\nMental Math and the Division Algorithm
\nEvaluate the expression 4,564 \u00f7 3. 5 using mental math techniques and the division algorithm.
\nAnswer:
\n\\(\\frac{4,564 \\times 2}{3.5 \\times 2}=\\frac{9,128}{7}\\)
\n
![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-6-Module-2-Lesson-15-Example-Answer-Key-1.png\")
<\/p>\nUse Mental Math to Find Quotients<\/p>\n
Example 1.
\nUse mental math to evaluate 105 \u00f7 35.
\nAnswer:
\n\\(\\frac{105 \\times 2}{35 \\times 2}=\\frac{210}{70}=\\frac{21}{7}=3\\)<\/p>\n
Example 2.
\nMental Math and Division of Decimals
\nEvaluate the expression 175 \u00f7 3. 5 using mental math techniques.
\nAnswer:
\n\\(\\frac{175 \\times 2}{3.5 \\times 2}\\) = 50<\/p>\n
Example 3:
\nMental Math and the Division Algorithm
\nEvaluate the expression 4,564 \u00f7 3. 5 using mental math techniques and the division algorithm.
\nAnswer:
\n\\(\\frac{4,564 \\times 2}{3.5 \\times 2}=\\frac{9,128}{7}\\)
\n<\/p>\n
Example 4:
\nMental Math and Reasonable Work
\nShelly was given this number sentence and was asked to place the decimal point correctly in the quotient.
\n55. 6875 \u00f7 6.75 = 0.825
\nDo you agree with Shelly?
\nAnswer:
\nNo, I do not agree with Shelly. When I round the dividend to 54 and the divisor to 6, the quotient is 9. I know that 91 is in the ones place, so the decimal should be placed after the 8 in the quotient.<\/p>\n
Divide to prove your answer is correct.
\nAnswer:
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-6-Module-2-Lesson-15-Example-Answer-Key-2.png\")
<\/p>\n
Use mental math techniques to evaluate the expressions.<\/p>\n
Exercise 1.
\n770 \u00f7 14
\nAnswer:
\n\\(\\frac{770 \\div 7}{14 \\div 7}=\\frac{110}{2}=55\\)<\/p>\n
Exercise 2.
\n1005 \u00f7 5
\nAnswer:
\n\\(\\frac{1,005 \\times 2}{5 \\times 2}=\\frac{2010}{10}=201\\)<\/p>\n
Exercise 3.
\n1,500 \u00f7 8
\nAnswer:
\n\\(\\frac{1,500 \\div 2}{8 \\div 2}=\\frac{750 \\div 2}{4 \\div 2}=\\frac{375}{2}=187.5\\)<\/p>\n
Exercise 4.
\n1,260 \u00f7 5
\nAnswer:
\n\\(\\frac{1,250}{10}\\) = 126 \u00d7 2 = 252<\/p>\n
Use mental math techniques to evaluate the expressions.<\/p>\n
Exercise 5.
\n25 \u00f7 6.25
\nAnswer:
\n\\(\\frac{25 \\times 4}{6.25 \\times 4}=\\frac{100}{25}=4\\)<\/p>\n
Exercise 6.
\n6.3 \u00f7 1.5
\nAnswer:
\n\\(\\frac{6.3 \\times 2}{1.5 \\times 2}=\\frac{12.6}{3}=4.2\\)<\/p>\n
Exercise 7.
\n425 \u00f7 2.5
\nAnswer:
\n\\(\\frac{425 \\times 2}{2.5 \\times 2}=\\frac{850}{5}=170\\)<\/p>\n
Use mental math, estimation, and the division algorithm to evaluate the expressions.
\nQuestion 1.
\n118.4 \u00f7 6.4
\nAnswer:
\n18.5<\/p>\n
Question 2.
\n314.944 \u00f7 3.7
\nAnswer:
\n85. 12<\/p>\n
Question 3.
\n1,840.5072 \u00f7 23.56
\nAnswer:
\n78. 12<\/p>\n
Question 4.
\n325 \u00f7 2.5
\nAnswer:
\n130<\/p>\n
Question 5.
\n196 \u00f7 3.5
\nAnswer:
\n56<\/p>\n
Question 6.
\n405 \u00f7 4.5
\nAnswer:
\n90<\/p>\n
Question 7.
\n3,437.5 \u00f7 5.5
\nAnswer:
\n625<\/p>\n
Question 8.
\n393.75 \u00f7 5.25
\nAnswer:
\n75<\/p>\n
Question 9.
\n2,625 \u00f7 6.25
\nAnswer:
\n420<\/p>\n
Question 10.
\n231 \u00f7 8.25
\nAnswer:
\n28<\/p>\n
Question 11.
\n92 \u00f7 5.75
\nAnswer:
\n16<\/p>\n
Question 12.
\n196 \u00f7 12.25
\nAnswer:
\n16<\/p>\n
Question 13.
\n117\u00f76.5
\nAnswer:
\n18<\/p>\n
Question 14.
\n936 \u00f7 9.75
\nAnswer:
\n96<\/p>\n
Question 15.
\n305 \u00f7 12.2
\nAnswer:
\n25<\/p>\n
Place the decimal point in the correct place to make the number sentence true.<\/p>\n
Question 16.
\n83.375 \u00f7 2.3 = 3,625
\nAnswer:
\n83.375 \u00f7 2.3 = 36.25<\/p>\n
Question 17.
\n183.575 \u00f7 5,245 = 3.5
\nAnswer:
\n183.575 \u00f7 52.45 = 3.5<\/p>\n
Question 18.
\n326,025 \u00f7 9.45 = 3.45
\nAnswer:
\n32.6025 \u00f7 9.45 = 3.45<\/p>\n
Question 19.
\n449.5 \u00f7 725 = 6.2
\nAnswer:
\n449.5 \u00f7 72.5 = 6.2<\/p>\n
Question 20.
\n446,642 \u00f7 85.4 = 52.3
\nAnswer:
\n4,466.42 \u00f7 85.4 = 52.3<\/p>\n
Question 1.
\nEvaluate the expression using mental math techniques and the division algorithm. Explain your reasoning.
\n18.75 \u00f7 2.5
\nAnswer:
\n\\(\\frac{18.75 \\times 2}{2.5 \\times 2}=\\frac{37.5}{5}\\)
\nI find it easier to divide by 5, so I doubled both the divisor and the dividend. I knew that the dividend would be divisible by 5 since it has a 5 in the hundredths place.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-6-Module-2-Lesson-15-Exit-Ticket-Answer-Key-3.png\")
\n18.75 \u00f7 2.5 = 7.5<\/p>\n
Use mental math to evaluate the numeric expressions.<\/p>\n
a. 99 + 44
\nAnswer:
\n44 gives 1 to 99.
\n100 + 43 = 143<\/p>\n
b. 86 – 39
\nAnswer:
\nIncrease both by 1.
\n87 – 40 = 47<\/p>\n
c. 50 \u00d7 14
\nAnswer:
\nDouble 50; halve 14.
\n100 \u00d7 7 = 700<\/p>\n
d. 180 \u00f7 5
\nAnswer:
\nDouble both.
\n360 \u00f7 10 = 36<\/p>\n","protected":false},"excerpt":{"rendered":"
Engage NY Eureka Math 6th Grade Module 2 Lesson 15 Answer Key Eureka Math Grade 6 Module 2 Lesson 15 Example Answer Key Use Mental Math to Find Quotients Example 1. Use mental math to evaluate 105 \u00f7 35. Answer: Example 2. Mental Math and Division of Decimals Evaluate the expression 175 \u00f7 3. 5 … 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\/80759"}],"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=80759"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/80759\/revisions"}],"predecessor-version":[{"id":137642,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/80759\/revisions\/137642"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=80759"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=80759"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=80759"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}