{"id":80686,"date":"2022-06-10T08:58:58","date_gmt":"2022-06-10T03:28:58","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=80686"},"modified":"2022-05-10T14:14:39","modified_gmt":"2022-05-10T08:44:39","slug":"eureka-math-grade-6-module-2-lesson-14","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/eureka-math-grade-6-module-2-lesson-14\/","title":{"rendered":"Eureka Math Grade 6 Module 2 Lesson 14 Answer Key"},"content":{"rendered":"

Engage NY Eureka Math 6th Grade Module 2 Lesson 14 Answer Key<\/h2>\n

Eureka Math Grade 6 Module 2 Lesson 14 Example Answer Key<\/h3>\n

Evaluate the expression. Use a tape diagram to support your answer.<\/p>\n

Example 1.
\n0.5 \u00f7 0.1
\nAnswer:
\n\"Eureka<\/p>\n

Rewrite 0. 5 \u00f7 0.1 as a fraction.
\nAnswer:
\n\\(\\frac{0.5}{0.1}\\)<\/p>\n

Express the divisor as a whole number.
\nAnswer:
\n\\(\\frac{0.5}{0.1} \\times \\frac{10}{10}=\\frac{5}{1}=5\\)<\/p>\n

Example 2.
\nEvaluate the expression. First, convert the decimal division expression to a fractional division expression in order to create a whole number divisor.
\n25.2 \u00f7 0.72
\nAnswer:
\n\\(\\frac{25.2}{0.72} \\times \\frac{100}{100}=\\frac{2,520}{72}\\)
\n\"Eureka<\/p>\n

Use the division algorithm to find the quotient.
\nAnswer:
\n25.2 \u00f7 0.72 = 35<\/p>\n

Example 3.
\nA plane travels 3, 625. 26 miles in 6. 9 hours. What is the plane\u2019s unit rate?
\nRepresent this situation with a fraction.
\nAnswer:
\n\\(\\frac{3,625.26}{6.9}\\)<\/p>\n

Represent this situation using the same units.
\nAnswer:
\n36,252.6 tenths \u00f7 69 tenths<\/p>\n

Estimate the quotient.
\nAnswer:
\n35,000 \u00f7 70 = 500<\/p>\n

Express the divisor as a whole number.
\nAnswer:
\n\\(\\frac{3,625.26}{6.9} \\times \\frac{10}{10}=\\frac{36,252.6}{69}\\)<\/p>\n

Use the division algorithm to find the quotient.
\nAnswer:
\n\"Eureka<\/p>\n

Use multiplication to check your work.
\nAnswer:
\n525.4 \u00d7 69 = 36,252.6<\/p>\n

Eureka Math Grade 6 Module 2 Lesson 14 Exercise Answer Key<\/h3>\n

Convert the decimal division expressions to fractional division expressions in order to create whole number divisors. You do not need to find the quotients. Explain the movement of the decimal point. The first exercise has been completed for you.<\/p>\n

Exercise 1.
\n18.6 \u00f7 2.3
\nAnswer:
\n\\(\\frac{18.6}{2.3} \\times \\frac{10}{10}=\\frac{186}{23}\\)
\n18.6 \u00f7 23
\nI multiplied both the dividend and the divisor by ten, or by one power of ten, so each decimal point moved one place to the right because they grew larger by ten.<\/p>\n

Exercise 2.
\n14.04 \u00f7 4.68
\nAnswer:
\n\\(\\frac{14.04}{4.86} \\times \\frac{100}{100}=\\frac{1404}{486}\\)
\n1,404 \u00f7 486
\nI multiplied both the dividend and divisor by one hundred, or by two powers of ten, so each decimal point moved two places to the right because they grew larger by two powers of ten.<\/p>\n

Exercise 3.
\n0.162 \u00f7 0036
\nAnswer:
\n\\(\\frac{0.162}{0.036} \\times \\frac{1,000}{1,000}=\\frac{162}{36}\\)
\n162 \u00f7 36
\nI multiplied both the dividend and divisor by one thousand, or three powers often, so each decimal point moved three places to the right because they grew larger by three powers of ten.<\/p>\n

Convert the decimal division expressions to fractional division expressions in order to create whole number divisors. Compute the quotients using the division algorithm. Check your work with a calculator.<\/p>\n

Exercise 4.
\n2,000 \u00f7 3.2
\nAnswer:
\n\\(\\frac{2,000}{3.2} \\times \\frac{10}{10}=\\frac{20,000}{32}\\)
\n\"Eureka
\n20000 \u00f7 32 = 625
\n625 \u00d7 32 = 20000
\n2,000 \u00f7 3.2 = 625
\n625 \u00d7 3.2 = 2,000<\/p>\n

Exercise 5.
\n3,581.9 \u00f7 4.9
\nAnswer:
\n\\(\\frac{3,581.9}{4.9} \\times \\frac{10}{10}=\\frac{35,819}{49}\\)
\n\"Eureka
\n35,819 \u00f7 49 = 731
\n731 \u00d7 49 = 35,819
\n3,581.9 \u00f7 4.9 = 731
\n731 \u00d7 4.9 = 3,581.9<\/p>\n

Exercise 6.
\n893.76 \u00f7 0.21
\nAnswer:
\n\\(\\frac{893.76}{0.21} \\times \\frac{100}{100}=\\frac{89,376}{21}\\)
\n\"Eureka
\n89,376 \u00f7 21 = 4,256
\n4,256 \u00d7 21 = 89,376
\n893.76 \u00f7 0.21 = 4,256
\n4,256 \u00d7 0.21 = 893.76<\/p>\n

Exercise 7.
\n6.194 \u00f7 0.326
\nAnswer:
\n\\(\\frac{6.194}{0.326} \\times \\frac{1,000}{1,000}=\\frac{6,194}{326}\\)
\n\"Eureka
\n6,194 \u00f7 326 = 19
\n19 \u00d7 326 = 6,194
\n6.194 \u00f7 0.326 = 19
\n19 \u00d7 0.326 = 6.194<\/p>\n

Eureka Math Grade 6 Module 2 Lesson 14 Problem Set Answer Key<\/h3>\n

Convert decimal division expressions to fractional division expressions to create whole number divisors.<\/p>\n

Question 1.
\n35.7 \u00f7 0.07
\nAnswer:
\n\\(\\frac{35.7}{0.07} \\times \\frac{100}{100}=\\frac{3570}{7}\\)<\/p>\n

Question 2.
\n486.12 \u00f7 0.6
\nAnswer:
\n\\(\\frac{486.12}{0.6} \\times \\frac{10}{10}=\\frac{4,861.2}{6}\\)<\/p>\n

Question 3.
\n3.43 \u00f7 0.035
\nAnswer:
\n\\(\\frac{3.43}{0.035} \\times \\frac{1,000}{1,000}=\\frac{3430}{35}\\)<\/p>\n

Question 4.
\n5418.54 \u00f7 0.009
\nAnswer:
\n\\(\\frac{5,418.54}{0.009} \\times \\frac{1,000}{1,000}=\\frac{5,418,540}{9}\\)<\/p>\n

Question 5.
\n812.5 \u00f7 1.25
\nAnswer:
\n\\(\\frac{812.5}{125} \\times \\frac{100}{100}=\\frac{81,250}{125}\\)<\/p>\n

Question 6.
\n17.343 \u00f7 36.9
\nAnswer:
\n\\(\\frac{17.343}{36.9} \\times \\frac{10}{10}=\\frac{173.43}{369}\\)<\/p>\n

Estimate quotients. Convert decimal division expressions to fractional division expressions to create whole number divisors. Compute the quotients using the division algorithm. Check your work with a calculator and your estimates.<\/p>\n

Question 7.
\nNorman purchased 3. 5 lb. of his favorite mixture of dried fruits to use in a trail mix. The total cost was $16.87. How much does the fruit cost per pound?
\nAnswer:
\n\\(\\frac{16.87}{3.5} \\times \\frac{10}{10}=\\frac{168.7}{35}\\)
\nEstimate 16 \u00f7 4 = 4
\nThe dried fruit costs $4.82 per pound. This is close to my estimate of 4.<\/p>\n

Question 8.
\nDivide: 994.14\u00f7 18.9
\nAnswer:
\n\\(\\frac{994.14}{18.9} \\times \\frac{10}{10}=\\frac{9,941.4}{189}\\)
\nEstimate: 100 \u00f7 2 = 50
\nThe quotient is 52.6. This is close to my estimate of 50.<\/p>\n

Question 9.
\nDaryl spent $4. 68 on each pound of trail mix. He spent a total of $14. 04. How many pounds of trail mix did he purchase?
\nAnswer:
\n\\(\\frac{14.04}{4.68} \\times \\frac{100}{100}=\\frac{1,404}{468}\\)
\nEstimate: 15 \u00f7 5 = 3
\nDaryl purchased 3 pounds of trail mix. This is my estimate.<\/p>\n

Question 10.
\nMamie saved $161. 25. This is 25% of the amount she needs to save. How much money does Mamie need to save?
\nAnswer:
\n\\(\\frac{161.25}{0.25} \\times \\frac{100}{100}=\\frac{16,125}{25}\\)
\nEstimate: 1,600 \u00f7 2 = 800
\nMamie needs to save $645. This Is close to my estimate of 800.<\/p>\n

Question 11.
\nKareem purchased several packs of gum to place in gift baskets for $1.26 each. He spent a total of $8. 82. How many packs of gum did he buy?
\nAnswer:
\n\\(\\frac{8.82}{1.26} \\times \\frac{100}{100}=\\frac{882}{126}\\)
\nEstimate: 9 \u00f7 1 = 9
\nKareem bought 7 packs of gum. This is close to my estimate of 9.<\/p>\n

Question 12.
\nJerod is making candles from beeswax. He has 132. 72 ounces of beeswax. If each candle uses 8.4 ounces of beeswax, how many candles can he make? Will there be any wax left over?
\nAnswer:
\n\\(\\frac{132.72}{8.4} \\times \\frac{10}{10}=\\frac{1,327.2}{84}\\)
\nEstimate: 120 \u00f7 8 = 15
\nThe quotient is 15.8. This means that Jerod can make 15 candles. This is close to my estimate. There will be wax left over.<\/p>\n

Question 13.
\nThere are 20. 5 cups of batter in the bowl. This represents 0.4 of the entire amount of batter needed for a recipe. How many cups of batter are needed?
\nAnswer:
\n\\(\\frac{20.5}{0.4} \\times \\frac{10}{10}=\\frac{205}{4}\\)
\nEstimate: 200 \u00f7 4 = 50
\nThe number of cups of batter needed for the recipe is 51.25. This is close to my estimate.<\/p>\n

Question 14.
\nDivide: 159.12 \u00f7 6.8
\nAnswer:
\n\\(\\frac{159.12}{6.8} \\times \\frac{10}{10}=\\frac{1,591.2}{68}\\)
\nEstimate: 160 \u00f7 8 = 20
\nThe quotient is 23.4. This is close to my estimate.<\/p>\n

Question 15.
\nDivide: 167.67 \u00f7 8.1
\nAnswer:
\n\\(\\frac{167.67}{8.1} \\times \\frac{10}{10}=\\frac{1,676.7}{81}\\)
\nEstimate: 160 \u00f7 8 = 20
\nThe quotient is 20.7. This is close to my estimate.<\/p>\n

Eureka Math Grade 6 Module 2 Lesson 14 Exit Ticket Answer Key<\/h3>\n

Estimate quotients. Convert decimal division expressions to fractional division expressions to create whole number divisor. Compute the quotient using the division algorithm. Check your work with a calculator and your estimate.<\/p>\n

Question 1.
\nLisa purchased almonds for $3. 50 per pound. She spent a total of $24. 50. How many pounds of almonds did she purchase?
\nAnswer:
\n\\(\\frac{24.50}{3.50} \\times \\frac{100}{100}=\\frac{245}{35}\\)
\nEstimate: 270 \u00f7 30 = 9
\n\"Eureka
\nLisa purchased 7 pounds of almonds. This is close to my estimate of 9.
\n7 \u00d7 35 = 245
\n7 \u00d7 3.5 = 24.5<\/p>\n

Question 2.
\nDivide: 125.01 \u00f7 5.4.
\nAnswer:
\n\\(\\frac{125.01}{5.4} \\times \\frac{10}{10}=\\frac{1250.1}{54}\\)
\nEstimate: 125 \u00f7 5 = 25
\n\"Eureka
\nThe quotient of 125.01 and 5.4 is 23.15. This is close to my estimate of 25.
\n23.15 \u00d7 54 = 1250.1
\n23.15 \u00d7 5.4 = 125.01<\/p>\n

Eureka Math Grade 6 Module 2 Lesson 14 Opening Exercise Answer Key<\/h3>\n

Divide \\(\\frac{1}{2} \\div \\frac{1}{10}\\) Use a tape diagram to support your reasoning.
\nAnswer:
\nThis question is asking the following: \\(\\frac{1}{2} \\text { is } \\frac{1}{10}\\) of what number?
\n\"Eureka<\/p>\n

Relate the model to the invert and multiply rule.
\nAnswer:
\n\\(\\frac{1}{2} \\div \\frac{1}{10}=\\frac{1}{2} \\times \\frac{10}{1}=\\frac{10}{2}=5\\)<\/p>\n

Another way \\(\\frac{1}{2} \\div \\frac{1}{10}\\)
\nAnswer:
\n\u2192 Let\u2019s look at the Opening Exercise another way. We can represent \\(\\frac{1}{2} \\div \\frac{1}{10}\\) using decimals.
\n\u2192 We can represent the fractions \\(\\frac{1}{2}\\) and \\(\\frac{1}{10}\\) with which decimals?
\nOne-half can be represented with 0.5, and one-tenth can be represented by 0.1.
\n\u2192 Display the following:
\n\\(\\frac{1}{2} \\div \\frac{1}{10}\\)
\n0.5 \u00f7 0.1
\n\u2192 This expression can be represented with the same interpretation as the Opening Exercise: 5 tenths is 1 tenth of what number?
\n\u2192 Let\u2019s model this question with a tape diagram.
\n\"Eureka
\n1 unit \u2192 0.5
\n10 units \u2192 10 \u00d7 0.5 = 5<\/p>\n

\u2192 What do you notice about the diagram and the quotient?
\nThe diagram is set up exactly the same as in the Opening Exercise with the fraction, and the quotient is the same. Since \\(\\frac{1}{2}\\) is equivalent to 0.5, and \\(\\frac{1}{10}\\) is equivalent to 0.1, the quotients must be the same.<\/p>\n

\u2192 Look back at the problem: 0.5 \u00f7 0.1. Rewrite this division expression as a fraction.
\n\\(\\frac{0.5}{0.1}\\)<\/p>\n

\u2192 How can we express the divisor as a whole number?
\nMultiply by a fraction equal to one.<\/p>\n

\u2192 Choose a fraction to multiply in order to express the divisor as a whole number.
\nI could multiply by \\(\\frac{0.5}{0.1}\\) by \\(\\frac{10}{10}\\) to represent the divisor as the whole number 1.<\/p>\n

\u2192 Find the Product of \\(\\frac{0.5}{0.1} \\times \\frac{10}{10}\\)
\n\\(\\frac{0.5}{0.1} \\times \\frac{10}{10}=\\frac{5}{1}=5\\)<\/p>\n

\u2192 What do you notice about the quotient?
\nIt is the same as when we used a tape diagram to determine the quotient.<\/p>\n

\u2192 Why do you think the quotients are the same?
\nThey are the same because I multiplied the divisor and the dividend by the same power of ten.<\/p>\n

\u2192 What conjecture can you make?
\nBecause the divisor and the dividend both became ten times greater, when we write the numbers as ten times as much, we move the decimal to the right one place.<\/p>\n","protected":false},"excerpt":{"rendered":"

Engage NY Eureka Math 6th Grade Module 2 Lesson 14 Answer Key Eureka Math Grade 6 Module 2 Lesson 14 Example Answer Key Evaluate the expression. Use a tape diagram to support your answer. Example 1. 0.5 \u00f7 0.1 Answer: Rewrite 0. 5 \u00f7 0.1 as a fraction. Answer: Express the divisor as a whole … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/80686"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=80686"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/80686\/revisions"}],"predecessor-version":[{"id":137643,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/80686\/revisions\/137643"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=80686"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=80686"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=80686"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}