{"id":79173,"date":"2022-06-10T08:58:29","date_gmt":"2022-06-10T03:28:29","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=79173"},"modified":"2022-05-10T14:14:39","modified_gmt":"2022-05-10T08:44:39","slug":"eureka-math-grade-6-module-2-lesson-1","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/eureka-math-grade-6-module-2-lesson-1\/","title":{"rendered":"Eureka Math Grade 6 Module 2 Lesson 1 Answer Key"},"content":{"rendered":"

Engage NY Eureka Math 6th Grade Module 2 Lesson 1 Answer Key<\/h2>\n

Eureka Math Grade 6 Module 2 Lesson 1 Example Answer Key<\/h3>\n

Example 1.
\n\\(\\frac{3}{4}\\) gallon of batter is poured equally into 2 bowls. How many gallons of batter are in each bowl?
\nAnswer:
\n\u2192 Since the whole is being put into 2 equal parts or bowls, this is the partitive model of division. What division expression can we write to match this story?
\n\u2192 \\(\\frac{3}{4}\\) \u00f7 2
\n\u2192 We can also think of this problem as asking, \u201c3 fourths is 2 groups of what?\u201d Let\u2019s take a look at how to solve this using an area model. What is the whole? How much batter is being shared?
\n\u2192 Three-fourths gallon
\n\u2192 The story tells us that the batter is poured equally into 2 bowls. How can we show this in the model?
\n\u2192 We can draw another line, horizontally, to partition the model into 2 equal units.
\n\u2192 Now our model shows 3 fourths being partitioned into 2 equal parts. Could we also say that our model shows \\(\\frac{1}{2}\\) of 3 fourths?
\n\u2192 Yes, it\u2019s just like in the Opening Exercise where dividing by 2 and multiplying by are the same.
\n\u2192 Let\u2019s label our model to show that. What is half of 3 fourths?
\nHalf of 3 fourths is 3 eighths.
\n\u2192 Yes, and what is 3 fourths divided by 2?
\n\u2192 It\u2019s also 3 eighths!
\n\u2192 We said that we could also think of this problem as, \u201c3 fourths is 2 groups of what?\u201d Is it true that 3 fourths is 2 groups of 3 eighths? Use a repeated addition or multiplication sentence to support your response.
\n\u2192 Yes, it\u2019s true. 3 eighths plus 3 eighths is 6 eighths, which is equal to 3 fourths. \u2192. It\u2019s true.
\n2 \u00d7 \\(\\frac{3}{8}=\\frac{6}{8}=\\frac{3}{4}\\).
\n\"Eureka
\n\\(\\frac{3}{4}\\) \u00f7 2 = \\(\\frac{1}{2}\\) of \\(\\frac{3}{4}\\) = \\(\\frac{3}{8}\\)
\n\\(\\frac{3}{8}\\) gallon of batter in each bowl.<\/p>\n

Example 2.
\n\\(\\frac{3}{4}\\) gallon of batter is poured equally into 2 bowls. How many gallons of batter are in each bowl?
\nAnswer:
\n\u2192 Again, this is partitive division problem since we\u2019re told that there are 6 parts, or that the lasagna is being shared equally among 6 friends. Write a division expression to represent this story problem.
\n\u2192 \\(\\frac{3}{4}\\) \u00f7 6
\n\u2192 Remember when solving this problem, we can also think, \u201c3 fourths is 6 groups of what?\u201d Let\u2019s draw another area model to solve. Think, what is our whole? Draw a model to show how much lasagna is being shared.
\n\u2192 Now, partition your model again to show how it can be equally shared by 6 friends.
\n\u2192 Remind me; dividing by 6 is the same as multiplying by what?
\n\u2192 Multiplying by \\(\\frac{1}{6}\\)
\n\u2192 Look at our model. Explain to your neighbor how it shows division by 6 and also shows multiplication by \\(\\frac{1}{6}\\).
\n\u2192 Now write a multiplication expression that is equal to 3 fourths divided by 6.
\n\u2192 \\(\\frac{1}{6}\\) of \\(\\frac{3}{4}\\) or \\(\\frac{1}{6}\\) \u00d7 \\(\\frac{3}{4}\\)<\/p>\n

\\(\\frac{3}{4}\\) \u00f7 6 = \\(\\frac{1}{6}\\) of \\(\\frac{3}{4}\\) = \\(\\frac{3}{24}\\) = \\(\\frac{1}{8}\\)
\n\"Eureka
\n\u2192 According to our model, what fraction of the pan will each friend get?
\n\u2192 3 twenty-fourths of the pan
\n\u2192 Express 3 twenty-fourths in its simplest form.
\n1 eighth<\/p>\n

Example 3.
\nA rope of length \\(\\frac{2}{5}\\) m is cut into 4 equal cords. What is the length of each cord?
\nAnswer:
\n\u2192 Again, this is a partitive division problem since we\u2019re told that there are 4 parts or that the rope is cut equally into 4 cords. Write a division expression to represent this story problem.
\n\\(\\frac{2}{5}\\) \u00f7 4
\n\u2192 For this example, let\u2019s draw a tape diagram and a number line.
\n\u2192 The length of rope is cut into 4 equal cords. How can we show that in our models?
\nPartition the 2 shaded units into 4 equal parts.
\n\"Eureka
\n\u2192 We originally drew fifths and shaded 2 of them to represent the length of the rope, but now what fractional unit does our model show?
\nTenths
\n\u2192 Answer the question. What is the length of each cord?
\nEach cord is \\(\\frac{1}{10}\\) meter long.
\n\\(\\frac{2}{5} \\div 4=\\frac{1}{4} \\text { of } \\frac{2}{5}=\\frac{2}{20}=\\frac{1}{10}\\)
\nEach chord is \\(\\frac{1}{10}\\) m.
\n\\(\\frac{2}{5}\\) \u00f7 4 = 4 tenths \u00f7 4 = 1 tenth = \\(\\frac{1}{10}\\)
\n\u2192 Take a look at the division sentence I\u2019ve written using unit language. How do our models support this thought? How does the use of unit language support your understanding of this division problem?
\n\u2192 We can also construct a number line to support our solution. When the number line is drawn beneath the tape diagram, we can see the similarities between the two models.
\n\"EurekaEncourage students to study the models and discuss the similarities between dividing by 4 and multiplying by \\(\\frac{1}{4}\\). Students should articulate that both operations yield the same result.<\/p>\n

Eureka Math Grade 6 Module 2 Lesson 1 Exercise Answer Key<\/h3>\n

Exercises 1.
\nFill in the blanks to complete the equation. Then, find the quotient and draw a model to support your solution.
\n\"Eureka
\nAnswer:
\n\"Eureka
\n\\(\\frac{1}{2} \\div 3=\\frac{1}{3} \\times \\frac{1}{2}=\\frac{1}{6}\\)<\/p>\n

Exercises 2.
\n\"Eureka
\nAnswer:
\n\"Eureka
\n\\(\\frac{1}{3} \\div 4=\\frac{1}{4} \\times \\frac{1}{3}=\\frac{1}{12}\\)
\n\\(\\frac{1}{3}\\) \u00f7 4 = 4 twefiths \u00f7 4 = 1 twelfth = \\(\\frac{1}{12}\\)<\/p>\n

Find the value of each of the following.<\/p>\n

Exercises 3.
\n\\(\\frac{1}{4}\\) \u00f7 5
\nAnswer:
\n\\(\\frac{1}{4} \\div 5=\\frac{1}{5} \\text { of } \\frac{1}{4}=\\frac{1}{20}\\)<\/p>\n

Exercises 4.
\n\\(\\frac{3}{4}\\) \u00f7 5
\nAnswer:
\n\\(\\frac{3}{4} \\div 5=\\frac{1}{5} \\text { of } \\frac{3}{4}=\\frac{3}{20}\\)<\/p>\n

Exercises 5.
\n\\(\\frac{1}{5}\\) \u00f7 4
\nAnswer:
\n\\(\\frac{1}{5} \\div 4=\\frac{1}{4} \\text { of } \\frac{1}{5}=\\frac{1}{20}\\)<\/p>\n

Solve. Draw a model to support your solution.<\/p>\n

Exercises 6.
\n\\(\\frac{3}{5}\\)pt. of juice is poured equally into 6 glasses. How much juice is in each glass?
\nAnswer:
\n\"Eureka<\/p>\n

Eureka Math Grade 6 Module 2 Lesson 1 Problem Set Answer Key<\/h3>\n

Find the value of each of the following in its simplest form.<\/p>\n

Question 1.
\na. \\(\\frac{1}{3}\\) \u00f7 4
\nAnswer:
\n\\(\\frac{1}{12}\\)<\/p>\n

b. \\(\\frac{2}{5}\\) \u00f7 4
\nAnswer:
\n\\(\\frac{1}{10}\\)<\/p>\n

c. \\(\\frac{4}{7}\\) \u00f7 4
\nAnswer:
\n\\(\\frac{1}{7}\\)<\/p>\n

Question 2.
\na. \\(\\frac{2}{5}\\) \u00f7 3
\nAnswer:
\n\\(\\frac{2}{15}\\)<\/p>\n

b. \\(\\frac{5}{6}\\) \u00f7 5
\nAnswer:
\n\\(\\frac{1}{6}\\)<\/p>\n

c. \\(\\frac{5}{8}\\) \u00f7 10
\nAnswer:
\n\\(\\frac{1}{16}\\)<\/p>\n

Question 3.
\na. \\(\\frac{6}{7}\\) \u00f7 3
\nAnswer:
\n\\(\\frac{2}{7}\\)<\/p>\n

b. \\(\\frac{10}{8}\\) \u00f7 5
\nAnswer:
\n\\(\\frac{1}{4}\\)<\/p>\n

c. \\(\\frac{20}{6}\\) \u00f7 2
\nAnswer:
\n\\(\\frac{5}{3}\\)<\/p>\n

Question 4.
\n4 loads of stone weigh \\(\\frac{2}{3}\\) ton. Find the weight of 1 load of stone.
\nAnswer:
\n\\(\\frac{2}{3}\\) \u00f7 4 = \\(\\frac{1}{6}\\)
\nEach load of stone weighs \\(\\frac{1}{6}\\) ton.<\/p>\n

Question 5.
\nWhat is the width of a rectangle with an area of in and a length of 10 inches?
\nAnswer:
\n\\(\\frac{5}{8}\\) \u00f7 10 = \\(\\frac{1}{16}\\)
\nThe width of the rectangle is \\(\\frac{1}{16}\\) in.<\/p>\n

Question 6.
\nLenox ironed \\(\\frac{1}{4}\\) of the shirts over the weekend. She plans to split the remainder of the work equally over the next 5 evenings.
\na. What fraction of the shirts will Lenox iron each day after school?
\nAnswer:
\n\\(\\frac{3}{4}\\) \u00f7 5 = \\(\\frac{3}{20}\\)
\nLenox will iron \\(\\frac{3}{20}\\) of the shirts each day after school.<\/p>\n

b If Lenox has 40 shirts how many shirts wlll she need to iron on Thursday and Friday?
\nAnswer:
\n\\(\\frac{3}{20}\\)(40) = 6
\nLenox will need to iron 6 shirts on Thursday and 6 shirts on Friday.
\nTherefore, Lenox will need to iron 12 shirts on Thursday and Friday.<\/p>\n

Question 7.
\nBo paid bills with \\(\\frac{1}{2}\\) of his paycheck and put \\(\\frac{1}{5}\\) of the remainder in savings. The rest of his paycheck he divided equally among the college accounts of his 3 children.
\na. What fraction of his paycheck went into each child\u2019s account?
\nAnswer:
\n\\(\\frac{1}{2}\\left(\\frac{1}{5}\\right)=\\frac{1}{10}\\). This means \\(\\frac{1}{10}\\) of Bo\u2019s paycheck goes into savings. \\(\\frac{1}{2}+\\frac{1}{10}=\\frac{5}{10}+\\frac{1}{10}=\\frac{6}{10}=\\frac{3}{5}\\).
\nThis means that \\(\\frac{3}{5}\\) of Bo\u2019s paycheck goes to bills and savings, which leaves \\(\\frac{2}{5}\\) of his paycheck for college accounts.
\n\\(\\frac{2}{5}\\) \u00f7 3 = \\(\\frac{2}{15}\\)
\nTherefore, Bo put \\(\\frac{2}{15}\\) of his paycheck in each child\u2019s account.<\/p>\n

b. If Bo deposited $400 in each child\u2019s account, how much money was in Bo\u2019s original paycheck?
\nAnswer:
\n$400 is \\(\\frac{2}{15}\\) group of what size?
\n2 unIts = $400
\n1 unit= $400 \u00f7 2 = $200
\n15 units = 15 \u00d7 $200 = $3, 000
\nBo was originally paid $3, 000.<\/p>\n

Eureka Math Grade 6 Module 2 Lesson 1 Exit Ticket Answer Key<\/h3>\n

Write an equivalent multiplication expression. Then, find the quotient In its simplest form. Use a model to support your response.<\/p>\n

Question 1.
\n\\(\\frac{1}{4}\\) \u00f7 2
\nAnswer:
\n\"Eureka
\n\\(\\frac{1}{4} \\div 2=\\frac{1}{2} \\times \\frac{1}{4}=\\frac{1}{8}\\)<\/p>\n

Question 2.
\n\\(\\frac{2}{3}\\) \u00f7 6
\nAnswer:
\n\"Eureka
\n\\(\\frac{2}{3} \\div 6=\\frac{1}{6} \\times \\frac{2}{3}=\\frac{2}{18}=\\frac{1}{9}\\)<\/p>\n","protected":false},"excerpt":{"rendered":"

Engage NY Eureka Math 6th Grade Module 2 Lesson 1 Answer Key Eureka Math Grade 6 Module 2 Lesson 1 Example Answer Key Example 1. gallon of batter is poured equally into 2 bowls. How many gallons of batter are in each bowl? Answer: \u2192 Since the whole is being put into 2 equal parts … 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\/79173"}],"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=79173"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/79173\/revisions"}],"predecessor-version":[{"id":137656,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/79173\/revisions\/137656"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=79173"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=79173"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=79173"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}