its sign. Namely, |x| = x\u00a0 and |-x| = x .
\nThe\u00a0absolute value\u00a0of a number is its real distance from zero on a number line; therefore, we need to calculate how many spaces the number is tot he left of zero on a number line. This number is a distance from zero and will not be negative. All\u00a0absolute values\u00a0are positive.<\/p>\n
Question 5.
\n\\(\\left|-7 \\frac{1}{3}\\right|\\)
\nAnswer:
\n\\(\\left|-7 \\frac{1}{3}\\right|\\) = – 7.33
\n|-7.33|=7.33
\nExplanation:
\nThe absolute value\u00a0or modulus of a real number x, denoted |x|, is the non-negative\u00a0value of x without regard to its sign. Namely, |x| = x\u00a0 and |-x| = x .
\nThe\u00a0absolute value\u00a0of a number is its real distance from zero on a number line; therefore, we need to calculate how many spaces the number is tot he left of zero on a number line. This number is a distance from zero and will not be negative. All\u00a0absolute values\u00a0are positive.<\/p>\n
Question 6.
\n|- 12.9|
\nAnswer:
\n|- 12.9| = 12.9
\nExplanation:
\nThe absolute value\u00a0or modulus of a real number x, denoted |x|, is the non-negative\u00a0value of x without regard to its sign. Namely, |x| = x\u00a0 and |-x| = x .
\nThe\u00a0absolute value\u00a0of a number is its real distance from zero on a number line; therefore, we need to calculate how many spaces the number is tot he left of zero on a number line. This number is a distance from zero and will not be negative. All\u00a0absolute values\u00a0are positive.<\/p>\n
Copy and complete the statement using <, >, or =.<\/strong><\/p>\nQuestion 7.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.4-3.png\")
\nAnswer:
\n|-4|=4
\n4 > -2
\nExplanation:
\nAll positive integers are greater than negative integers.
\nThe absolute value\u00a0or modulus of a real number x, denoted |x|, is the non-negative\u00a0value of x without regard to its sign. Namely, |x| = x\u00a0 and |-x| = x .<\/p>\n
Question 8.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.4-4.png\")
\nAnswer:
\n|5| = 5
\n-5 < 5
\nExplanation:
\nAll positive integers are greater than negative integers
\nThe absolute value\u00a0or modulus of a real number x, denoted |x|, is the non-negative\u00a0value of x without regard to its sign. Namely, |x| = x\u00a0 and |-x| = x .<\/p>\n
Question 9.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.4-5.png\")
\nAnswer:
\n|9|=9
\n9 < 10
\nExplanation:
\nAll positive integers are greater than negative integers.
\nThe absolute value\u00a0or modulus of a real number x, denoted |x|, is the non-negative\u00a0value of x without regard to its sign. Namely, |x| = x\u00a0 and |-x| = x .<\/p>\n
Question 10.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.4-6.png\")
\nAnswer:
\n|-3.9| = 3.9
\n3.9 = 3.9
\nExplanation:
\nBoth the integers are same so equal.
\nThe absolute value\u00a0or modulus of a real number x, denoted |x|, is the non-negative\u00a0value of x without regard to its sign. Namely, |x| = x\u00a0 and |-x| = x .<\/p>\n
Self-Assessment for Concepts & Skills<\/strong><\/p>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.
\nCOMPARING VALUES<\/strong> Copy and complete the statement using <, >, or =.
\nQuestion 11.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.4-7.png\")
\nAnswer:
\n|-6| = 6
\n6 > 3
\nExplanation:
\nThe absolute value\u00a0or modulus of a real number x, denoted |x|, is the non-negative\u00a0value of x without regard to its sign. Namely, |x| = x\u00a0 and |-x| = x .<\/p>\nQuestion 12.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.4-8.png\")
\nAnswer:
\n|-3.5| = 3.5
\n3.5 < 4
\nExplanation:
\nThe absolute value\u00a0or modulus of a real number x, denoted |x|, is the non-negative\u00a0value of x without regard to its sign. Namely, |x| = x\u00a0 and |-x| = x .<\/p>\n
Question 13.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.4-9.png\")
\nAnswer:
\n3\\(\\frac{1}{2}\\) = \\(\\frac{5}{2}\\)=2.5
\n-4\\(\\frac{3}{4}\\)=-\\(\\frac{19}{4}\\) = – 4.75
\n|-4.75|= 4.75
\n2.5 > 4.75
\nExplanation:
\nConvert the fraction form into decimals form . later write absolute values and compare the values. The absolute value\u00a0or modulus of a real number x, denoted |x|, is the non-negative\u00a0value of x without regard to its sign. Namely, |x| = x\u00a0 and |-x| = x .<\/p>\n
Question 14.
\nDIFFERENT WORDS, SAME QUESTION<\/strong>
\nWhich is different? Find \u201cboth\u201d answers.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.4-10.png\")
\nAnswer:
\nWhat is the absolute value of – 3.
\nWhat integer is 3 units to the left of 0
\nExplanation:
\nRest of the two statements describe the distance between -3 to 0.<\/p>\nQuestion 15.
\nDescribe the position of an object in your classroom using a negative rational number. Then describe the position of a second object using a positive rational number. Which number has a greater absolute value? What does this mean?
\nAnswer:
\nThe position of my pen is -6 cms from my bench.
\nThe position of my books is +3 cms from my bench.
\nThe absolute value of -6 = 6
\nThe absolute value of 3 = 3
\n6 > 3
\nExplanation:
\nExplanation:
\nThe absolute value or modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sign. Namely, |x| = x\u00a0 and |-x| = x . All absolute values are positive.<\/p>\n
Question 16.
\nDIG DEEPER!<\/strong>
\nThe table shows the elevations of several checkpoints along a hiking trail.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.4-11.png\")
\na. Which checkpoint is farthest from sea level?
\nb. Which checkpoint is closest to sea level?
\nc. Between which checkpoints do you reach sea level? Explain your reasoning.
\nAnswer a :
\nThe Farthest checkpoint from sea level = 5
\nExplanation:
\nIt is -142 in elevation feet
\nAnswer b :
\nThe closest checkpoint from sea level = 4
\nExplanation:
\nIt is 12 in elevation feet
\nAnswer c :
\nNo we cant .
\nExplanation:
\nSea level = 0
\nWe need to get 0 between two check points then the check points reach sea level.
\nElevation feet between 1 and 2 check points = 110 – 38 = 72
\nElevation feet between 2 and 3 check points = 38 – (-24) = 72
\nElevation feet between 3 and 4 check points = – 24 -12 = -36
\nElevation feet between 4 and 5 check points =12 – (-142) = 154<\/p>\nAbsolute Value Homework & Practice 8.4<\/h3>\n
Review & Refresh<\/strong><\/p>\nOrder the numbers from least to greatest.<\/strong>
\nQuestion 1.
\n2.4, – 3.2, – 1.8, 0.6, – 1.3
\nAnswer:
\n-3.2 < -1.8 < -1.3<0.6<2.4
\nExplanation:
\nThe Negative Numbers which are near to the 0 are greater .Numbers to the right are greater. With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.<\/p>\nQuestion 2.
\n– 0.3, 0.7, – 1.5, 0, 2.2
\nAnswer:
\n-1.5< -0.3<0<0.7<2.2
\nExplanation:
\nThe Negative Numbers which are near to the 0 are greater .Numbers to the right are greater .With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.<\/p>\n
Question 3.
\n\\(\\frac{3}{4}, \\frac{1}{2}, \\frac{2}{3}, 2, \\frac{1}{4}\\)
\nAnswer:
\n0.75, 0.5, 0.6, 2,0.25
\nAll the above fractions are represented in decimals now compare
\n0.25<0.5<0.6<0.75<2
\nExplanation:
\nThe Negative Numbers which are near to the 0 are greater .Numbers to the right are greater .With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.<\/p>\n
Question 4.
\n\\(\\frac{1}{5}, 1 \\frac{2}{5},-2 \\frac{3}{4}, \\frac{4}{5},-2 \\frac{1}{2}\\)
\nAnswer:
\n0.2, 1.4, -2.75, 0.8, -2.5
\nAll the above fractions are represented in decimals now compare
\n-2.75<-2.5<0.2<0.8<1.4
\nExplanation:
\nThe Negative Numbers which are near to the 0 are greater .Numbers to the right are greater .With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller.<\/p>\n
Represent the ratio relationship using a graph.<\/strong>
\nQuestion 5.
\n![\"Big](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-8-Integers-Number-Lines-and-the-Coordinate-Plane-8.4-12.png\")
\nAnswer:
\nSlope = 0
\nY-intercept : (0 , 9\/5)
\nPlot each graph on the same coordinate system.
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\nQuestion 6.
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\nAnswer:
\nSlope = 0
\nY-intercept : (0 , 7\/3)
\nPlot each graph on the same coordinate system.
\n7\/3 , 14\/6, 21\/9 .<\/p>\n
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Evaluate the expression when a = 2, b = 5, and c = 8.<\/strong>
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