{"id":81426,"date":"2022-06-08T19:44:39","date_gmt":"2022-06-08T14:14:39","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=81426"},"modified":"2022-05-10T14:18:33","modified_gmt":"2022-05-10T08:48:33","slug":"eureka-math-grade-6-module-2-lesson-19","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/eureka-math-grade-6-module-2-lesson-19\/","title":{"rendered":"Eureka Math Grade 6 Module 2 Lesson 19 Answer Key"},"content":{"rendered":"

Engage NY Eureka Math 6th Grade Module 2 Lesson 19 Answer Key<\/h2>\n

Eureka Math Grade 6 Module 2 Lesson 19 Opening Exercise Answer Key<\/h3>\n

Euclid\u2019s algorithm is used to find the greatest common factor (GCF) of two whole numbers.
\n1. Divide the larger of the two numbers by the smaller one.
\n2. If there is a remainder, divide it into the divisor.
\n3. Continue dividing the last divisor by the last remainder until the remainder is zero.
\n4. The final divisor is the GCF of the original pair of numbers.<\/p>\n

383 \u00f7 4 =
\nAnswer:
\n95.75<\/p>\n

432 \u00f7 12 =
\nAnswer:
\n36<\/p>\n

403 \u00f7 13 =
\nAnswer:
\n31<\/p>\n

Eureka Math Grade 6 Module 2 Lesson 19 Example Answer Key<\/h3>\n

Example 1:
\nEuclid\u2019s Algorithm Conceptualized
\n\"Eureka
\nAnswer:
\n\u2192 Notice that we can use the GCF of 20 to create the largest square tile that covers the rectangle without any overlap or gaps. We used a 20 \u00d7 20 tile.
\n\u2192 But, what if we did not know that? We could start by guessing. What is the biggest square tile that we can guess?
\n60 \u00d7 60<\/p>\n

Display the following diagram:
\n\"Eureka<\/p>\n

\u2192 It fits, but there are 40 units left over. Do the division problem to prove this.
\n\u2192 What is the leftover area?
\n60 \u00d7 40
\n\u2192 What is the largest square tile that we can fit in the leftover area?
\n40 \u00d7 40
\n\"Eureka<\/p>\n

Display the following diagram:
\n\"Eureka<\/p>\n

\u2192 What is the leftover area?
\n20 \u00d7 40
\n\u2192 What is the largest square tile that we can fit in the leftover area? 20)40
\n20 \u00d7 20
\n\u2192 When we divide 40 by 20, there is no remainder. So, we have tiled the entire rectangle.
\n\u2192 If we had started tiling the whole rectangle with squares, the largest square we could have used would be 20 by 20.
\n\"Eureka<\/p>\n

Example 2.
\na. Let\u2019s apply Euclid\u2019s algorithm to some of the problems from our last lesson.
\ni. What is the GCF of 30 and 50?
\nAnswer:
\n10<\/p>\n

ii. Using Euclid\u2019s algorithm, we follow the steps that are listed In the Opening Exercise.
\nAnswer:
\n\"Eureka
\nWhen the remainder is zero, the final divisor is the GCF.<\/p>\n

b. Apply Euclid\u2019s algorithm to find the GCF (30, 45).
\nAnswer:
\n\"Eureka
\n15<\/p>\n

Example 3.
\nLarger Numbers
\nGCF (96, 144)
\nAnswer:
\n\"Eureka<\/p>\n

Example 4:
\nArea Problems
\nThe greatest common factor has many uses. Among them, the GCF lets us find out the maximum size of squares that cover a rectangle. When we solve problems like this, we cannot have any gaps or any overlapping squares. Of course, the maximum size squares is the minimum number of squares needed.<\/p>\n

A rectangular computer table measures 30 inches by 50 inches. We need to cover it with square tiles. What is the side length of the largest square tile we can use to completely cover the table without overlap or gaps?
\nAnswer:
\n\"Eureka<\/p>\n

a. If we use squares that are 10 by 10, how many do we need?
\nAnswer:
\n3 . 5, or 15 squares<\/p>\n

b. If this were a giant chunk of cheese \u00a1n a factory, would \u00a1t change the thinking or the calculations we just did?
\nAnswer:
\nNo<\/p>\n

c. How many 10 inch \u00d7 10 inch squares of cheese could be cut from the giant 30 inch \u00d7 50 inch slab?
\nAnswer:
\n15<\/p>\n

Eureka Math Grade 6 Module 2 Lesson 19 Problem Set Answer Key<\/h3>\n

Question 1.
\nUse Euclid\u2019s algorithm to find the greatest common factor of the following pairs of numbers:
\na. GCF(12, 78)
\nAnswer:
\n\"Eureka
\nGCF (12, 78) = 6<\/p>\n

b. GCF(18, 176)
\nAnswer:
\n\"11Eureka
\nGCF (18, 176) = 2<\/p>\n

Question 2.
\nJuanita and Samuel are planning a pizza party. They order a rectangular sheet pizza that measures 21 inches by 36 inches. They tell the pizza maker not to cut it because they want to cut it themselves.
\na. All pieces of pizza must be square with none left over. What is the side length of the largest square pieces into which Juanita and Samuel can cut the pizza?
\nAnswer:
\nGCF (21, 36) = 3 They can cut the pizza into 3 inch by 3 inch squares.<\/p>\n

b. How many pieces of this size can be cut?
\nAnswer:
\n7. 12 = 84 Juanita and Samuel can cut 84 pieces.<\/p>\n

Question 3.
\nShelly and Mickelle are making a quilt. They have a piece of fabric that measures 48 inches by 168 inches.
\na. All pieces of fabric must be square with none left over. What is the side length of the largest square pieces into which Shelly and Mickelle can cut the fabric?
\nAnswer:
\nGCF (48, 168) = 24<\/p>\n

b. How many pieces of this size can Shelly and Mickelle cut?
\nAnswer:
\n2 . 7 = 14 They can cut 14 pieces.<\/p>\n

Eureka Math Grade 6 Module 2 Lesson 19 Exit Ticket Answer Key<\/h3>\n

Question 1.
\nUse Euclid\u2019s algorithm to find the greatest common factor of 45 and 75.
\nAnswer:
\n\"11Eureka
\nGCF (45, 75) = 15<\/p>\n","protected":false},"excerpt":{"rendered":"

Engage NY Eureka Math 6th Grade Module 2 Lesson 19 Answer Key Eureka Math Grade 6 Module 2 Lesson 19 Opening Exercise Answer Key Euclid\u2019s algorithm is used to find the greatest common factor (GCF) of two whole numbers. 1. Divide the larger of the two numbers by the smaller one. 2. If there is … 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\/81426"}],"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=81426"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/81426\/revisions"}],"predecessor-version":[{"id":137565,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/81426\/revisions\/137565"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=81426"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=81426"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=81426"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}