{"id":80180,"date":"2022-06-10T08:58:51","date_gmt":"2022-06-10T03:28:51","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=80180"},"modified":"2022-05-10T14:14:39","modified_gmt":"2022-05-10T08:44:39","slug":"eureka-math-grade-6-module-2-lesson-7","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/eureka-math-grade-6-module-2-lesson-7\/","title":{"rendered":"Eureka Math Grade 6 Module 2 Lesson 7 Answer Key"},"content":{"rendered":"

Engage NY Eureka Math 6th Grade Module 2 Lesson 7 Answer Key<\/h2>\n

Eureka Math Grade 6 Module 2 Lesson 7 Example Answer Key<\/h3>\n

Example 1.
\nModel the following using a partitive interpretation.
\n\\(\\frac{3}{4} \\div \\frac{2}{5}\\)
\nAnswer:
\n\\(\\frac{2}{5}\\) of what number is \\(\\frac{3}{4}\\)?
\n\"Eureka<\/p>\n

Shade 2 of the 5 sections \\(\\left(\\frac{2}{5}\\right)\\).
\nLabel the part that is known \\(\\left(\\frac{3}{4}\\right)\\).
\nMake notes below on the math sentences needed to solve the problem.
\nAnswer:
\n\u2192 Let\u2019s relate what we just did to multiplication.
\nLook back at the model. What was the first thing you did? What was the next thing you did?
\nWe found half of \\(\\frac{3}{4}\\). Then we took the result and multiplied by 5.<\/p>\n

\u2192 We can record this process using multiplication:
\n\\(\\frac{3}{4} \\div \\frac{2}{5}=\\left(\\frac{1}{2} \\cdot \\frac{3}{4}\\right) \\cdot 5\\)<\/p>\n

\u2192 How can you show that \\(\\left(\\frac{1}{2} \\cdot \\frac{3}{4}\\right)\\) . 5 is equivalent to \\(\\frac{3}{4} \\cdot \\frac{5}{2}\\)? What does that tell you about \\(\\frac{3}{4} \\div \\frac{2}{5}\\) and \\(\\frac{3}{4} \\times \\frac{5}{2}\\)?
\nSince we are multiplying, we can rearrange the order of our factors:
\n\\(\\frac{1}{2} \\cdot \\frac{3}{4} \\cdot 5=\\frac{3}{4} \\cdot\\left(\\frac{1}{2} \\cdot 5\\right)=\\frac{3}{4} \\cdot \\frac{5}{2}\\)
\nSince \\(\\frac{3}{4} \\div \\frac{2}{5}\\) is equal to \\(\\left(\\frac{1}{2} \\cdot \\frac{3}{4}\\right)\\) . 5, and that\u2019s equal to \\(\\frac{3}{4} \\cdot \\frac{5}{2}\\), we can say that \\(\\frac{3}{4} \\div \\frac{2}{5}=\\frac{3}{4} \\cdot \\frac{5}{2}\\).<\/p>\n

\u2192 To solve this division problem, we can invert the divisor and multiply. This is called the invert and multiply
\nmethod.<\/p>\n

Example 2.
\nModel the following using a measurement interpretation.
\n\\(\\frac{3}{5} \\div \\frac{1}{4}\\)
\nAnswer:
\n\\(\\frac{3}{5}\\) is how many fourths?
\n\"Eureka
\nConvert the whole and the divisor to the same fractional units first. Then divide the numerators.
\n\\(\\frac{3}{5} \\div \\frac{1}{4}=\\frac{12}{20} \\div \\frac{5}{20}\\) = 12 twentieths \u00f7 5 twentieths \\(\\frac{12}{5}=2 \\frac{2}{5}\\)<\/p>\n

Example 3.
\n\\(\\frac{2}{3} \\div \\frac{3}{4}\\)
\nAnswer:
\nAnswer may vary.
\n\"Eureka
\n\"Eureka<\/p>\n

Show the number sentences below.
\nAnswer:
\n\\(\\frac{2}{3} \\div \\frac{3}{4}=\\frac{8}{12} \\div \\frac{9}{12}=\\frac{8}{9}\\)
\n\\(\\frac{1}{3} \\cdot \\frac{2}{3} \\cdot 4=\\frac{8}{9}\\)
\n\\(\\frac{2}{3} \\div \\frac{3}{4}=\\frac{2}{3} \\cdot \\frac{4}{3}=\\frac{8}{9}\\)<\/p>\n

Eureka Math Grade 6 Module 2 Lesson 7 Problem Set Answer Key<\/h3>\n

Invert and multiply to divide.<\/p>\n

Question 1.
\na. \\(\\frac{2}{3} \\div \\frac{1}{4}\\)
\nAnswer:
\n= \\(\\frac{2}{3} \\times \\frac{4}{1}=\\frac{8}{3}\\)<\/p>\n

b. \\(\\frac{2}{3}\\) \u00f7 4
\nAnswer:
\n= \\(\\frac{2}{3} \\times \\frac{1}{4}=\\frac{1}{6}\\)<\/p>\n

c. 4 \u00f7 \\(\\frac{2}{3}\\)
\nAnswer:
\n= 4 \u00d7 \\(\\frac{3}{2}\\) = 6<\/p>\n

Question 2.
\na. \\(\\frac{1}{3} \\div \\frac{1}{4}\\)
\nAnswer:
\n= \\(\\frac{1}{3} \\times \\frac{4}{1}=\\frac{4}{3}\\)<\/p>\n

b. \\(\\frac{1}{8} \\div \\frac{3}{4}\\)
\nAnswer:
\n= \\(\\frac{1}{8} \\times \\frac{4}{3}=\\frac{1}{6}\\)<\/p>\n

c. \\(\\frac{9}{4} \\div \\frac{6}{5}\\)
\nAnswer:
\n= \\(\\frac{9}{4} \\times \\frac{5}{6}=\\frac{15}{8}\\)<\/p>\n

Question 3.
\na. \\(\\frac{2}{3} \\div \\frac{3}{4}\\)
\nAnswer:
\n= \\(\\frac{2}{3} \\times \\frac{4}{3}=\\frac{8}{9}\\)<\/p>\n

b. \\(\\frac{3}{5} \\div \\frac{3}{2}\\)
\nAnswer:
\n= \\(\\frac{3}{5} \\times \\frac{2}{3}=\\frac{2}{5}\\)<\/p>\n

c. \\(\\frac{22}{4} \\div \\frac{2}{5}\\)
\nAnswer:
\n= \\(\\frac{22}{4} \\times \\frac{5}{2}=\\frac{55}{4}\\)<\/p>\n

Question 4.
\nSummer used \\(\\frac{2}{5}\\) of her ground beef to make burgers. If she used \\(\\frac{3}{4}\\) pounds of beef, how much beef did she have at first?
\nAnswer:
\n\\(\\frac{3}{4}\\) is \\(\\frac{2}{5}\\) of what? So, \\(\\frac{3}{4} \\div \\frac{2}{5}=\\frac{3}{4} \\times \\frac{5}{2}=\\frac{15}{8}=1 \\frac{7}{8}\\)<\/p>\n

Question 5.
\nAlistair has 5 half-pound chocolate bars. It takes 1\\(\\frac{1}{2}\\) pounds of chocolate, broken into chunks, to make a batch of cookies. How many batches can Alistair make with the chocolate he has on hand?
\nAnswer:
\n\\(1 \\frac{1}{2}=\\frac{3}{2}\\)
\n\\(\\frac{5}{2}\\) is how many \\(\\frac{3}{2}\\)
\n\\(\\frac{5}{2} \\div \\frac{3}{2}=\\frac{5}{2} \\times \\frac{2}{3}=\\frac{5}{3}\\)
\nAlistair can only make 1 full batch, but he has enough to make another \\(\\frac{2}{3}\\) batch.<\/p>\n

Question 6.
\nDraw a model that shows \\(\\frac{2}{5} \\div \\frac{1}{3}\\). Find the answer as well.
\nAnswer:
\n\"Eureka
\n\\(\\frac{2}{5} \\div \\frac{1}{3}=\\frac{2}{5} \\cdot \\frac{3}{1}=\\frac{6}{5}\\) or 1\\(\\frac{1}{5}\\)<\/p>\n

Question 7.
\nDraw a model that shows \\(\\frac{3}{4} \\div \\frac{1}{2}\\). Find the answer as well.
\nAnswer:
\n\"Eureka
\n\\(\\frac{3}{4} \\div \\frac{1}{2}=\\frac{3}{4} \\cdot \\frac{2}{1}=\\frac{6}{4}\\) or 1\\(\\frac{1}{2}\\)<\/p>\n

Eureka Math Grade 6 Module 2 Lesson 7 Exit Ticket Answer Key<\/h3>\n

Question 1.
\nWrite the reciprocal of the following numbers.
\n\"Eureka
\nAnswer:
\n\"Eureka<\/p>\n

Question 2.
\nRewrite this division expression as an equivalent multiplication expression: \\(\\frac{5}{8} \\div \\frac{2}{3}\\)
\nAnswer:
\n\\(\\frac{5}{8} \\cdot \\frac{3}{2} \\text { or } \\frac{1}{2} \\cdot \\frac{5}{8} \\cdot 3\\)<\/p>\n

Question 3.
\nSolve problem 2. Draw a model to support your solution.
\nAnswer:
\n\"Eureka
\n\\(\\frac{5}{8} \\div \\frac{2}{3}=\\frac{5}{8} \\cdot \\frac{3}{2}=\\frac{15}{16}\\)<\/p>\n","protected":false},"excerpt":{"rendered":"

Engage NY Eureka Math 6th Grade Module 2 Lesson 7 Answer Key Eureka Math Grade 6 Module 2 Lesson 7 Example Answer Key Example 1. Model the following using a partitive interpretation. Answer: of what number is ? Shade 2 of the 5 sections . Label the part that is known . Make notes below … 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\/80180"}],"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=80180"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/80180\/revisions"}],"predecessor-version":[{"id":137647,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/80180\/revisions\/137647"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=80180"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=80180"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=80180"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}