\n
![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-6-Module-2-Lesson-9-Example-Answer-Key-1.png\")
<\/p>\nExample 1.
\n25\\(\\frac{3}{10}\\) + 376\\(\\frac{77}{100}\\)
\nAnswer:
\nConvert the mixed numbers into decimals.
\n\u2192 25.3 + 376.77<\/p>\n
\u2192 Round the addends to the nearest whole number. Then, find the estimated sum.
\n25 + 377 = 402<\/p>\n
\u2192 Line up the addends appropriately using place value, and add.
\n<\/p>\n
Example 2.
\n426\\(\\frac{1}{5}\\) – 275\\(\\frac{1}{2}\\)
\nAnswer:
\nEach group should get the same value as their answer; however, the fraction group has 150\\(\\frac{7}{10}\\) and the decimal group has 150.7.<\/p>\n
It is important for students to see that these numbers have the same value. Students solving the problem using fractions most likely take longer to solve the problem and make more mistakes. Point out to students that the answers represent the same value, but using decimals made the problem easier to solve.<\/p>\n
When discussing the problem, use the correct vocabulary. 426\\(\\frac{1}{5}\\) is the minuend, 275\\(\\frac{1}{2}\\) is the subtrahend, and 150\\(\\frac{7}{10}\\) is the difference.<\/p>\n
Calculate each sum or difference.<\/p>\n
Exercise 1.
\nSamantha and her friends are going on a road trip that is 245\\(\\frac{7}{50}\\) miles long. They have already driven How much farther do they have to drive?
\nAnswer:
\nExpression: 245\\(\\frac{7}{50}\\) – 128\\(\\frac{53}{100}\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Estimated answer: 245 – 129 = 116
\nActual answer: 245. 14 – 128.53 = 116.61<\/p>\n
Exercise 2.
\nBen needs to replace two sides of his fence. One side is 367\\(\\frac{9}{100}\\) meters long, and the other is 329 meters long. How much fence does Ben need to buy?
\nAnswer:
\nExpression: 367\\(\\frac{9}{100}\\) + 329\\(\\frac{3}{10}\\) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Estimated answer: 367 + 329 = 696
\nActual answer: 367.09 + 329.3 = 696.39<\/p>\n
Exercise 3.
\nMike wants to paint his new office with two different colors. If he needs 4\\(\\frac{4}{5}\\) gallons of red paint and 3\\(\\frac{1}{10}\\) gallons of brown paint, how much paint does he need in total?
\nAnswer:
\nThis problem is an example of where it may not be easiest to convert mixed numbers into decimals. Either method would result in a correct answer, but discuss with students why it may just be easier to find the sum by keeping the addends as mixed numbers.
\nExpression: 4\\(\\frac{4}{5}\\) + 3\\(\\frac{1}{10}\\) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Estimated answer: 5 + 3 = 8
\nActual answer: \\(4 \\frac{8}{10}+3 \\frac{1}{10}=7 \\frac{9}{10}\\)<\/p>\n
Exercise 4.
\nAfter Arianna completed some work, she figured she still had 78\\(\\frac{21}{100}\\) pictures to paint. If she completed another 34\\(\\frac{23}{25}\\) pictures, how many pictures does Arianna still have to paint?
\nAnswer:
\nExpression: 78\\(\\frac{21}{100}\\) – 34\\(\\frac{23}{25}\\) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Estimated answer: 78 – 35 = 43
\nActual answer: 78.21 – 34.92 = 43.29<\/p>\n
Use a calculator to convert the fractions into decimals before calculating the sum or difference.<\/p>\n
Exercise 5.
\nRahzel wants to determine how much gasoline he and his wife use In a month. He calculated that he used
\n78\\(\\frac{1}{3}\\) gallons of gas last month. Rahzel\u2019s wife used 41\\(\\frac{3}{8}\\) gallons of gas last month. How much total gas did Rahzel and his wife use last month? Round your answer to the nearest hundredth.
\nAnswer:
\nExpression: 78\\(\\frac{1}{3}\\) + 41\\(\\frac{3}{8}\\) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Estimated answer: 78 + 41 = 119
\nActual answer: 78.333 + 41. 375 \u2248 119.71<\/p>\n
Question 1.
\nFind each sum or difference.
\na. 381\\(\\frac{1}{10}\\) – 214\\(\\frac{43}{100}\\)
\nAnswer:
\n381.1 – 214.43 = 166.67<\/p>\n
b. 32\\(\\frac{3}{4}\\) – 12\\(\\frac{1}{2}\\)
\nAnswer:
\n32\\(\\frac{3}{4}\\) – 12\\(\\frac{2}{4}\\) = 20\\(\\frac{1}{4}\\) or 20.25<\/p>\n
c. 517\\(\\frac{37}{50}\\) + 312\\(\\frac{3}{100}\\)
\nAnswer:
\n517.74 + 312.03 = 829.77<\/p>\n
d. 632\\(\\frac{16}{25}\\) + 32\\(\\frac{3}{10}\\)
\nAnswer:
\n632. 64 + 32.3 = 664.94<\/p>\n
e. 421\\(\\frac{3}{50}\\) – 212\\(\\frac{9}{10}\\)
\nAnswer:
\n421.06 – 212.9 = 208.16<\/p>\n
Question 2.
\nUse a calculator to find each sum or difference. Round your answer to the nearest hundredth.
\na. 422\\(\\frac{3}{7}\\) – 367\\(\\frac{5}{9}\\)
\nAnswer:
\n422. 428571 – 367.555556 \u2248 54.87<\/p>\n
b. 23\\(\\frac{1}{5}\\) + 45\\(\\frac{7}{8}\\)
\nAnswer:
\n23.2 + 45.875 \u2248 69.08<\/p>\n
Solve each problem. Show that the placement of the decimal is correct through either estimation or fraction calculation.<\/p>\n
Question 1.
\n382\\(\\frac{3}{10}\\) – 191\\(\\frac{87}{100}\\)
\nAnswer:
\nEstimation: 382 – 192 = 190
\n382.3 – 191.87 = 190.43<\/p>\n
Question 2.
\n594\\(\\frac{7}{25}\\) + 89\\(\\frac{37}{100}\\)
\nAnswer:
\nEstimation: 594 + 89 = 683
\n594.28 + 89.37 = 683.65<\/p>\n","protected":false},"excerpt":{"rendered":"
Engage NY Eureka Math 6th Grade Module 2 Lesson 9 Answer Key Eureka Math Grade 6 Module 2 Lesson 9 Example Answer Key Example 1. 25 + 376 Answer: Convert the mixed numbers into decimals. \u2192 25.3 + 376.77 \u2192 Round the addends to the nearest whole number. Then, find the estimated sum. 25 + … 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\/80309"}],"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=80309"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/80309\/revisions"}],"predecessor-version":[{"id":137649,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/80309\/revisions\/137649"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=80309"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=80309"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=80309"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}