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Common Core: 5th Grade Math : Solve Real World Problems Involving Multiplication of Fractions and Mixed Numbers: CCSS.Math.Content.5.NF.B.6

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Example Questions

Example Question #1 : Solve Real World Problems Involving Multiplication Of Fractions And Mixed Numbers: Ccss.Math.Content.5.Nf.B.6

A recipe calls for $\frac{3}{4}$ $\displaystyle \frac{3}{4}$ of a cup of flour. If you double the recipe, how much flour do you need?

Possible Answers:

$2\frac{3}{4}\ cups$ $\displaystyle 2\frac{3}{4}\ cups$

$1\frac{1}{2}\ cups$ $\displaystyle 1\frac{1}{2}\ cups$

$1\frac{1}{3}\ cups$ $\displaystyle 1\frac{1}{3}\ cups$

$1\frac{1}{4}\ cups$ $\displaystyle 1\frac{1}{4}\ cups$

$1\ cup$ $\displaystyle 1\ cup$

Correct answer:

$1\frac{1}{2}\ cups$ $\displaystyle 1\frac{1}{2}\ cups$

Explanation:

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Example Question #2 : Solve Real World Problems Involving Multiplication Of Fractions And Mixed Numbers: Ccss.Math.Content.5.Nf.B.6

Sara collected $\small \frac{2}{9}$ $\displaystyle \small \frac{2}{9}$ of a bag of leaves. Joe collected $\small 7$ $\displaystyle \small 7$ times as many bags as Sara. How many bags did Joe collect?

Possible Answers:

$\small \frac{5}{9}$ $\displaystyle \small \frac{5}{9}$

$\small \frac{9}{14}$ $\displaystyle \small \frac{9}{14}$

$\small \frac{9}{13}$ $\displaystyle \small \frac{9}{13}$

$\small 1\frac{5}{9}$ $\displaystyle \small 1\frac{5}{9}$

$\small 1\frac{3}{9}$ $\displaystyle \small 1\frac{3}{9}$

Correct answer:

$\small 1\frac{5}{9}$ $\displaystyle \small 1\frac{5}{9}$

Explanation:

When we multiply a fraction by a whole number, we first want to make the whole number into a fraction. We do that by putting the whole number over $\small 1.$ $\displaystyle \small 1.$ Then we multiply like normal.

$\small \frac{7}{1}\times\frac{2}{9}=\frac{14}{9}$ $\displaystyle \small \frac{7}{1}\times\frac{2}{9}=\frac{14}{9}$

$\small \frac{14}{9}=1\frac{5}{9}$ $\displaystyle \small \frac{14}{9}=1\frac{5}{9}$ Because $\small 9$ $\displaystyle \small 9$ can go into $\small 14$ $\displaystyle \small 14$ only $\small 1$ $\displaystyle \small 1$ time and $\small \frac{5}{9}$ $\displaystyle \small \frac{5}{9}$ is left over.

Joe collected $\small 1\frac{5}{9}$ $\displaystyle \small 1\frac{5}{9}$ bags of leaves.

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Example Question #3 : Solve Real World Problems Involving Multiplication Of Fractions And Mixed Numbers: Ccss.Math.Content.5.Nf.B.6

Alison collected $\small \frac{1}{5}$ $\displaystyle \small \frac{1}{5}$ of a bag of leaves. Karen collected $\small 6$ $\displaystyle \small 6$ times as many bags as Alison. How many bags did Karen collect?

Possible Answers:

$\small \frac{3}{6}$ $\displaystyle \small \frac{3}{6}$

$\small 1\frac{1}{5}$ $\displaystyle \small 1\frac{1}{5}$

$\small 1\frac{1}{6}$ $\displaystyle \small 1\frac{1}{6}$

$\small \frac{6}{7}$ $\displaystyle \small \frac{6}{7}$

$\small \frac{2}{3}$ $\displaystyle \small \frac{2}{3}$

Correct answer:

$\small 1\frac{1}{5}$ $\displaystyle \small 1\frac{1}{5}$

Explanation:

$\small \small \frac{6}{1}\times\frac{1}{5}=\frac{6}{5}$ $\displaystyle \small \small \frac{6}{1}\times\frac{1}{5}=\frac{6}{5}$

$\small \frac{6}{5}=1\frac{1}{5}$ $\displaystyle \small \frac{6}{5}=1\frac{1}{5}$ Because $\small 5$ $\displaystyle \small 5$ can go into $\displaystyle 6$ only $\small 1$ $\displaystyle \small 1$ time and $\small \frac{1}{5}$ $\displaystyle \small \frac{1}{5}$ is left over.

Karen collected $\small 1\frac{1}{5}$ $\displaystyle \small 1\frac{1}{5}$ bags of leaves.

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Example Question #4 : Solve Real World Problems Involving Multiplication Of Fractions And Mixed Numbers: Ccss.Math.Content.5.Nf.B.6

Jess collected $\small \frac{2}{3}$ $\displaystyle \small \frac{2}{3}$ of a bag of leaves. Sam collected $\displaystyle 6$ times as many bags as Jess. How many bags did Sam collect?

Possible Answers:

$\displaystyle 3$

$\small \frac{1}{9}$ $\displaystyle \small \frac{1}{9}$

$\small \frac{2}{18}$ $\displaystyle \small \frac{2}{18}$

$\small \frac{7}{5}$ $\displaystyle \small \frac{7}{5}$

$\small 4$ $\displaystyle \small 4$

Correct answer:

$\small 4$ $\displaystyle \small 4$

Explanation:

$\small \frac{6}{1}\times\frac{2}{3}=\frac{12}{3}$ $\displaystyle \small \frac{6}{1}\times\frac{2}{3}=\frac{12}{3}$

$\small \frac{12}{3}=4$ $\displaystyle \small \frac{12}{3}=4$ Because $\displaystyle 3$ can go into $\displaystyle 12$ an even $\displaystyle 4$ times.

Sam collected $\displaystyle 4$ bags of leaves.

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Example Question #5 : Solve Real World Problems Involving Multiplication Of Fractions And Mixed Numbers: Ccss.Math.Content.5.Nf.B.6

Kara collected $\small \frac{5}{7}$ $\displaystyle \small \frac{5}{7}$ of a bag of leaves. Drew collected $\displaystyle 3$ times as many bags as Kara. How many bags did Drew collect?

Possible Answers:

$\small 2\frac{1}{7}$ $\displaystyle \small 2\frac{1}{7}$

$\small 1\frac{8}{7}$ $\displaystyle \small 1\frac{8}{7}$

$\small \frac{5}{21}$ $\displaystyle \small \frac{5}{21}$

$\small 1\frac{1}{7}$ $\displaystyle \small 1\frac{1}{7}$

$\small \frac{6}{10}$ $\displaystyle \small \frac{6}{10}$

Correct answer:

$\small 2\frac{1}{7}$ $\displaystyle \small 2\frac{1}{7}$

Explanation:

$\small \frac{3}{1}\times\frac{5}{7}=\frac{15}{7}$ $\displaystyle \small \frac{3}{1}\times\frac{5}{7}=\frac{15}{7}$

$\small \frac{15}{7}=2\frac{1}{7}$ $\displaystyle \small \frac{15}{7}=2\frac{1}{7}$ Because $\displaystyle 7$ can go into $\displaystyle 15$ only $\small 2$ $\displaystyle \small 2$ times and $\small \frac{1}{7}$ $\displaystyle \small \frac{1}{7}$ is left over.

Drew collected $\small 2\frac{1}{7}$ $\displaystyle \small 2\frac{1}{7}$ bags of leaves.

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Example Question #6 : Solve Real World Problems Involving Multiplication Of Fractions And Mixed Numbers: Ccss.Math.Content.5.Nf.B.6

Jenny collected $\small \frac{9}{11}$ $\displaystyle \small \frac{9}{11}$ of a bag of leaves. Brian collected $\displaystyle 4$ times as many bags as Jenny. How many bags did Brian collect?

Possible Answers:

$\small \frac{44}{9}$ $\displaystyle \small \frac{44}{9}$

$\small 4\frac{3}{11}$ $\displaystyle \small 4\frac{3}{11}$

$\small \frac{9}{44}$ $\displaystyle \small \frac{9}{44}$

$\small 3\frac{3}{11}$ $\displaystyle \small 3\frac{3}{11}$

$\small \frac{5}{7}$ $\displaystyle \small \frac{5}{7}$

Correct answer:

$\small 3\frac{3}{11}$ $\displaystyle \small 3\frac{3}{11}$

Explanation:

When we multiply a fraction by a whole number, we first want to make the whole number into a fraction. We do that by putting the whole number over $\displaystyle 1.$ Then we multiply like normal.

$\small \frac{4}{1}\times\frac{9}{11}=\frac{36}{11}$ $\displaystyle \small \frac{4}{1}\times\frac{9}{11}=\frac{36}{11}$

$\small \frac{36}{11}=3\frac{3}{11}$ $\displaystyle \small \frac{36}{11}=3\frac{3}{11}$ Because $\small 11$ $\displaystyle \small 11$ can go into $\small 36$ $\displaystyle \small 36$ only $\small 3$ $\displaystyle \small 3$ times and $\small \frac{3}{11}$ $\displaystyle \small \frac{3}{11}$ is left over.

Brian collected $\small 3\frac{3}{11}$ $\displaystyle \small 3\frac{3}{11}$ bags of leaves.

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Example Question #7 : Solve Real World Problems Involving Multiplication Of Fractions And Mixed Numbers: Ccss.Math.Content.5.Nf.B.6

Liz collected $\small \frac{3}{4}$ $\displaystyle \small \frac{3}{4}$ of a bag of leaves. Tammy collected $\small 12$ $\displaystyle \small 12$ times as many bags as Liz. How many bags did Tammy collect?

Possible Answers:

$\small 7$ $\displaystyle \small 7$

$\small \frac{48}{3}$ $\displaystyle \small \frac{48}{3}$

$\small 9$ $\displaystyle \small 9$

$\small 8$ $\displaystyle \small 8$

$\small \frac{3}{48}$ $\displaystyle \small \frac{3}{48}$

Correct answer:

$\small 9$ $\displaystyle \small 9$

Explanation:

$\small \frac{12}{1}\times\frac{3}{4}=\frac{36}{4}$ $\displaystyle \small \frac{12}{1}\times\frac{3}{4}=\frac{36}{4}$

$\small \frac{36}{4}=9$ $\displaystyle \small \frac{36}{4}=9$ Because $\small 4$ $\displaystyle \small 4$ can go into $\small 36$ $\displaystyle \small 36$ an even $\small 9$ $\displaystyle \small 9$ times.

Tammy collected $\small 9$ $\displaystyle \small 9$ bags of leaves.

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Example Question #8 : Solve Real World Problems Involving Multiplication Of Fractions And Mixed Numbers: Ccss.Math.Content.5.Nf.B.6

Heather collected $\small \frac{1}{2}$ $\displaystyle \small \frac{1}{2}$ of a bag of leaves. Matt collected $\displaystyle 3$ times as many bags as Heather. How many bags did Matt collect?

Possible Answers:

$\small 1\frac{1}{2}$ $\displaystyle \small 1\frac{1}{2}$

$\small 1$ $\displaystyle \small 1$

$\small 2$ $\displaystyle \small 2$

$\small \frac{1}{6}$ $\displaystyle \small \frac{1}{6}$

$\small 1\frac{1}{3}$ $\displaystyle \small 1\frac{1}{3}$

Correct answer:

$\small 1\frac{1}{2}$ $\displaystyle \small 1\frac{1}{2}$

Explanation:

$\small \frac{3}{1}\times\frac{1}{2}=\frac{3}{2}$ $\displaystyle \small \frac{3}{1}\times\frac{1}{2}=\frac{3}{2}$

$\small \frac{3}{2}=1\frac{1}{2}$ $\displaystyle \small \frac{3}{2}=1\frac{1}{2}$ Because $\displaystyle 2$ can go into $\small 3$ $\displaystyle \small 3$ only $\small 1$ $\displaystyle \small 1$ time and $\small \frac{1}2{}$ $\displaystyle \small \frac{1}2{}$ is left over.

Matt collected $\small 1\frac{1}2{}$ $\displaystyle \small 1\frac{1}2{}$ bags of leaves.

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Example Question #9 : Solve Real World Problems Involving Multiplication Of Fractions And Mixed Numbers: Ccss.Math.Content.5.Nf.B.6

Dave collected $\small \frac{5}{7}$ $\displaystyle \small \frac{5}{7}$ of a bag of leaves. Wes collected $\small 4$ $\displaystyle \small 4$ times as many bags as Dave. How many bags did Wes collect?

Possible Answers:

$\displaystyle 2$

$\displaystyle 3$

$\small 2\frac{6}{7}$ $\displaystyle \small 2\frac{6}{7}$

$\small 3\frac{6}{7}$ $\displaystyle \small 3\frac{6}{7}$

$\small \frac{5}{28}$ $\displaystyle \small \frac{5}{28}$

Correct answer:

$\small 2\frac{6}{7}$ $\displaystyle \small 2\frac{6}{7}$

Explanation:

$\small \frac{4}{1}\times \frac{5}{7}=\frac{20}{7}$ $\displaystyle \small \frac{4}{1}\times \frac{5}{7}=\frac{20}{7}$

$\small \frac{20}{7}=2\frac{6}{7}$ $\displaystyle \small \frac{20}{7}=2\frac{6}{7}$ Because $\small 7$ $\displaystyle \small 7$ can go into $\displaystyle 20$ only $\displaystyle 2$ times and $\small \frac{6}{7}$ $\displaystyle \small \frac{6}{7}$ is left over.

Wes collected $\small 2\frac{6}{7}$ $\displaystyle \small 2\frac{6}{7}$ bags of leaves.

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Example Question #10 : Solve Real World Problems Involving Multiplication Of Fractions And Mixed Numbers: Ccss.Math.Content.5.Nf.B.6

Megan collected $\small \frac{1}{3}$ $\displaystyle \small \frac{1}{3}$ of a bag of leaves. Sally collected $\displaystyle 3$ times as many bags as Megan. How many bags did Sally collect?

Possible Answers:

$\small 1\frac{1}3{}$ $\displaystyle \small 1\frac{1}3{}$

$\small \frac{1}{2}$ $\displaystyle \small \frac{1}{2}$

$\displaystyle 1$

$\small \frac{1}{9}$ $\displaystyle \small \frac{1}{9}$

$\small \frac{2}{3}$ $\displaystyle \small \frac{2}{3}$

Correct answer:

$\displaystyle 1$

Explanation:

When we multiply a fraction by a whole number, we first want to make the whole number into a fraction. We do that by putting the whole number over $\displaystyle 1.$ Then we multiply like normal.

$\small \small \frac{3}{1}\times\frac{1}{3}=\frac{3}{3}$ $\displaystyle \small \small \frac{3}{1}\times\frac{1}{3}=\frac{3}{3}$

$\small \frac{3}{3}=1$ $\displaystyle \small \frac{3}{3}=1$ Because $\displaystyle 3$ can go into $\small 3$ $\displaystyle \small 3$ an even $\small 1$ $\displaystyle \small 1$ time.

Sally collected $\small 1$ $\displaystyle \small 1$ bag of leaves.

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Common Core: 5th Grade Math : Solve Real World Problems Involving Multiplication of Fractions and Mixed Numbers: CCSS.Math.Content.5.NF.B.6

Study concepts, example questions & explanations for Common Core: 5th Grade Math

All Common Core: 5th Grade Math Resources

Example Questions

Example Question #1 : Solve Real World Problems Involving Multiplication Of Fractions And Mixed Numbers: Ccss.Math.Content.5.Nf.B.6

Example Question #2 : Solve Real World Problems Involving Multiplication Of Fractions And Mixed Numbers: Ccss.Math.Content.5.Nf.B.6

Example Question #3 : Solve Real World Problems Involving Multiplication Of Fractions And Mixed Numbers: Ccss.Math.Content.5.Nf.B.6

Example Question #4 : Solve Real World Problems Involving Multiplication Of Fractions And Mixed Numbers: Ccss.Math.Content.5.Nf.B.6

Example Question #5 : Solve Real World Problems Involving Multiplication Of Fractions And Mixed Numbers: Ccss.Math.Content.5.Nf.B.6

Example Question #6 : Solve Real World Problems Involving Multiplication Of Fractions And Mixed Numbers: Ccss.Math.Content.5.Nf.B.6

Example Question #7 : Solve Real World Problems Involving Multiplication Of Fractions And Mixed Numbers: Ccss.Math.Content.5.Nf.B.6

Example Question #8 : Solve Real World Problems Involving Multiplication Of Fractions And Mixed Numbers: Ccss.Math.Content.5.Nf.B.6

Example Question #9 : Solve Real World Problems Involving Multiplication Of Fractions And Mixed Numbers: Ccss.Math.Content.5.Nf.B.6

Example Question #10 : Solve Real World Problems Involving Multiplication Of Fractions And Mixed Numbers: Ccss.Math.Content.5.Nf.B.6

All Common Core: 5th Grade Math Resources

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