unit fraction operations homework 5

• Texas Go Math
• Big Ideas Math
• Engageny Math
• McGraw Hill My Math
• enVision Math
• 180 Days of Math
• Math in Focus Answer Key
• Math Expressions Answer Key
• Privacy Policy

Everyday Math Grade 5 Answers Unit 5 Operations with Fractions

Everyday mathematics 5th grade answer key unit 5 operations with fractions, everyday mathematics grade 5 home link 5.1 answers.

Using Equivalent Fractions to Solve Problems

Estimate. Then solve by finding fractions with a common denominator. Write a number sentence to show which fractions you used. Example: \(\frac{1}{3}\) + \(\frac{7}{12}\) = ? Estimate: close to 1, because \(\frac{1}{3}\) is less than \(\frac{1}{2}\), and \(\frac{7}{12}\) is a little more than \(\frac{1}{2}\). Common denominator: 12 Number sentence: \(\frac{4}{12}\) + \(\frac{7}{12}\) = ? Answer: \(\frac{11}{12}\),

Explanation: Given to find \(\frac{1}{3}\) + \(\frac{7}{12}\) = , As both denominators are different first we need to make common denominators means we need to multiply numerator and denominator by 4 as \(\frac{1}{3}\) X 4 = \(\frac{1 X 4}{3 X 4}\) = \(\frac{4}{12}\) now we add as \(\frac{4}{12}\) + \(\frac{7}{12}\) as denominators are common as 12 we add numerators as \(\frac{4 + 7}{12}\) = \(\frac{11}{12}\), therefore common denominator is 12 and Number sentence: \(\frac{4}{12}\) + \(\frac{7}{12}\) = \(\frac{11}{12}\).

Explanation: Given to find \(\frac{6}{8}\) – \(\frac{1}{2}\) = , As both denominators are different first we need to make common denominators means we need to multiply numerator and denominator by 4 as \(\frac{1}{2}\) X 4 = \(\frac{1 X 4}{2 X 4}\) = \(\frac{4}{8}\) now we subtract as \(\frac{6}{8}\) – \(\frac{4}{8}\) as denominators are common as 8 we subtract numerators as \(\frac{6 – 4}{8}\) = \(\frac{2}{8}\), therefore common denominator is 8 and Number sentence: \(\frac{6}{8}\) – \(\frac{4}{8}\) = \(\frac{2}{8}\).

Explanation: Given to find \(\frac{1}{6}\) + \(\frac{2}{3}\) = , As both denominators are different first we need to make common denominators means we need to multiply numerator and denominator by 2 as \(\frac{2}{3}\) X 2 = \(\frac{2 X 2}{3 X 2}\) = \(\frac{4}{6}\) now we add as \(\frac{1}{6}\) + \(\frac{4}{6}\) as denominators are common as 6 we add numerators as \(\frac{1 + 4}{6}\) = \(\frac{5}{6}\), therefore common denominator is 6 and Number sentence: \(\frac{1}{6}\) + \(\frac{4}{6}\) = \(\frac{5}{6}\).

Practice Estimate. Then solve using U.S. traditional multiplication. Show your work on the back of this page. Question 4. 723 ∗ 89 = __64,347________ Estimate: ___723 X 89 = 64,347_______ Answer: 723 X 89 = 64,347, Estimate : 723 X 89 =64,347,

Explanation: Estimate : 723 X 89 = 64,347, So 723 X 89 = 723 X 89    6507 57840 64,347

Question 5. 1,20 7 ∗ 54 = ___65,178_______ Estimate: ___1,20 7 ∗ 54 = 65,178_______ Answer: 1,207 X 54 = 65,178, Estimate: 1,20 7 ∗ 54 = 65,178,

Explanation: Estimate : 1,207 X 54 =65,178, So 723 X 89 = 1,207 X 54  4828 60350 65,178

Everyday Math Grade 5 Home Link 5.2 Answer Key

Using a Common Denominator

Question 1. For each pair of fractions in the table, find a common denominator. Then rewrite the two fractions as equivalent fractions with a common denominator. Write > or < in the space provided to create a true number sentence. Remember the three strategies you have learned:

• List equivalent fractions.
• Check to see if one denominator is a multiple of the other denominator.

Explanation: For each pair of fractions in the table, found a common denominator. Then rewrote the two fractions as equivalent fractions with a common denominator. Wrote > or < in the space provided to create a true number sentence as shown above as a. Given \(\frac{4}{7}\) , \(\frac{3}{5}\) As both denominators are different first we need to make common denominators 35 means we need to multiply numerator and denominator by 5 for \(\frac{4}{7}\) and by 7 for \(\frac{3}{5}\) we get \(\frac{20}{35}\) and \(\frac{21}{35}\), Now if we compare we get \(\frac{20}{35}\) < \(\frac{21}{35}\), so \(\frac{4}{7}\) < \(\frac{3}{5}\).

b. Given \(\frac{5}{9}\) , \(\frac{2}{3}\) As both denominators are different first we need to make common denominators 9 means we need to multiply numerator and denominator by 3 for \(\frac{2}{3}\) we get \(\frac{6}{9}\),Now if we compare we get \(\frac{5}{9}\) < \(\frac{6}{9}\), \(\frac{5}{9}\) < \(\frac{2}{3}\).

c. Given \(\frac{1}{4}\) , \(\frac{2}{10}\) As both denominators are different first we need to make common denominators 20 means we need to multiply numerator and denominator by 5 for \(\frac{1}{4}\) and by 2 for \(\frac{2}{10}\) we get \(\frac{5}{20}\) and \(\frac{4}{20}\), Now if we compare we get \(\frac{5}{20}\) > \(\frac{4}{20}\), so \(\frac{1}{4}\) < \(\frac{2}{10}\).

d. Given \(\frac{7}{9}\) , \(\frac{5}{6}\) As both denominators are different first we need to make common denominators 18 means we need to multiply numerator and denominator by 2 for \(\frac{7}{9}\) and by 3 for \(\frac{5}{6}\) we get \(\frac{14}{18}\) and \(\frac{15}{18}\), Now if we compare we get \(\frac{14}{18}\) < \(\frac{15}{18}\), so \(\frac{7}{9}\) < \(\frac{5}{6}\).

e. Given \(\frac{5}{12}\) , \(\frac{3}{8}\) As both denominators are different first we need to make common denominators 24 means we need to multiply numerator and denominator by 2 for \(\frac{5}{12}\) and by 3 for \(\frac{3}{8}\) we get \(\frac{10}{24}\) and \(\frac{9}{24}\), Now if we compare we get \(\frac{10}{24}\) > \(\frac{9}{24}\), so \(\frac{5}{12}\) > \(\frac{3}{8}\).

Use the table to help you rewrite the problems with common denominators. Then solve. Question 2. \(\frac{3}{5}\) – \(\frac{4}{7}\) = _________ – ________ = __________ Answer: \(\frac{3}{5}\) – \(\frac{4}{7}\) =\(\frac{21}{35}\) – \(\frac{20}{35}\) =\(\frac{1}{35}\),

Explanation: Used the table to help me to rewrite the problems with common denominators as given \(\frac{3}{5}\) – \(\frac{4}{7}\) = As both denominators are different first we need to make common denominators 35 means we need to multiply numerator and denominator by 7 for \(\frac{3}{5}\) and by 5 for \(\frac{4}{7}\) we get \(\frac{21}{35}\) and \(\frac{20}{35}\), Now we subtract we get \(\frac{21}{35}\) – \(\frac{20}{35}\), as we have common denominators we subtract denominators as \(\frac{21-20}{35}\) =\(\frac{1}{35}\).

Question 3. \(\frac{1}{4}\) + \(\frac{2}{10}\) = _________ – ________ = __________ Answer: \(\frac{1}{4}\) + \(\frac{2}{10}\) = \(\frac{5}{20}\) + \(\frac{4}{20}\) =\(\frac{9}{20}\),

Explanation: Used the table to help me to rewrite the problems with common denominators as given \(\frac{1}{4}\) +\(\frac{2}{10}\) = As both denominators are different first we need to make common denominators 20 means we need to multiply numerator and denominator by 5 for \(\frac{1}{4}\) and by 2 for \(\frac{2}{10}\) we get \(\frac{5}{20}\) and \(\frac{4}{20}\), Now we add numerators as we have common denominators we get \(\frac{5 + 4}{20}\) = \(\frac{9}{20}\).

Question 4. \(\frac{5}{9}\) + \(\frac{2}{3}\) = _________ – ________ = __________ Answer: \(\frac{5}{9}\) + \(\frac{2}{3}\) = \(\frac{5}{9}\) + \(\frac{6}{9}\) = \(\frac{11}{9}\) or 1\(\frac{2}{9}\),

Explanation: Used the table to help me to rewrite the problems with common denominators as given \(\frac{5}{9}\) +\(\frac{2}{3}\) = As both denominators are different first we need to make common denominators 9 means we need to multiply numerator and denominator by 3 for \(\frac{2}{3}\) we get \(\frac{6}{9}\), Now we add numerators as we have common denominators as \(\frac{5 + 6}{9}\) = \(\frac{11}{9}\) as numerator is greater than denominator we write in mixed fraction as (1 X 9 + 2 by 9), So \(\frac{5}{9}\) + \(\frac{2}{3}\) = \(\frac{5}{9}\) + \(\frac{6}{9}\) = \(\frac{11}{9}\) or 1\(\frac{2}{9}\).

Practice Solve. Show your work on the back of the page. Question 5. 8,170 ÷ 75 → ___108 R70______ Answer: 8,170 ÷ 75 = 108 R70,

Explanation: Given to solve 8,170 ÷ 75 =      108 75)8,170(      750      670     600       70 Therefore, 8,170 ÷ 75 = 108 R70.

Question 6. 298 ÷ 17 → ___17R9______ Answer: 298 ÷ 17 = 17 R9,

Explanation: Given to solve 298 ÷ 17 =      17 17)298(      17     128     119        9 Therefore, 298 ÷ 17 = 17 R9.

Everyday Mathematics Grade 5 Home Link 5.3 Answers

Adding Fractions and Mixed Numbers

Estimate and then solve. Show your work. Use your estimates to check your answers. Remember: Before adding fractions and mixed numbers with different denominators, you must rename one or both fractions so both fractions have a common denominator.

Example: 2\(\frac{3}{5}\) + 4 \(\frac{2}{3}\) = ?

• Find a common denominator for the fraction parts. The quick common denominator for \(\frac{3}{5}\) and \(\frac{2}{3}\) is the product of the denominators, 5 ∗ 3, or 15.
• Use the multiplication rule for equivalent fractions to rename each fraction so both fractions have the common denominator.

• Rename the sum. 6\(\frac{19}{15}\) = 6 + \(\frac{15}{15}\) + \(\frac{4}{15}\) = 6 + 1 \(\frac{4}{15}\) = 7 + \(\frac{4}{15}\) = 7\(\frac{4}{15}\)

Question 1. Estimate: ___5\(\frac{5}{6}\) ______ 3\(\frac{4}{6}\) + 2\(\frac{1}{6}\) = __________ Answer: 3\(\frac{4}{6}\) + 2\(\frac{1}{6}\) = 5\(\frac{5}{6}\),

Explanation: Given to solve 3\(\frac{4}{6}\) + 2\(\frac{1}{6}\) = both have common denominators as 6, So 3\(\frac{4}{6}\) = \(\frac{18 + 4}{6}\) = \(\frac{22}{6}\) and 2\(\frac{1}{6}\) = \(\frac{12 + 1}{6}\) = \(\frac{13}{6}\), now we add \(\frac{22}{6}\) + \(\frac{13}{6}\) = as both have common denominators 6 we add numerators as \(\frac{22 + 13}{6}\) = \(\frac{35}{6}\) as numerator is greater than denominator we write in mixed fraction as (5 X 6 + 5 by 6) = 5\(\frac{5}{6}\), therefore, 3\(\frac{4}{6}\) + 2\(\frac{1}{6}\) = 5\(\frac{5}{6}\).

Question 2. Estimate: _________ 6\(\frac{1}{3}\) + 2\(\frac{1}{6}\) = __________ Answer: 6\(\frac{1}{3}\) + 2\(\frac{1}{6}\) = \(\frac{19}{3}\) + \(\frac{13}{6}\) = \(\frac{38}{6}\) + \(\frac{13}{6}\) = \(\frac{51}{6}\) = 8\(\frac{3}{6}\),

Explanation: Given to solve 6\(\frac{1}{3}\) + 2\(\frac{1}{6}\) = first we write mixed fraction into fraction as 6\(\frac{1}{3}\) = \(\frac{18 + 1}{3}\) = \(\frac{19}{3}\) and 2\(\frac{1}{6}\) = \(\frac{12 + 1}{6}\) = \(\frac{13}{6}\), Now we need to make both common denominators as 6 so we need to multiply numerator and denominator by 2 for \(\frac{19}{3}\) we get \(\frac{19}{3}\) X 2 = \(\frac{38}{6}\) , now we add \(\frac{38}{6}\) + \(\frac{13}{6}\) as both have common denominators 6 we add numerators as \(\frac{38 + 13}{6}\) = \(\frac{51}{6}\) as numerator is greater than denominator we write in mixed fraction as (8 X 6 + 3 by 6) = 8\(\frac{3}{6}\), therefore, 6\(\frac{1}{3}\) + 2\(\frac{1}{6}\) = \(\frac{51}{6}\) = 8\(\frac{3}{6}\).

Question 3. Estimate: ___________ \(\frac{3}{4}\) + \(\frac{7}{12}\) = ____________ Answer: \(\frac{3}{4}\) + \(\frac{7}{12}\) = \(\frac{16}{12}\) = 1\(\frac{4}{12}\),

Explanation: Given to solve \(\frac{3}{4}\) + \(\frac{7}{12}\), Now we need to make both common denominators as 12 so we need to multiply numerator and denominator by 3 for \(\frac{3}{4}\) we get \(\frac{3}{4}\) X 3 = \(\frac{9}{12}\) , now we add \(\frac{9}{12}\) + \(\frac{7}{12}\) as both have common denominators 12 we add numerators as \(\frac{9 + 7}{12}\) = \(\frac{16}{12}\) as numerator is greater than denominator we write in mixed fraction as (1 X 12 + 4 by 12) = 1\(\frac{4}{12}\), therefore, \(\frac{3}{4}\) + \(\frac{7}{12}\) = \(\frac{16}{12}\) = 1\(\frac{4}{12}\).

Question 4. Estimate: ____________ 15\(\frac{1}{2}\) + 12\(\frac{2}{5}\) = _________ Answer: 15\(\frac{1}{2}\) + 12\(\frac{2}{5}\) = \(\frac{31}{2}\) + \(\frac{62}{5}\) = \(\frac{155}{10}\) + \(\frac{124}{10}\) = \(\frac{279}{10}\) = 27\(\frac{9}{10}\),

Explanation: Given to solve 15\(\frac{1}{2}\) + 12\(\frac{2}{5}\) = first we write mixed fraction into fraction as 15\(\frac{1}{2}\) = \(\frac{30 + 1}{2}\) = \(\frac{31}{2}\) and 12\(\frac{2}{5}\) = \(\frac{60 + 2}{5}\) = \(\frac{62}{5}\), Now we need to make both common denominators as 10 so we need to multiply numerator and denominator by 5 for \(\frac{31}{2}\) we get \(\frac{31}{2}\) X 5 = \(\frac{155}{10}\)  and  \(\frac{62}{5}\) by 2 we get \(\frac{124}{10}\) now we add \(\frac{155}{10}\) + \(\frac{124}{10}\) as both have common denominators 10 we add numerators as \(\frac{155 + 124}{10}\) = \(\frac{279}{10}\) as numerator is greater than denominator we write in mixed fraction as (27 X 10 + 9 by 10) = 27\(\frac{9}{10}\), therefore, 15\(\frac{1}{2}\) + 12\(\frac{2}{5}\) = \(\frac{31}{2}\) + \(\frac{62}{5}\) = \(\frac{155}{10}\) + \(\frac{124}{10}\) = \(\frac{279}{10}\) = 27\(\frac{9}{10}\).

Practice Write each decimal using numerals. Question 5. three and six hundred twenty-four thousandths ___3.624____ Answer: three and six hundred twenty-four thousandths = 3.624,

Explanation: Given to write three and six hundred twenty-four thousandths using numerals, So three and six hundred twenty-four thousandths = 3 + 6 X  \(\frac{1}{100}\) + 24 X \(\frac{1}{1,000}\) = 3 + 0.6 + 0.024 = 3.624, therefore, three and six hundred twenty-four thousandths = 3.624.

Question 6. fourteen and twelve thousandths ____14.012________ Answer: fourteen and twelve thousandths = 14.012,

Explanation: Given to write fourteen and twelve thousandths using numerals, So fourteen and twelve thousandths = 14 + 12 X \(\frac{1}{1,000}\) = 14 + 0.012 = 14.012, therefore, fourteen and twelve thousandths = 14.012.

Write each decimal using words. Question 7 1.46 ____________ Answer: 1.46 = one and forty-six hundredths,

Explanation: Given to write 1.46 decimal in words as 1 is at units place,4 is at tenths place and 6 at hundredths place, therefore, 1.46 in words isone and forty-six hundredths.

Question 8. 4.309 ____________ Answer: 4.309 = four and three hundred and nine thousandths,

Explanation: Given to write 4.309 decimal in words as 4 is at units place and 309 is at hundred and thousandths place, therefore, 4.309 = four and three hundred and nine thousandths.

Everyday Math Grade 5 Home Link 5.4 Answer Key

Marathon Training

Explanation: Katie ran on Day 1 is 8\(\frac{1}{8}\) and on Day 2 is 4\(\frac{3}{8}\), So miles did Katie run on Day 1 than on Day 2 is 8\(\frac{1}{8}\) – 4\(\frac{3}{8}\), first we write mixed fractions in fractions as 8\(\frac{1}{8}\) = \(\frac{64 + 1}{8}\) = \(\frac{65}{8}\) and 4\(\frac{3}{8}\) = \(\frac{32 + 3}{8}\) = \(\frac{35}{8}\), Now we subtract numerators as we have common denominators as 8 so \(\frac{65}{8}\) – \(\frac{35}{8}\) = \(\frac{65 – 35}{8}\)miles = \(\frac{30}{8}\)miles as numerator is greater than denomintor we write in mixed fraction as (3 X 8 + 6 by 8) = 3\(\frac{6}{8}\) miles, therefore more miles did Katie ran on Day 1 than on Day 2 is \(\frac{30}{8}\)miles or 3\(\frac{6}{8}\) miles.

Question 2. How many miles did Katie run on Day 3 and Day 4 combined? Number model: __12\(\frac{3}{4}\)miles +5\(\frac{1}{3}\) miles________ Estimate: ____________ Show your work: ____________ ____________ miles Answer: Number model: 12\(\frac{3}{4}\)miles + 5\(\frac{1}{3}\) miles, Estimate : 12\(\frac{3}{4}\)miles + 5\(\frac{1}{3}\) miles = \(\frac{51}{4}\)miles + \(\frac{16}{3}\) miles = \(\frac{217}{12}\)miles or 18\(\frac{1}{12}\) miles did Katie run on Day 3 and Day 4 combinedly,

Explanation: Katie ran on Day 3 is 12\(\frac{3}{4}\) and on Day 4 is 5\(\frac{1}{3}\), So miles did Katie ran on Day 3 and Day 4 combinedly is 12\(\frac{3}{4}\) + 5\(\frac{1}{3}\), first we write mixed fractions in fractions as 12\(\frac{3}{4}\) = \(\frac{48 + 3}{4}\) = \(\frac{51}{4}\) and 5\(\frac{1}{3}\) = \(\frac{15 + 1}{3}\) = \(\frac{16}{3}\), Now we add them as \(\frac{51}{4}\) + \(\frac{16}{3}\) = \(\frac{51 X 3 + 16 X 4}{12}\)miles = \(\frac{153 + 64}{12}\) = \(\frac{217}{12}\)miles as numerator is greater than denomintor we write in mixed fraction as (18 X 12 + 1 by 12) = 18\(\frac{1}{12}\) miles, therefore more miles did Katie ran on Day 3 and on Day 4 combinedly is \(\frac{217}{12}\)miles or 18\(\frac{1}{12}\) miles.

Question 3. Katie set a goal to run 4 \(\frac{1}{2}\) miles on Day 5. How much farther than her goal did she run? Number model: ____________ Estimate: ____________ Show your work: ____________ ____________ miles Answer: Number model : 9\(\frac{1}{8}\) – 4\(\frac{1}{2}\), Estimate : 9\(\frac{1}{8}\) – 4\(\frac{1}{2}\) = \(\frac{73}{8}\) – \(\frac{9}{2}\) = \(\frac{37}{8}\)miles or 4\(\frac{5}{8}\) miles farther more miles did Katie ran on Day 5,

Explanation: Katie ran on Day 5 is 9\(\frac{1}{8}\) and Katie set a goal to run 4 \(\frac{1}{2}\) miles on Day 5 So farther more miles did Katie ran on Day 5 is 9\(\frac{1}{8}\) – 4\(\frac{1}{2}\), first we write mixed fractions in fractions as 9\(\frac{1}{8}\) = \(\frac{72 + 1}{8}\) = \(\frac{73}{8}\) and 4\(\frac{1}{2}\) = \(\frac{8 + 1}{2}\) = \(\frac{9}{2}\), Now we subtract as \(\frac{73}{8}\) – \(\frac{9}{2}\) = \(\frac{73 – 36}{8}\)miles = \(\frac{37}{8}\)miles as numerator is greater than denomintor we write in mixed fraction as (4 X 8 + 5 by 8) = 4\(\frac{5}{8}\) miles, therefore more miles did Katie ran on Day 5 than her setted goal is \(\frac{37}{8}\)miles or 4\(\frac{5}{8}\) miles.

Explanation: Choosing from the list the number that has a 7 in the hundredths place is in 128.174.

Question 5. a 5 in the thousandths place. Answer: 1,737.405,

Explanation: Choosing from the list the number that has a 5 in the thousandths place is in 1,737.405.

Question 6. a 2 that is worth 0.2. Answer: 8.25,

Explanation: Choosing from the list the number that has a 2 that is worth 0.2 is 8.25.

Everyday Mathematics Grade 5 Home Link 5.5 Answers

Fraction-Of Problems

Solve each fraction-of problem. Include a unit in your answer. Then write a multiplication number model for each problem. Question 1. Suri made 6 gallons of lemonade to sell at her lemonade stand. In one day she sold \(\frac{2}{3}\) of the lemonade. How much lemonade did she sell? Number model: _________ Answer: Suri sells 4 gallons of lemonade, Number model : \(\frac{2}{3}\) X 6 =4,

Explanation: Given Suri made 6 gallons of lemonade to sell at her lemonade stand. In one day she sold \(\frac{2}{3}\) of the lemonade. So lemonade did Suri sell is \(\frac{2}{3}\) X 6 = \(\frac{2 X 6}{3}\) = \(\frac{12}{3}\) = 4 gallons, therefore, Suri sells 4 gallons of lemonade and Number model : \(\frac{2}{3}\) X 6 = 4.

Question 2. Antonio planned to read 15 books over the summer for the library’s summer reading challenge. At the end of July he had read \(\frac{4}{5}\) of the books. How many books had he read? Number model: _________ Answer: Antonio read 12 books, Number model : \(\frac{4}{5}\) X 15 = 12,

Explanation: Given Antonio planned to read 15 books over the summer for the library’s summer reading challenge. At the end of July he had read \(\frac{4}{5}\) of the books. So number of many books had he read is \(\frac{4}{5}\) X 15 = \(\frac{4 X 15}{5}\) = \(\frac{60}{5}\) = 12, therefore Antonio read 12 books, Number model : \(\frac{4}{5}\) X 15 = 12.

Question 3. Elliot is riding in a 100-mile bike race to raise money for a charity. So far he has completed \(\frac{7}{10}\) of the race. How far has Elliot biked? Number model: _________ Answer: Elliot has biked 70 miles, Number model : \(\frac{7}{10}\) X 100 = 70,

Explanation: Given Elliot is riding in a 100-mile bike race to raise money for a charity. So far he has completed \(\frac{7}{10}\) of the race. So far has Elliot biked is \(\frac{7}{10}\) X 100 = \(\frac{7 X 100}{10}\) = \(\frac{700}{10}\) = 70, therefore, Elliot has biked 70 miles, Number model : \(\frac{7}{10}\) X 100 = 70.

Question 4. Erica’s garden has an area of 24 square feet. She will use \(\frac{3}{4}\) of the space for vegetables and \(\frac{1}{4}\) of the space for flowers. How much space will she use for vegetables? Number model: _________ Answer: Erica’s used space for vegetables is 18 square feet, Number model : \(\frac{3}{4}\) X 24 = 18,

Explanation: Given Erica’s garden has an area of 24 square feet. She will use \(\frac{3}{4}\) of the space for vegetables and \(\frac{1}{4}\) of the space for flowers. So space will she use for vegetables is \(\frac{3}{4}\) X 24 = \(\frac{3 X 24}{4}\) = \(\frac{72}{4}\) =18 square feet, therefore, Erica’s used space for vegetables is 18 square feet, Number model : \(\frac{3}{4}\) X 24 = 18.

Practice Write <, >, or = to make true number sentences. Question 5. 0.3 ____<_____ 0.32 Answer: 0.3 < 0.32,

Explanation: Given 0.3 and 0.32, True number sentence: 0.3 < 0.32.

Question 6. 0.428 ____<_____ 0.43 Answer: 0.428 < 0.43,

Explanation: Given 0.428 and 0.43, True number sentence: 0.428 < 0.43.

Question 7. 1.68 ____=_____ 1.680 Answer: 1.68 = 1.680,

Explanation: Given 1.68 and 1.680, True number sentence: 1.68 = 1.680.

Question 8. 2.988 ___>____ 1.989 Answer: 2.988 > 1.989,

Explanation: Given 2.988 and 1.989, True number sentence: 2.988 > 1.989.

Question 9. 0.06 ____>_____ 0.006 Answer: 0.06 > 0.006,

Explanation: Given 0.06 and 0.006, True number sentence: 0.06 < 0.006.

Question 10. 5.64 ____>_____ 5.46 Answer: 5.64 > 5.46,

Explanation: Given 5.64 and 5.46, True number sentence: 5.64 > 5.46.

Everyday Math Grade 5 Home Link 5.6 Answer Key

Multiplying Whole Numbers and Fractions

Question 1. a. What is 199–200 \(\frac{1}{6}\) of 18? _________ b. What is \(\frac{4}{6}\) of 18? _________ c. Fill in the blank to make a true number sentence. 18 ∗ \(\frac{4}{6}\) = _________ Answer: a. 3, b. 12, c.12,

Explanation: Given to find thw values of a. (199 – 200) \(\frac{1}{6}\) of 18 = (199 – 200)\(\frac{1}{6}\) X 18 = 1 X \(\frac{1 X 18}{6}\) = 1 X \(\frac{18}{6}\) =1 X 3 = 3.

b. \(\frac{4}{6}\) of 18 = \(\frac{4}{6}\) X 18 = \(\frac{4 X 18}{6}\) = \(\frac{72}{6}\) =12.

c. 18 ∗ \(\frac{4}{6}\) = \(\frac{18 X 4}{6}\) = \(\frac{72}{6}\) = 12.

Question 2. a. What is 15 ∗ 3? ____45_____ b. What is 45 ÷ 8? ___5 R5______ c. What is 15 ∗ 3 ÷ 8? ___5 R5______ d. Fill in the blank to make a true number sentence. 15 ∗ \(\frac{3}{8}\) = ___5 R5______ Answer: a. 15 X 3 = 45, b. 45 ÷ 8 = 5 R5, c. 15 X 3 ÷ 8 = 5 R5, d. 15 ∗ \(\frac{3}{8}\) = 5 R5,

Explanation: a. Given to find 15 X 3 = 45, so multiplying 15 by 3 we get 45.

b. 45 ÷ 8 =    5 R5 8)45(    40 5 _ Therfore, 45 ÷ 8 = 5 R5.

c. 15 X 3 ÷ 8 = 45 ÷ 8 =    5 R5 8)45( 40 5 _ Therfore, 15 X 3 ÷ 8 = 5 R5.

d. 15 ∗ \(\frac{3}{8}\) = \(\frac{15 X 3}{8}\) = \(\frac{45}{8}\) =  5 R5 8)45( 40 5 _ Therfore, 15 ∗ \(\frac{3}{8}\) = 5 R5. Question 3. The art teacher has 7 bottles of glue that are each \(\frac{2}{5}\) full. He combines them so he will have fewer bottles. How many bottles of glue does he have after he combines them? Number model: _7 X \(\frac{2}{5}\)________ __ \(\frac{14}{5}\) or 2\(\frac{4}{5}\)_______ bottles Answer: Number model: 7 X \(\frac{2}{5}\), \(\frac{14}{5}\) or 2\(\frac{4}{5}\) bottles of glue he have after he combines them,

Explanation: Given the art teacher has 7 bottles of glue that are each \(\frac{2}{5}\) full. He combines them so he will have fewer bottles. 2So number of bottles of glue does he have after he combines themis 7 X \(\frac{2}{5}\) = \(\frac{7 X 2}{5}\) = \(\frac{14}{5}\) as numerator is greater than denominator we write in mixed fraction as (2 X 5 + 4 by 5) =2\(\frac{4}{5}\), Therefore, Number model: 7 X \(\frac{2}{5}\), \(\frac{14}{5}\) or 2\(\frac{4}{5}\) bottles of glue he have after he combines them.

Question 4. The librarian needs to return 24 books to the shelf. In one hour she finished \(\frac{3}{4}\) of the job. How many books has she returned to the shelf so far? Number model: ____24 X \(\frac{3}{4}\),_____ ______18____ books Answer: 24 X \(\frac{3}{4}\), 18 books she has returned to the shell so far,

Explanation: Given the librarian needs to return 24 books to the shelf. In one hour she finished \(\frac{3}{4}\) of the job. Number of books has she returned to the shelf so far are 24 X \(\frac{3}{4}\) = \(\frac{24 X 3}{4}\) = \(\frac{72}{4}\) = 18, therefore 18 books she has returned to the shell so far.

Practice For Problems 5–7, round each decimal to the nearest tenth. Question 5. 0.93 ___0.9____ Answer: 0.93 the nearest tenth is 0.9,

Explanation: Rounded the decimal 0.93 to the nearest tenth is 0.9.

Question 6. 0.417 ___0.4____ Answer: 0.417 the nearest tenth is 0.4,

Explanation: Rounded the decimal 0.417 to the nearest tenth is 0.4.

Question 7. 7.06 ___7.1_____ Answer: 7.06 the nearest tenth is 7.1,

Explanation: Rounded the decimal 7.06 to the nearest tenth is 7.1.

For Problems 8–10, round each decimal to the nearest hundredth. Question 8. 1.482 __1.48_____ Answer: 1.482 the nearest hundredth is 1.48,

Explanation: Rounded the decimal 1.482 the nearest hundredth is 1.48.

Question 9. 5.715 ____5.72_____ Answer: 5.715 the nearest hundredth is 5.72,

Explanation: Rounded the decimal 5.715 the nearest hundredth is 5.72.

Question 10. 2.996 ___3.00_____ Answer: 2.996 the nearest hundredth is 3.00,

Explanation: Rounded the decimal 2.996 the nearest hundredth is 3.00.

Everyday Mathematics Grade 5 Home Link 5.7 Answers

Finding Fractions of Fractions

Explanation: Given to solve \(\frac{1}{3}\) of \(\frac{2}{4}\) = \(\frac{2}{4}\) X \(\frac{1}{3}\) = \(\frac{2 X 1}{4 X 3}\) = \(\frac{2}{12}\), a. Folded the paper into fourths. Unfolded it and shaded two of the fourths as shown above,

b. Folded the paper into thirds the other way, with the new folds crossing your folds from Part a. Unfolded the paper and double-shaded one -third of the shaded part as shown above.

c. Recorded how it looks like on the paper,

d. The amount of paper that is double-shaded \(\frac{1}{3}\) of \(\frac{2}{4}\) = \(\frac{2}{4}\) X \(\frac{1}{3}\) = \(\frac{2 X 1}{4 X 3}\) = \(\frac{2}{12}\).

e. \(\frac{1}{3}\) of \(\frac{2}{4}\) is \(\frac{2}{4}\) X \(\frac{1}{3}\) = \(\frac{2 X 1}{4 X 3}\) = \(\frac{2}{12}\).

Explanation: Given to solve \(\frac{3}{4}\) of \(\frac{2}{3}\) = \(\frac{3}{4}\) X \(\frac{2}{3}\) = \(\frac{3 X 2}{4 X 3}\) = \(\frac{6}{12}\), a. Folded the paper into thirds. Unfolded it and shaded two of the thirds as shown above,

b. Folded the paper into fourths the other way, with the new folds crossing your folds from Part a. Unfolded the paper and double-shaded three-fourths of the shaded part as shown above.

d. The amount of paper that is double-shaded \(\frac{3}{4}\) of \(\frac{2}{3}\) = \(\frac{3}{4}\) X \(\frac{2}{3}\) = \(\frac{3 X 2}{4 X 3}\) = \(\frac{6}{12}\).

e. \(\frac{3}{4}\) of \(\frac{2}{3}\) is \(\frac{3}{4}\) X \(\frac{2}{3}\) = \(\frac{3 X 2}{4 X 3}\) = \(\frac{6}{12}\).

Everyday Math Grade 5 Home Link 5.8 Answer Key

Using Area Models to Multiply Fractions

Label the blank tick marks on the number lines.

• Use the number lines to write the length and width of the shaded rectangle.
• Find the area of the shaded rectangle. (The area of the big square is 1 square unit.) Think: Into how many equal parts is the big square divided? How many parts are shaded?
• Write a multiplication number sentence for the area of the shaded rectangle.

Explanation: * Used the number lines to write the length and width of the shaded rectangle as Length of shaded rectangle: 3/4 unit Width of shaded rectangle: 1/2 unit * Founded  the area of the shaded rectangle as (The area of the big square is 1 square unit.) Thinking: Into how many equal parts is the big square divided and How many parts are shaded as \(\frac{3}{4}\) X \(\frac{1}{2}\) = \(\frac{3 X 1}{4 X 2}\) = \(\frac{3}{8}\), * Wrote a multiplication number sentence for the area of the shaded rectangle as \(\frac{3}{4}\) X \(\frac{1}{2}\) = \(\frac{3}{8}\) respectively.

Explanation: * Used the number lines to write the length and width of the shaded rectangle as Length of shaded rectangle: 1/3 unit Width of shaded rectangle: 2/3 unit * Founded  the area of the shaded rectangle as (The area of the big square is 1 square unit.) Thinking: Into how many equal parts is the big square divided and How many parts are shaded as \(\frac{1}{3}\) X \(\frac{2}{3}\) = \(\frac{1 X 2}{3 X 3}\) = \(\frac{2}{9}\), * Wrote a multiplication number sentence for the area of the shaded rectangle as \(\frac{1}{3}\) X \(\frac{2}{3}\) = \(\frac{2}{9}\) respectively.

Everyday Mathematics Grade 5 Home Link 5.9 Answers

Using an Algorithm to Multiply Fractions

A Fraction Multiplication Algorithm To multiply two fractions, multiply the numerators and multiply the denominators. For example: \(\frac{2}{3} * \frac{3}{8}=\frac{(2 * 3)}{(3 * 8)}=\frac{6}{24}\)

For Problems 1–6, use the algorithm to multiply the fractions. Question 1. \(\frac{1}{3}\) * \(\frac{1}{2}\) = ___1/6______ Answer: \(\frac{1}{3}\) * \(\frac{1}{2}\) = \(\frac{1}{3}\),

Explanation: Multiplying the fractions \(\frac{1}{3}\) * \(\frac{1}{2}\) by multiplying the numerators and multiplying the denominators as \(\frac{1 X 1}{3 X 2}\) = \(\frac{1}{6}\).

Question 2. \(\frac{2}{4}\) * \(\frac{2}{3}\) = ____4/12_______ Answer: \(\frac{2}{4}\) * \(\frac{2}{3}\) = \(\frac{4}{12}\),

Explanation: Multiplying the fractions \(\frac{2}{4}\) * \(\frac{2}{3}\) by multiplying the numerators and multiplying the denominators as \(\frac{2 X 2}{4 X 3}\) = \(\frac{4}{12}\).

Question 3. \(\frac{4}{5}\) * \(\frac{2}{5}\) = ____8/25______ Answer: \(\frac{2}{4}\) * \(\frac{2}{3}\) = \(\frac{4}{12}\),

Question 4. \(\frac{2}{10}\) * \(\frac{2}{3}\) = _____4/30_____ Answer: \(\frac{2}{10}\) * \(\frac{2}{3}\) = \(\frac{4}{30}\),

Explanation: Multiplying the fractions \(\frac{2}{10}\) * \(\frac{2}{3}\) by multiplying the numerators and multiplying the denominators as \(\frac{2 X 2}{10 X 3}\) = \(\frac{4}{30}\).

Question 5. \(\frac{2}{8}\) * \(\frac{5}{6}\) = _____10/48______ Answer: \(\frac{2}{8}\) * \(\frac{5}{6}\) = \(\frac{10}{48}\),

Explanation: Multiplying the fractions \(\frac{2}{8}\) * \(\frac{5}{6}\) by multiplying the numerators and multiplying the denominators as \(\frac{2 X 5}{8 X 6}\) = \(\frac{10}{48}\).

Question 6. \(\frac{5}{12}\) * \(\frac{2}{7}\) = ____10/84_______ Answer: \(\frac{5}{12}\) * \(\frac{2}{7}\) = \(\frac{10}{84}\),

Explanation: Multiplying the fractions \(\frac{5}{12}\) * \(\frac{2}{7}\) by multiplying the numerators and multiplying the denominators as \(\frac{5 X 2}{12 X 7}\) = \(\frac{10}{84}\).

Question 7. If you multiply \(\frac{2}{3}\) ∗ \(\frac{6}{10}\), will the product be more than \(\frac{2}{3}\) or less than \(\frac{2}{3}\)? How do you know? Answer: Less than \(\frac{2}{3}\) by checking,

Explanation: First we multiply \(\frac{2}{3}\) X \(\frac{6}{10}\) = \(\frac{2 X 6}{3 X 10}\) = \(\frac{12}{30}\), Now \(\frac{12}{30}\) = 0.4 and \(\frac{2}{3}\) = 0.66, as 0.4 < 0.66, So \(\frac{12}{30}\) < \(\frac{2}{3}\).

Question 8. If you multiply \(\frac{2}{3}\) ∗ \(\frac{6}{10}\), will the product be more than \(\frac{6}{10}\) or less than \(\frac{6}{10}\)? How do you know? Answer: Less than \(\frac{6}{10}\) by checking,

Explanation: First we multiply \(\frac{2}{3}\) X \(\frac{6}{10}\) = \(\frac{2 X 6}{3 X 10}\) = \(\frac{12}{30}\), Now \(\frac{12}{30}\) = 0.4 and \(\frac{6}{10}\) = 0.6, as 0.4 < 0.6, So \(\frac{12}{30}\) < \(\frac{6}{10}\).

In Problems 9–12, write true or false. Do not multiply. Question 9. \(\frac{3}{4}\) ∗ \(\frac{7}{10}\) is less than \(\frac{3}{4}\). Answer: True,

Explanation: First we multiply \(\frac{3}{4}\) X \(\frac{7}{10}\) = \(\frac{3 X 7}{4 X 10}\) = \(\frac{21}{40}\), Now \(\frac{21}{40}\) = 0.525 and \(\frac{3}{4}\) = 0.75, So true \(\frac{3}{4}\) ∗ \(\frac{7}{10}\) is less than \(\frac{3}{4}\).

Question 10. \(\frac{7}{9}\) ∗ \(\frac{11}{12}\) is greater than \(\frac{11}{12}\). Answer: False,

Explanation: First we multiply \(\frac{7}{9}\) X \(\frac{11}{12}\) = \(\frac{7 X 11}{9 X 12}\) = \(\frac{77}{108}\), Now \(\frac{77}{108}\) = 0.712 and \(\frac{11}{12}\) = 0.916, So false as \(\frac{7}{9}\) ∗ \(\frac{11}{12}\) is not greater than \(\frac{11}{12}\).

Question 11. \(\frac{4}{5}\) ∗ \(\frac{2}{8}\) is greater than\(\frac{2}{8}\) but less than \(\frac{4}{5}\). Answer: False,

Explanation: First we multiply \(\frac{4}{5}\) X \(\frac{2}{8}\) = \(\frac{4 X 2}{5 X 8}\) = \(\frac{8}{40}\), Now \(\frac{8}{40}\) = 0.2, \(\frac{2}{8}\) = 0.25 and \(\frac{4}{5}\) = 0.8, So false as \(\frac{4}{5}\) ∗ \(\frac{2}{8}\) is not greater than \(\frac{2}{8}\) but less than \(\frac{4}{5}\).

Question 12. \(\frac{6}{7}\) ∗ \(\frac{1}{4}\) is less than \(\frac{6}{7}\) and less than \(\frac{1}{4}\). Answer: True,

Explanation: First we multiply \(\frac{6}{7}\) X \(\frac{1}{4}\) = \(\frac{6 X 1}{7 X 4}\) = \(\frac{6}{28}\), Now \(\frac{6}{28}\) = 0.214, \(\frac{6}{7}\) = 0. 857 and \(\frac{1}{4}\) = 0.250, So true as \(\frac{6}{7}\) ∗ \(\frac{1}{4}\) is less than \(\frac{6}{7}\) and also less than \(\frac{1}{4}\).

Practice Question 13. \(\frac{2}{3}\) + \(\frac{1}{6}\) = ___5/6_____ Answer: \(\frac{2}{3}\) + \(\frac{1}{6}\) = \(\frac{5}{6}\),

Explanation: Given \(\frac{2}{3}\) + \(\frac{1}{6}\) before adding as both denominators need to be same so we multiply \(\frac{2}{3}\) by 2 before adding as \(\frac{2 x 2}{3 x 6}\) = \(\frac{4}{6}\), now denominators are same 6 so we add numerators as \(\frac{4}{6}\)  + \(\frac{1}{6}\) = \(\frac{4 + 1}{6}\) = \(\frac{5}{6}\), Therefore, \(\frac{2}{3}\) + \(\frac{1}{6}\) = \(\frac{5}{6}\).

Question 14. \(\frac{3}{4}\) + \(\frac{3}{8}\) = ___9/8 or 1_1/8_____ Answer: \(\frac{3}{4}\) + \(\frac{3}{8}\) = \(\frac{9}{8}\) or 1\(\frac{1}{8}\),

Explanation: Given \(\frac{3}{4}\) + \(\frac{3}{8}\) before adding as both denominators need to be same so we multiply \(\frac{3}{4}\) by 2 before adding as \(\frac{3 x 2}{4 x 2}\) = \(\frac{6}{8}\), now denominators are same 8 so we add numerators as \(\frac{6}{8}\)  + \(\frac{3}{8}\) = \(\frac{6 + 3}{8}\) = \(\frac{9}{8}\), as numerator is greater we can write in mixed fraction as (1 X 8 + 1 by 8) = 1\(\frac{1}{8}\), Therefore, \(\frac{3}{4}\) + \(\frac{3}{8}\) = \(\frac{9}{8}\) or 1\(\frac{1}{8}\).

Question 15. \(\frac{2}{5}\) + \(\frac{1}{4}\) = ___13/20_____ Answer: \(\frac{2}{5}\) + \(\frac{1}{4}\) = \(\frac{13}{20}\),

Explanation: Given \(\frac{2}{5}\) + \(\frac{1}{4}\) before adding as both denominators need to be same so we multiply numerator and denominator by 4 to\(\frac{2}{5}\) before adding as \(\frac{2 x 4}{5 x 4}\) = \(\frac{8}{20}\) and \(\frac{1}{4}\) by 5 before adding as \(\frac{1 x 5}{4 x 5}\) = \(\frac{5}{20}\) now denominators are same 20 so we add numerators as \(\frac{8}{20}\)  + \(\frac{5}{20}\) = \(\frac{8 + 5}{20}\) = \(\frac{13}{20}\), Therefore, \(\frac{2}{5}\) + \(\frac{1}{4}\) = \(\frac{13}{20}\).

Everyday Math Grade 5 Home Link 5.10 Answer Key

Mystery Models

Practice Solve. Question 3. 1\(\frac{1}{2}\) + 2\(\frac{2}{8}\) = __________ Answer: 1\(\frac{1}{2}\) + 2\(\frac{2}{8}\) = \(\frac{30}{8}\) or 3\(\frac{6}{8}\),

Explanation: Given 1\(\frac{1}{2}\) + 2\(\frac{2}{8}\), First we will write mixed fractions into  fractions as 1\(\frac{1}{2}\) = (1 X 2 + 1 by 2) = \(\frac{3}{2}\) and 2\(\frac{2}{8}\) = (2 x 8 + 2 by 8) = \(\frac{18}{8}\), before adding as both denominators need to be same so we multiply numerator and denominator by 4 to \(\frac{3}{2}\) before adding as \(\frac{3 x 4}{2 x 4}\) = \(\frac{12}{8}\) now denominators are same 8 so we add numerators as \(\frac{12}{8}\)  + \(\frac{18}{8}\) = \(\frac{12 + 18}{8}\) = \(\frac{30}{8}\), as numerator is greater than denominator we write in mixed fraction as (3 X 8 + 6 by 8) = 3\(\frac{6}{8}\), Therefore, 1\(\frac{1}{2}\) + 2\(\frac{2}{8}\) = \(\frac{30}{8}\) or 3\(\frac{6}{8}\).

Question 4. 6 – 3\(\frac{1}{3}\) = ___2 2/3______ Answer: 6 – 3\(\frac{1}{3}\) = \(\frac{8}{3}\) or 2\(\frac{2}{3}\),

Explanation: Given 6 – 3\(\frac{1}{3}\), First we will write mixed fraction into fractions as 3\(\frac{1}{3}\) = (3 X 3 + 1 by 3) = \(\frac{10}{3}\) before subtracting as both denominators need to be same so we multiply numerator and denominator by 3 to \(\frac{6}{1}\) before adding as \(\frac{6 x 3}{1 x 3}\) = \(\frac{18}{3}\) now denominators are same 3 so we subtract numerators as \(\frac{18}{3}\)  – \(\frac{10}{3}\) = \(\frac{18 – 10}{3}\) = \(\frac{8}{3}\), as numerator is greater than denominator we write in mixed fraction as (2 X 3 + 2 by 3) = 2\(\frac{2}{3}\), Therefore, 6 – 3\(\frac{1}{3}\) = \(\frac{8}{3}\) or 2\(\frac{2}{3}\),

Question 5. 1\(\frac{4}{9}\) + 5\(\frac{2}{3}\) = _________ Answer: 1\(\frac{4}{9}\) + 5\(\frac{2}{3}\) = \(\frac{64}{9}\) or 7\(\frac{1}{9}\),

Explanation: Given 1\(\frac{4}{9}\) + 5\(\frac{2}{3}\), First we will write mixed fractions into  fractions as 1\(\frac{4}{9}\) = (1 X 9 + 4 by 9) = \(\frac{13}{9}\) and 5\(\frac{2}{3}\) = (5 x 3 + 2 by 3) = \(\frac{17}{3}\), before adding as both denominators need to be same so we multiply numerator and denominator by 3 to \(\frac{17}{3}\)  before adding as \(\frac{17 x 3}{3 x 3}\) = \(\frac{51}{9}\) now denominators are same 9 so we add numerators as \(\frac{13}{9}\)  + \(\frac{51}{9}\) = \(\frac{13 + 51}{9}\) = \(\frac{64}{9}\), as numerator is greater than denominator we write in mixed fraction as (7 X 9 + 1 by 9) = 7\(\frac{1}{9}\), Therefore, 1\(\frac{4}{9}\) + 5\(\frac{2}{3}\) = \(\frac{64}{9}\) or 7\(\frac{1}{9}\).

Question 6. 8\(\frac{1}{3}\) – 3\(\frac{3}{4}\) = ___4 7/12_______ Answer: 8\(\frac{1}{3}\) – 3\(\frac{3}{4}\) = \(\frac{55}{12}\) or 4\(\frac{7}{12}\),

Explanation: Given 8\(\frac{1}{3}\) – 3\(\frac{3}{4}\), First we will write mixed fractions into  fractions as 8\(\frac{1}{3}\) = (8 X 3 + 1 by 3) = \(\frac{25}{3}\) and 3\(\frac{3}{4}\) = (3 x 4 + 3 by 4) = \(\frac{15}{4}\), before subtracting as both denominators need to be same so we multiply numerator and denominator by 4 to \(\frac{25}{3}\)  before subtracting as \(\frac{25 x 4}{3 x 4}\) = \(\frac{100}{12}\) and multiply numerator and denominator by 3 to \(\frac{15}{4}\) as \(\frac{15 X 3}{4 X 3}\) = \(\frac{45}{12}\) now denominators are same 12 so we subtract numerators as \(\frac{100}{12}\) – \(\frac{45}{12}\) = \(\frac{100 – 45}{12}\) = \(\frac{55}{12}\), as numerator is greater than denominator we write in mixed fraction as (4 X 12 + 7 by 12) = 4\(\frac{7}{12}\), Therefore, 8\(\frac{1}{3}\) – 3\(\frac{3}{4}\) = \(\frac{55}{12}\) or 4\(\frac{7}{12}\).

Everyday Mathematics Grade 5 Home Link 5.11 Answers

Finding Equivalent Fractions

Explanation: a. Three fractions that are equivalent to 1 are \(\frac{2}{2}\), \(\frac{3}{3}\), \(\frac{5}{5}\),

b. Using the fractions I wrote in Part a to find three fractions equivalent to \(\frac{6}{7}\) are \(\frac{24}{28}\), \(\frac{54}{63}\), \(\frac{150}{175}\) because as \(\frac{2}{2}\) X \(\frac{12}{14}\) = \(\frac{24}{28}\) = \(\frac{6}{7}\), \(\frac{3}{3}\) X \(\frac{18}{21}\) = \(\frac{54}{63}\) = \(\frac{6}{7}\), \(\frac{5}{5}\) X \(\frac{30}{35}\) = \(\frac{150}{175}\) =\(\frac{6}{7}\) respectively.

Question 2. You are solving fraction addition problems. Use the information to find equivalent fractions. a. Original fraction: \(\frac{4}{5}\) Denominator needed: 20 Multiply by: ____4/4______ Equivalent fraction: ____16/20_______ Answer: Denominator needed: 20 Multiply by: \(\frac{4}{4}\) Equivalent fraction: \(\frac{16}{20}\),

Explanation: Given \(\frac{4}{5}\) the equivalent fraction is as numerator is 4 so we multiply numerator and denominator by 4 as \(\frac{4}{5}\) X \(\frac{4}{4}\) = \(\frac{4 X 4}{5 X 4}\) = \(\frac{16}{20}\), therefore denominator needed is 20, Multiply by: \(\frac{4}{4}\) and Equivalent fraction: \(\frac{16}{20}\).

b. Original fraction: \(\frac{1}{3}\) Denominator needed: 18 Multiply by: ____6/6______ Equivalent fraction: ____6/18______ Answer: Denominator needed: 18 Multiply by: \(\frac{6}{6}\) Equivalent fraction: \(\frac{6}{18}\),

Explanation: Given \(\frac{1}{3}\) the equivalent fraction is as numerator is 6 so we multiply numerator and denominator by 6 as \(\frac{1}{3}\) X \(\frac{6}{6}\) = \(\frac{1 X 6}{3 X 6}\) = \(\frac{6}{18}\), therefore denominator needed is 18, Multiply by: \(\frac{6}{6}\) and Equivalent fraction: \(\frac{6}{18}\).

Question 3. Addison wanted to find a fraction equivalent to \(\frac{3}{8}\) with 16 in the denominator. He thought: “8 ∗ 2 = 16, so I need to multiply \(\frac{3}{8}\) by 2.” He got an answer of \(\frac{3}{16}\). a. Is \(\frac{3}{16}\) equivalent to \(\frac{3}{8}\)? How do you know? Answer: No, \(\frac{3}{16}\) ≠ \(\frac{3}{8}\),

Explanation: Given Addison wanted to find a fraction equivalent to \(\frac{3}{8}\) with 16 in the denominator. He thought: “8 ∗ 2 = 16, so I need to multiply \(\frac{3}{8}\) by 2.” He got an answer of \(\frac{3}{16}\) but Addison is incorrect as \(\frac{3}{16}\) is not equivalent to \(\frac{3}{8}\).

b. What mistake did Addison make? Answer: Addison multiplyed only denominator by 2 not numerator,

Explanation: Given Addison wanted to find a fraction equivalent to \(\frac{3}{8}\) with 16 in the denominator. He thought: “8 ∗ 2 = 16, so I need to multiply \(\frac{3}{8}\) by 2.” He got an answer of \(\frac{3}{16}\) but Addison is incorrect as \(\frac{3}{16}\) is not equivalent to \(\frac{3}{8}\) as he multipled only denominator by 2 not numerator.

Practice Solve. Question 4. What is \(\frac{2}{3}\) of 9? Answer: \(\frac{2}{3}\) of 9 is 6,

Explanation: Given to solve \(\frac{2}{3}\) of 9, So \(\frac{2}{3}\) X 9 = \(\frac{2 X 9}{3}\) = \(\frac{18}{3}\) = 6.

Question 5. What is \(\frac{3}{5}\) of 20? Answer: \(\frac{3}{5}\) of 20 is 12,

Explanation: Given to solve \(\frac{3}{5}\) of 20, So \(\frac{3}{5}\) X 20 = \(\frac{3 X 20}{5}\) = \(\frac{60}{5}\) = 12.

Question 6. Explain how you found your answer for Problem 5. Answer: Solving and multiplying \(\frac{3}{5}\) X 20,

Explanation: By solving \(\frac{3}{5}\) X 20 \(\frac{3 X 20}{5}\) = \(\frac{60}{5}\) = 12 I found the answer for Problem 5.

Everyday Math Grade 5 Home Link 5.12 Answer Key

Writing Fraction Multiplication Stories

Explanation: Given 4 ∗ \(\frac{2}{3}\) = \(\frac{4 X 2}{3}\) = \(\frac{8}{3}\) or 2\(\frac{2}{3}\), Number Story : Our class has 4 groups each group have 10 children who can play cricket, in that \(\frac{2}{3}\) of children participated in the competition, So how many groups of children participated in all? Wrote number story above.

Explanation: Given \(\frac{1}{2}\) X 16 = 8, Number Story : There are 16 books in library out which \(\frac{1}{2}\) of books are moral stories, Therefore how many books are moral stories in library?, Wrote number story above.

Practice Make an estimate. Then add or subtract. Show your work on the back of this page. Question 3 4.79 + 2.03 = ? Estimate: ____6.82______ 4.79 + 2.03 = ___6.82_______ Answer: Estimate: 6.82, 4.79 + 2.03 = 6.82,

Explanation: My estimate is 6.82, 4.79 +2.03 6.82.

Question 4. 8.25 – 3.91 = ? Estimate: ____4.34______ 8.25 – 3.91 = __4.34________ Answer: Estimate : 4.34, 8.25 – 3.91 = 4.34,

Explanation: My estimate is 4.34, 8.25 -3.91 4.34.

Everyday Mathematics Grade 5 Home Link 5.13 Answers

Solving Fraction Division Problems

Explanation: Given Ben has \(\frac{1}{2}\) of a loaf of bread. If he and his 3 friends share the \(\frac{1}{2}\) loaf equally, Part of the whole loaf will each person get is Number model: \(\frac{1}{2}\) ÷ 4 = \(\frac{1}{2}\) X \(\frac{1}{4}\) = \(\frac{1}{8}\), Each person will get \(\frac{1}{8}\) X 4 = [/latex] = \(\frac{4}{8}\) = \(\frac{1}{2}\)  loaf of bread.

Explanation: Given Amanda has a piece of ribbon that is \(\frac{1}{4}\) yard long. She wants to share the ribbon with 2 friends so that they can each wear a ribbon for Breast Cancer Awareness Month. If each of the 3 friends gets the same amount, Number model: \(\frac{1}{4}\) ÷ 3 = \(\frac{1}{4}\) X \(\frac{1}{3}\) = \(\frac{1}{12}\), Each person will get ribbon is \(\frac{1}{12}\) X 3 = \(\frac{3}{12}\) = \(\frac{1}{4}\).

Explanation: Given 3,408 X 21 = Estimate = 3,408 X 21 =71,568 which is reasonable as shown above.

Everyday Math Grade 5 Home Link 5.14 Answer Key

More Fraction Division Problems

Explanation: Given Charity is packing a 2-pound container of trail mix into bags for a camping trip. Each bag holds \(\frac{1}{8}\) pound of trail mix. If Charity uses all 2 pounds of trail mix then Number model = 2 ÷\(\frac{1}{8}\) = 2 X 8 = 16, Charity will have 16, \(\frac{1}{8}\) pound bags she will have.

Explanation: Given Davis has a thin box that is 5 inches wide. He wants to use the box to store markers that are \(\frac{1}{2}\) inch wide. If he lines up the markers side by side and uses the entire width of the box, number of markers can Davis fit in the box are 5 ÷ \(\frac{1}{2}\) = 5 X 2 = 10, So 10 X \(\frac{1}{2}\) = 5 markers in the box.

Practice Make an estimate. Then solve. Show your work on the back of this page Question 3. 623 ÷ 8 → ____77R7_______ Estimate: ___77R7_____ Answer: 623 ÷ 8 = 77 remainder 7, Estimate: 77R7,

Explanation: Given 623 ÷ 8 = 77 R 7 8)623(    56      63 56 7 So, 623 ÷ 8 = 77 remainder 7 and estimate is also reasonable.

Question 4. 4,495 ÷ 50 → ___89R45________ Estimate: ___89R45________ Answer: 4,495 ÷ 50 = 89 remainder 45, Estimate: 89R45,

Explanation: Given 4,495 ÷ 50 = 89 R 45 50)4,495(       4,450 45 So, 4,495 ÷ 50 = 89 remainder 45 and estimate is also reasonable.

Leave a Comment Cancel Reply

You must be logged in to post a comment.

• For Parents
• For Teachers
• Teaching Topics

• Kindergarten
• EM3/CCSS at Home
• Family Letters
• Student Gallery
• Understanding EM
• Algorithms/ Computation
• Student Links

EM4 at Home Grade 5

Select a unit.

• Unit 1 Area and Volume
• Unit 2 Whole Number Place Value and Operations
• Unit 3 Fraction Concepts, Addition, and Subtraction
• Unit 4 Decimal Concepts; Coordinate Grids
• Unit 5 Operations with Fractions
• Unit 6 Investigations in Measurement; Decimal Multiplication and Division
• Unit 7 Multiplication of Mixed Numbers; Geometry; Graphs
• Unit 8 Applications of Measurement, Computation, and Graphing

Finding the Unit and Lesson Numbers

Everyday Mathematics is divided into Units, which are divided into Lessons. In the upper-left corner of the Home Link, you should see an icon like this:

The Unit number is the first number you see in the icon, and the Lesson number is the second number. In this case, the student is working in Unit 5, Lesson 4. To access the help resources, you would select "Unit 5" from the list above, and then look for the row in the table labeled "Lesson 5-4."

Everyday Mathematics for Parents: What You Need to Know to Help Your Child Succeed

The University of Chicago School Mathematics Project

University of Chicago Press

Learn more >>

Related Links

Help with algorithms.

Access video tutorials, practice exercises, and information on the research basis and development of various algorithms.

Everyday Mathematics Online

With a login provided by your child's teacher, access resources to help your child with homework or brush up on your math skills.

Parent Connections on Publisher's site

McGraw-Hill Education offers many resources for parents, including tips, activities, and helpful links.

Parent Resources on EverydayMath.com

EverydayMath.com features activity ideas, literature lists, and family resources for the EM curriculum.

Understanding Everyday Mathematics for Parents

Learn more about the EM curriculum and how to assist your child.

Common Core Grade 5 Math (Worksheets, Homework, Lesson Plans)

Related Pages Common Core Math Resources, Lesson Plans And Worksheets Common Core Math Video Lessons, Math Worksheets and Games for Grade 5 Common Core Math Video Lessons, Math Worksheets and Games for all grades

Looking for video lessons that will help you in your Common Core Grade 5 Math classwork or homework? Looking for Common Core Math Worksheets and Lesson Plans that will help you prepare lessons for Grade 5 students?

The following lesson plans and worksheets are from the New York State Education Department Common Core-aligned educational resources. The Lesson Plans and Worksheets are divided into six modules.

Grade 5 Homework, Lesson Plans And Worksheets

Printable Common Core Worksheets for 5th Grade

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

• Skills by Standard
• Skills by Grade
• Skills by Category

Go to profile

• Assignments
• Assessments
• Report Cards
• Our Teachers

Remove ads and gain access to the arcade and premium games!

Unlock harder levels by getting an average of 80% or higher.

Earn up to 5 stars for each level The more questions you answer correctly, the more stars you'll unlock!

Each game has 10 questions. Green box means correct. Yellow box means incorrect.

Need some help or instruction on how to do this skill?

Want a paper copy? Print a generated PDF for this skill.

Share MathGames with your students, and track their progress.

See how you scored compared to other students from around the world.

Learn Math Together.

Grade 5 - Number and Operations - Fractions

Standard 5.NF.B.7b - Solve division equations involving unit fractions.

Included Skills:

Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.

If you notice any problems, please let us know .