{"id":86360,"date":"2022-05-29T14:58:15","date_gmt":"2022-05-29T09:28:15","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=86360"},"modified":"2022-05-10T14:19:55","modified_gmt":"2022-05-10T08:49:55","slug":"eureka-math-grade-6-module-4-lesson-8","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/eureka-math-grade-6-module-4-lesson-8\/","title":{"rendered":"Eureka Math Grade 6 Module 4 Lesson 8 Answer Key"},"content":{"rendered":"

Engage NY Eureka Math 6th Grade Module 4 Lesson 8 Answer Key<\/h2>\n

Eureka Math Grade 6 Module 4 Lesson 8 Example Answer Key<\/h3>\n

Example 1.
\nAdditive Identity Property of Zero
\ng + 0 = g<\/p>\n

Remember a letter in a mathematical expression represents a number. Can we replace g with any number?
\nAnswer:
\nYes<\/p>\n

Choose a value for g, and replace g with that number in the equation. What do you observe?
\nAnswer:
\nThe value of g does not change when 0 is added to g.<\/p>\n

Repeat this process several times, each time choosing a different number for g.<\/p>\n

Will all values of result in a true number sentence?
\nAnswer:
\nYes<\/p>\n

Write the mathematical language for this property below:
\nAnswer:
\ng + 0 = g, additive identity property of zero. Any number added to zero equals itself.<\/p>\n

Example 2.
\nMultiplicative Identity Property of One
\ng \u00d7 1 = g
\nRemember a letter in a mathematical expression represents a number. Can we replace g with any number?
\nAnswer:
\nYes<\/p>\n

Choose a value for g, and replace g with that number in the equation. What do you observe?
\nAnswer:
\nThe value of g does not change when g is multiplied by 1.<\/p>\n

Will all values of result in a true number sentence? Experiment with different values before making your claim.
\nAnswer:
\nYes<\/p>\n

Write the mathematical language for this property below:
\nAnswer:
\ng \u00d7 1 = g, multiplicative identity property of one. Any number multiplied by one equals itself.<\/p>\n

Example 3.
\nCommutative Property of Addition and Multiplication
\n3 + 4 = 4 + 3
\n3 \u00d7 4 = 4 \u00d7 3<\/p>\n

Replace the 3’s in these number sentences with the letter
\nAnswer:
\na + 4 = 4 + a
\na \u00d7 4 = 4 \u00d7 a<\/p>\n

Choose a value for a, and replace with that number in each of the equations. What do you observe?
\nAnswer:
\nThe result is a true number sentence.<\/p>\n

Will all values of result in a true number sentence? Experiment with different values before making your claim.
\nAnswer:
\nYes, any number, even zero, can be used in place of the variable<\/p>\n

Now, write the equations again, this time replacing the number 4 with a variable, b.
\nAnswer:
\na + b = b + a
\na \u00d7 b = b \u00d7 a<\/p>\n

Will all values of and result in true number sentences for the first two equations? Experiment with different values before making your claim.
\nAnswer:
\nYes<\/p>\n

Write the mathematical language for this property below:
\nAnswer:
\na + b = b + a commutative property of addition. Order does not matter when adding.
\na \u00d7 b = b \u00d7 a commutative property of multiplication. Order does not matter when multiplying.<\/p>\n

Example 4.
\n3 + 3 + 3 + 3 = 4 \u00d7 3
\n3 \u00f7 4 = \\(\\frac{3}{4}\\)<\/p>\n

Replace the 3’s in these number sentences with the letter
\nAnswer:
\na + a + a + a = 4 \u00d7 a
\na \u00f7 4 = \\(\\frac{a}{4}\\)<\/p>\n

Choose a value for a, and replace a with that number in each of the equations. What do you observe?
\nAnswer:
\nThe result is a true number sentence.<\/p>\n

Will all values of a result in a true number sentence? Experiment with different values before making your claim.
\nAnswer:
\nYes, any number, even zero, can be used in place of the variable<\/p>\n

Now, write the equations again, this time replacing the number 4 with a variable, b.
\nAnswer:
\na + a + a + a = b \u00d7 a
\na \u00f7 b = \\(\\frac{a}{b}\\), b \u2260 0<\/p>\n

Will all values of and result in true number sentences for the equations? Experiment with different values before making your claim.
\nAnswer:
\nIn the equation a + a + a + a = b \u00d7 a, any value can be substituted for the variable a, but only 4 can be used for b since there are exactly 4 copies of a in the equation.
\nIt is true for all values of and all values of b \u2260 0.<\/p>\n

Eureka Math Grade 6 Module 4 Lesson 8 Problem Set Answer Key<\/h3>\n

Question 1.
\nState the commutative property of addition using the variables a and b.
\nAnswer:
\na + b = b + a<\/p>\n

Question 2.
\nState the commutative property of multiplication using the variables a and b.
\nAnswer:
\na \u00d7 b = b \u00d7 a<\/p>\n

Question 3.
\nState the additive property of zero using the variable b.
\nAnswer:
\nb + 0 = b<\/p>\n

Question 4.
\nState the multiplicative identity property of one using the variable b.
\nAnswer:
\nb \u00d7 1 = b<\/p>\n

Question 5.
\nDemonstrate the property listed in the first column by filling in the third column of the table.
\n\"Eureka
\nAnswer:
\n\"Eureka<\/p>\n

Question 6.
\nWhy is there no commutative property for subtraction or division? Show examples.
\nAnswer:
\nAnswers will vary. Examples should show reasoning and proof that the commutative property does not work for subtraction and division. An example would be 8 \u00f7 2 and 2 \u00f7 8. 8 \u00f7 2 = 4, but 2 \u00f7 8 = \\(\\frac{1}{4}\\).<\/p>\n

Eureka Math Grade 6 Module 4 Lesson 8 Exit Ticket Answer Key<\/h3>\n

Question 1.
\nState the commutative property of addition, and provide an example using two different numbers.
\nAnswer:
\nAny two different addends can be chosen, such as 5 + 6 = 6 + 5.<\/p>\n

Question 2.
\nState the commutative property of multiplication, and provide an example using two different numbers.
\nAnswer:
\nAny two different factors can be chosen, such as 4 \u00d7 9 = 9 \u00d7 4.<\/p>\n

Question 3.
\nState the additive property of zero, and provide an example using any other number.
\nAnswer:
\nAny nonzero addend can be chosen, such as 3 + 0 = 3.<\/p>\n

Question 4.
\nState the multiplicative identity property of one, and provide an example using any other number.
\nAnswer:
\nAny nonzero factor can be chosen, such as 12 \u00d7 1 = 12.<\/p>\n

Eureka Math Grade 6 Module 4 Lesson 8 Opening Exercise Answer Key<\/h3>\n

4 + 0 = 4
\n4 \u00d7 1 = 4
\n4 \u00f7 1 = 4
\n4 \u00d7 0 = 0
\n1 \u00f7 4 = \\(\\frac{1}{4}\\)<\/p>\n

How many of these statements are true?
\nAnswer:
\nAll of them<\/p>\n

How many of those statements would be true if the number was replaced with the number in each of the number sentences?
\nAnswer:
\nAll of them<\/p>\n

Would the number sentences be true if we were to replace the number with any other number?<\/p>\n

What if we replaced the number 4 with the number 0? Would each of the number sentences be true?
\nAnswer:
\nNo. The first four are true, but the last one, dividing by zero, is not true.<\/p>\n

What if we replace the number 4 with a letter g? Please write all 4 expressions below, replacing each 4 with a g.
\nAnswer:
\ng + 0 = g
\ng \u00d7 1 = g
\ng \u00f7 1 = g
\ng \u00d7 0 = 0
\n1 \u00f7 g = \\(\\frac{1}{g}\\)<\/p>\n

Are these all true (except for g= 0) when dividing?
\nAnswer:
\nYes<\/p>\n

Eureka Math Grade 6 Module 4 Lesson 8 Division of Fractions II Answer Key<\/h3>\n

Division of Fractions II – Round 1<\/p>\n

Directions: Determine the quotient of the fractions and simplify.<\/p>\n

\"Eureka<\/p>\n

Question 1.
\n\\(\\frac{4}{10} \\div \\frac{2}{10}\\)
\nAnswer:
\n\\(\\frac{4}{2}\\) = 2<\/p>\n

Question 2.
\n\\(\\frac{9}{12} \\div \\frac{3}{12}\\)
\nAnswer:
\n\\(\\frac{9}{3}\\) = 3<\/p>\n

Question 3.
\n\\(\\frac{6}{10} \\div \\frac{4}{10}\\)
\nAnswer:
\n\\(\\frac{6}{4}=\\frac{3}{2}=1 \\frac{1}{2}\\)<\/p>\n

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

Question 5.
\n\\(\\frac{2}{7} \\div \\frac{6}{7}\\)
\nAnswer:
\n\\(\\frac{2}{6}=\\frac{1}{3}\\)<\/p>\n

Question 6.
\n\\(\\frac{11}{9} \\div \\frac{8}{9}\\)
\nAnswer:
\n\\(\\frac{11}{8}=1 \\frac{3}{8}\\)<\/p>\n

Question 7.
\n\\(\\frac{5}{13} \\div \\frac{10}{13}\\)
\nAnswer:
\n\\(\\frac{5}{10}=\\frac{1}{2}\\)<\/p>\n

Question 8.
\n\\(\\frac{7}{8} \\div \\frac{13}{16}\\)
\nAnswer:
\n\\(\\frac{14}{13}=1 \\frac{1}{13}\\)<\/p>\n

Question 9.
\n\\(\\frac{3}{5} \\div \\frac{7}{10}\\)
\nAnswer:
\n\\(\\frac{6}{7}\\)<\/p>\n

Question 10.
\n\\(\\frac{9}{30} \\div \\frac{3}{5}\\)
\nAnswer:
\n\\(\\frac{9}{18}=\\frac{1}{2}\\)<\/p>\n

Question 11.
\n\\(\\frac{1}{3} \\div \\frac{4}{5}\\)
\nAnswer:
\n\\(\\frac{5}{12}\\)<\/p>\n

Question 12.
\n\\(\\frac{2}{5} \\div \\frac{3}{4}\\)
\nAnswer:
\n\\(\\frac{8}{15}\\)<\/p>\n

Question 13.
\n\\(\\frac{3}{4} \\div \\frac{5}{9}\\)
\nAnswer:
\n\\(\\frac{27}{20}=1 \\frac{7}{20}\\)<\/p>\n

Question 14.
\n\\(\\frac{4}{5} \\div \\frac{7}{12}\\)
\nAnswer:
\n\\(\\frac{48}{35}=1 \\frac{13}{35}\\)<\/p>\n

Question 15.
\n\\(\\frac{3}{8} \\div \\frac{5}{2}\\)
\nAnswer:
\n\\(\\frac{6}{40}=\\frac{3}{20}\\)<\/p>\n

Question 16.
\n\\(3 \\frac{1}{8} \\div \\frac{2}{3}\\)
\nAnswer:
\n\\(\\frac{75}{16}=4 \\frac{11}{16}\\)<\/p>\n

Question 17.
\n\\(1 \\frac{5}{6} \\div \\frac{1}{2}\\)
\nAnswer:
\n\\(\\frac{22}{6}=\\frac{11}{3}=3 \\frac{2}{3}\\)<\/p>\n

Question 18.
\n\\(\\frac{5}{8} \\div 2 \\frac{3}{4}\\)
\nAnswer:
\n\\(\\frac{20}{88}=\\frac{5}{22}\\)<\/p>\n

Question 19.
\n\\(\\frac{1}{3} \\div 1 \\frac{4}{5}\\)
\nAnswer:
\n\\(\\frac{5}{27}\\)<\/p>\n

Question 20.
\n\\(\\frac{3}{4} \\div 2 \\frac{3}{10}\\)
\nAnswer:
\n\\(\\frac{30}{92}=\\frac{15}{46}\\)<\/p>\n

Question 21.
\n\\(2 \\frac{1}{5} \\div 1 \\frac{1}{6}\\)
\nAnswer:
\n\\(\\frac{66}{35}=1 \\frac{31}{35}\\)<\/p>\n

Question 22.
\n\\(2 \\frac{4}{9} \\div 1 \\frac{3}{5}\\)
\nAnswer:
\n\\(\\frac{110}{72}=\\frac{55}{36}=1 \\frac{19}{36}\\)<\/p>\n

Question 23.
\n\\(1 \\frac{2}{9} \\div 3 \\frac{2}{5}\\)
\nAnswer:
\n\\(\\frac{55}{153}\\)<\/p>\n

Question 24.
\n\\(2 \\frac{2}{3} \\div 3\\)
\nAnswer:
\n\\(\\frac{8}{9}\\)<\/p>\n

Question 25.
\n\\(1 \\frac{3}{4} \\div 2 \\frac{2}{5}\\)
\nAnswer:
\n\\(\\frac{35}{48}\\)<\/p>\n

Question 26.
\n\\(4 \\div 1 \\frac{2}{9}\\)
\nAnswer:
\n\\(\\frac{36}{11}=3 \\frac{3}{11}\\)<\/p>\n

Question 27.
\n\\(3 \\frac{1}{5} \\div 6\\)
\nAnswer:
\n\\(\\frac{16}{30}=\\frac{8}{15}\\)<\/p>\n

Question 28.
\n\\(2 \\frac{5}{6} \\div 1 \\frac{1}{3}\\)
\nAnswer:
\n\\(\\frac{51}{24}=2 \\frac{3}{24}=2 \\frac{1}{8}\\)<\/p>\n

Question 29.
\n\\(10 \\frac{2}{3} \\div 8\\)
\nAnswer:
\n\\(\\frac{32}{24}=\\frac{4}{3}=1 \\frac{1}{3}\\)<\/p>\n

Question 30.
\n\\(15 \\div 2 \\frac{3}{5}\\)
\nAnswer:
\n\\(\\frac{75}{13}=5 \\frac{10}{13}\\)<\/p>\n

Division of Fractions II – Round 2<\/p>\n

Directions: Determine the quotient of the fractions and simplify.<\/p>\n

\"Eureka<\/p>\n

Question 1.
\n\\(\\frac{10}{2} \\div \\frac{5}{2}\\)
\nAnswer:
\n\\(\\frac{10}{5}\\) = 2<\/p>\n

Question 2.
\n\\(\\frac{6}{5} \\div \\frac{3}{5}\\)
\nAnswer:
\n\\(\\frac{6}{3}\\) = 2<\/p>\n

Question 3.
\n\\(\\frac{10}{7} \\div \\frac{2}{7}\\)
\nAnswer:
\n\\(\\frac{10}{2}\\) = 5<\/p>\n

Question 4.
\n\\(\\frac{3}{8} \\div \\frac{5}{8}\\)
\nAnswer:
\n\\(\\frac{3}{5}\\)<\/p>\n

Question 5.
\n\\(\\frac{1}{4} \\div \\frac{3}{12}\\)
\nAnswer:
\n\\(\\frac{3}{3}\\) = 1<\/p>\n

Question 6.
\n\\(\\frac{1}{4} \\div \\frac{3}{12}\\)
\nAnswer:
\n\\(\\frac{14}{3}=4 \\frac{2}{3}\\)<\/p>\n

Question 7.
\n\\(\\frac{8}{15} \\div \\frac{4}{5}\\)
\nAnswer:
\n\\(\\frac{8}{12}=\\frac{2}{3}\\)<\/p>\n

Question 8.
\n\\(\\frac{5}{6} \\div \\frac{5}{12}\\)
\nAnswer:
\n\\(\\frac{10}{5}\\) = 2<\/p>\n

Question 9.
\n\\(\\frac{3}{5} \\div \\frac{7}{9}\\)
\nAnswer:
\n\\(\\frac{27}{35}\\)<\/p>\n

Question 10.
\n\\(\\frac{3}{10} \\div \\frac{3}{9}\\)
\nAnswer:
\n\\(\\frac{27}{30}=\\frac{9}{10}\\)<\/p>\n

Question 11.
\n\\(\\frac{3}{4} \\div \\frac{7}{9}\\)
\nAnswer:
\n\\(\\frac{27}{28}\\)<\/p>\n

Question 12.
\n\\(\\frac{7}{10} \\div \\frac{3}{8}\\)
\nAnswer:
\n\\(\\frac{56}{30}=\\frac{28}{15}=1 \\frac{13}{15}\\)<\/p>\n

Question 13.
\n\\(4 \\div \\frac{4}{9}\\)
\nAnswer:
\n\\(\\frac{36}{4}\\) = 9<\/p>\n

Question 14.
\n\\(\\frac{5}{8} \\div 7\\)
\nAnswer:
\n\\(\\frac{5}{56}\\)<\/p>\n

Question 15.
\n\\(9 \\div \\frac{2}{3}\\)
\nAnswer:
\n\\(\\frac{27}{2}=13 \\frac{1}{2}\\)<\/p>\n

Question 16.
\n\\(\\frac{5}{8} \\div 1 \\frac{3}{4}\\)
\nAnswer:
\n\\(\\frac{20}{56}=\\frac{5}{14}\\)<\/p>\n

Question 17.
\n\\(\\frac{1}{4} \\div 2 \\frac{2}{5}\\)
\nAnswer:
\n\\(\\frac{5}{48}\\)<\/p>\n

Question 18.
\n\\(2 \\frac{3}{5} \\div \\frac{3}{8}\\)
\nAnswer:
\n\\(\\frac{104}{15}=6 \\frac{14}{15}\\)<\/p>\n

Question 19.
\n\\(1 \\frac{3}{5} \\div \\frac{2}{9}\\)
\nAnswer:
\n\\(\\frac{72}{10}=7 \\frac{2}{10}=7 \\frac{1}{5}\\)<\/p>\n

Question 20.
\n\\(4 \\div 2 \\frac{3}{8}\\)
\nAnswer:
\n\\(\\frac{32}{19}=1 \\frac{13}{19}\\)<\/p>\n

Question 21.
\n\\(1 \\frac{1}{2} \\div 5\\)
\nAnswer:
\n\\(\\frac{3}{10}\\)<\/p>\n

Question 22.
\n\\(3 \\frac{1}{3} \\div 1 \\frac{3}{4}\\)
\nAnswer:
\n\\(\\frac{40}{21}=1 \\frac{19}{21}\\)<\/p>\n

Question 23.
\n\\(2 \\frac{2}{5} \\div 1 \\frac{1}{4}\\)
\nAnswer:
\n\\(\\frac{48}{25}=1 \\frac{23}{25}\\)<\/p>\n

Question 24.
\n\\(3 \\frac{1}{2} \\div 2 \\frac{2}{3}\\)
\nAnswer:
\n\\(\\frac{21}{16}=1 \\frac{5}{16}\\)<\/p>\n

Question 25.
\n\\(1 \\frac{4}{5} \\div 2 \\frac{3}{4}\\)
\nAnswer:
\n\\(\\frac{36}{55}\\)<\/p>\n

Question 26.
\n\\(3 \\frac{1}{6} \\div 1 \\frac{3}{5}\\)
\nAnswer:
\n\\(\\frac{95}{48}=1 \\frac{47}{48}\\)<\/p>\n

Question 27.
\n\\(3 \\frac{3}{5} \\div 2 \\frac{1}{8}\\)
\nAnswer:
\n\\(\\frac{144}{85}=1 \\frac{59}{85}\\)<\/p>\n

Question 28.
\n\\(5 \\div 1 \\frac{1}{6}\\)
\nAnswer:
\n\\(\\frac{30}{7}=4 \\frac{2}{7}\\)<\/p>\n

Question 29.
\n\\(3 \\frac{3}{4} \\div 5 \\frac{1}{2}\\)
\nAnswer:
\n\\(\\frac{30}{44}=\\frac{15}{22}\\)<\/p>\n

Question 30.
\n\\(4 \\frac{2}{3} \\div 5 \\frac{1}{4}\\)
\nAnswer:
\n\\(\\frac{56}{63}=\\frac{8}{9}\\)<\/p>\n","protected":false},"excerpt":{"rendered":"

Engage NY Eureka Math 6th Grade Module 4 Lesson 8 Answer Key Eureka Math Grade 6 Module 4 Lesson 8 Example Answer Key Example 1. Additive Identity Property of Zero g + 0 = g Remember a letter in a mathematical expression represents a number. Can we replace g with any number? Answer: Yes Choose … 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\/86360"}],"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=86360"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/86360\/revisions"}],"predecessor-version":[{"id":137140,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/86360\/revisions\/137140"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=86360"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=86360"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=86360"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}