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Common Core: 5th Grade Math : Common Core Math: Grade 5

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

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All Common Core: 5th Grade Math Resources

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Example Questions

Example Question #1311 : Ssat Middle Level Quantitative (Math)

Solve:

$\small \frac{7}{8}\div\frac{1}{4}$ $\displaystyle \small \frac{7}{8}\div\frac{1}{4}$

Possible Answers:

$\small \frac{7}{32}$ $\displaystyle \small \frac{7}{32}$

$\small \frac{32}{7}$ $\displaystyle \small \frac{32}{7}$

$\small \frac{9}{15}$ $\displaystyle \small \frac{9}{15}$

$\small \frac{8}{28}$ $\displaystyle \small \frac{8}{28}$

$3\frac{1}{2}$ $\displaystyle 3\frac{1}{2}$

Correct answer:

$3\frac{1}{2}$ $\displaystyle 3\frac{1}{2}$

Explanation:

$\small \frac{7}{8}\div\frac{1}{4}$ $\displaystyle \small \frac{7}{8}\div\frac{1}{4}$

To divide fractions, we multiply by the reciprocal. In order to find the reciprocal, we simply flip the fraction over. The numerator becomes the denominator and the denominator becomes the numerator.

$\small \frac{7}{8}\times\frac{4}{1}=\frac{28}{8}$ $\displaystyle \small \frac{7}{8}\times\frac{4}{1}=\frac{28}{8}$

$\frac{28}{8}=3\frac{4}{8}=3\frac{1}{2}$ $\displaystyle \frac{28}{8}=3\frac{4}{8}=3\frac{1}{2}$ because $\displaystyle 8$ can go into $\displaystyle 28$ three times, with $\displaystyle 4$ left over.

$\frac{4}{8}$ $\displaystyle \frac{4}{8}$ can be reduced because both $\displaystyle 4$ and $\displaystyle 8$ are divisible by $\displaystyle 4$.

$\frac{4}{8}\div\frac{4}{4}=\frac{1}{2}$ $\displaystyle \frac{4}{8}\div\frac{4}{4}=\frac{1}{2}$

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Example Question #1 : Interpret Division Of A Unit Fraction By A Whole Number : Ccss.Math.Content.5.Nf.B.7a

It takes one person half of a day to clean Milton's house. Milton's grandparents are coming to visit, so Milton's mom tells Milton and his three siblings that they need to clean the house. If the four kids split up the cleaning time equally, what fraction of the day does Milton spend cleaning?

Possible Answers:

$\frac{1}{2}\div 4=\frac{1}{2}\times\frac{4}{1}=2\ days$ $\displaystyle \frac{1}{2}\div 4=\frac{1}{2}\times\frac{4}{1}=2\ days$

$\frac{1}{2}\div 4=\frac{1}{2}\times\frac{1}{4}=\frac{1}{8}\ of\ the\ day$ $\displaystyle \frac{1}{2}\div 4=\frac{1}{2}\times\frac{1}{4}=\frac{1}{8}\ of\ the\ day$

$\frac{1}{2}\div 4=\frac{1}{2}\times\frac{1}{4}=\frac{1}{6}\ of\ the\ day$ $\displaystyle \frac{1}{2}\div 4=\frac{1}{2}\times\frac{1}{4}=\frac{1}{6}\ of\ the\ day$

$\frac{1}{2}\div 3=\frac{1}{2}\times\frac{3}{1}=\frac{3}{2}\ of\ the\ day$ $\displaystyle \frac{1}{2}\div 3=\frac{1}{2}\times\frac{3}{1}=\frac{3}{2}\ of\ the\ day$

$\frac{1}{2}\div 3=\frac{1}{2}\times\frac{1}{3}=\frac{1}{6}\ of\ the\ day$ $\displaystyle \frac{1}{2}\div 3=\frac{1}{2}\times\frac{1}{3}=\frac{1}{6}\ of\ the\ day$

Correct answer:

$\frac{1}{2}\div 4=\frac{1}{2}\times\frac{1}{4}=\frac{1}{8}\ of\ the\ day$ $\displaystyle \frac{1}{2}\div 4=\frac{1}{2}\times\frac{1}{4}=\frac{1}{8}\ of\ the\ day$

Explanation:

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Example Question #1 : Interpret Division Of A Unit Fraction By A Whole Number : Ccss.Math.Content.5.Nf.B.7a

Sally has $\frac{1}{2}lb$ $\displaystyle \frac{1}{2}lb$ of gummy candies that she wants to divide evenly into $\displaystyle 13$ bags. How much will each bag of gummy candies weigh?

Possible Answers:

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

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

$\frac{1}{13}lb$ $\displaystyle \frac{1}{13}lb$

$\frac{1}{26}lb$ $\displaystyle \frac{1}{26}lb$

$\frac{13}{2}lb$ $\displaystyle \frac{13}{2}lb$

Correct answer:

$\frac{1}{26}lb$ $\displaystyle \frac{1}{26}lb$

Explanation:

We are splitting $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ into $\displaystyle 13$ equal groups, so we are dividing $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ by $\displaystyle 13$.

To solve $\frac{1}{2}\div13$ $\displaystyle \frac{1}{2}\div13$ we multiply by the reciprocal.

$\frac{1}{2}\times\frac{1}{13}=\frac{1}{26}$ $\displaystyle \frac{1}{2}\times\frac{1}{13}=\frac{1}{26}$

1 26

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Example Question #1231 : Ssat Middle Level Quantitative (Math)

Jessie has $\frac{1}{2}lb$ $\displaystyle \frac{1}{2}lb$ of gummy candies that she wants to divide evenly into $\displaystyle 2$ bags. How much will each bag of gummy candies weigh?

Possible Answers:

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

$\frac{1}{8}lb$ $\displaystyle \frac{1}{8}lb$

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

$\frac{4}{2}lb$ $\displaystyle \frac{4}{2}lb$

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

Correct answer:

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

Explanation:

We are splitting $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ into $\displaystyle 2$ equal groups, so we are dividing $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ by $\displaystyle 2$.

To solve $\frac{1}{2}\div2$ $\displaystyle \frac{1}{2}\div2$ we multiply by the reciprocal.

$\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$ $\displaystyle \frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$

1 4

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Example Question #1232 : Ssat Middle Level Quantitative (Math)

Jessie has $\frac{1}{2}lb$ $\displaystyle \frac{1}{2}lb$ of gummy candies that she wants to divide evenly into $\displaystyle 12$ bags. How much will each bag of gummy candies weigh?

Possible Answers:

$\frac{1}{24}lb$ $\displaystyle \frac{1}{24}lb$

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

$\frac{2}{12}lb$ $\displaystyle \frac{2}{12}lb$

$\frac{12}{2}lb$ $\displaystyle \frac{12}{2}lb$

$\frac{1}{12}lb$ $\displaystyle \frac{1}{12}lb$

Correct answer:

$\frac{1}{24}lb$ $\displaystyle \frac{1}{24}lb$

Explanation:

We are splitting $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ into $\displaystyle 12$ equal groups, so we are dividing $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ by $\displaystyle 12$.

To solve $\frac{1}{2}\div12$ $\displaystyle \frac{1}{2}\div12$ we multiply by the reciprocal.

$\frac{1}{2}\times\frac{1}{12}=\frac{1}{24}$ $\displaystyle \frac{1}{2}\times\frac{1}{12}=\frac{1}{24}$

1 24

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Example Question #1233 : Ssat Middle Level Quantitative (Math)

Erica has $\frac{1}{2}lb$ $\displaystyle \frac{1}{2}lb$ of gummy candies that she wants to divide evenly into $\displaystyle 11$ bags. How much will each bag of gummy candies weigh?

Possible Answers:

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

$\frac{1}{11}lb$ $\displaystyle \frac{1}{11}lb$

$\frac{1}{22}lb$ $\displaystyle \frac{1}{22}lb$

$\frac{11}{}2lb$ $\displaystyle \frac{11}{}2lb$

$\frac{1}{12}lb$ $\displaystyle \frac{1}{12}lb$

Correct answer:

$\frac{1}{22}lb$ $\displaystyle \frac{1}{22}lb$

Explanation:

We are splitting $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ into $\displaystyle 11$ equal groups, so we are dividing $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ by $\displaystyle 11$.

To solve $\frac{1}{2}\div11$ $\displaystyle \frac{1}{2}\div11$ we multiply by the reciprocal.

$\frac{1}{2}\times\frac{1}{11}=\frac{1}{22}$ $\displaystyle \frac{1}{2}\times\frac{1}{11}=\frac{1}{22}$

1 22

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Example Question #5 : Interpret Division Of A Unit Fraction By A Whole Number : Ccss.Math.Content.5.Nf.B.7a

Sally has $\frac{1}{2}lb$ $\displaystyle \frac{1}{2}lb$ of gummy candies that she wants to divide evenly into $\displaystyle 10$ bags. How much will each bag of gummy candies weigh?

Possible Answers:

$\frac{1}{10}lb$ $\displaystyle \frac{1}{10}lb$

$\frac{1}{20}lb$ $\displaystyle \frac{1}{20}lb$

$\frac{2}{10}lb$ $\displaystyle \frac{2}{10}lb$

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

$\frac{10}{2}lb$ $\displaystyle \frac{10}{2}lb$

Correct answer:

$\frac{1}{20}lb$ $\displaystyle \frac{1}{20}lb$

Explanation:

We are splitting $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ into $\displaystyle 10$ equal groups, so we are dividing $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ by $\displaystyle 10$.

To solve $\frac{1}{2}\div10$ $\displaystyle \frac{1}{2}\div10$ we multiply by the reciprocal.

$\frac{1}{2}\times\frac{1}{10}=\frac{1}{20}$ $\displaystyle \frac{1}{2}\times\frac{1}{10}=\frac{1}{20}$

1 20

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Example Question #96 : How To Divide Fractions

Melissa has $\frac{1}{2}lb$ $\displaystyle \frac{1}{2}lb$ of gummy candies that she wants to divide evenly into $\displaystyle 9$ bags. How much will each bag of gummy candies weigh?

Possible Answers:

$\frac{1}{12}lb$ $\displaystyle \frac{1}{12}lb$

$\frac{9}{8}lb$ $\displaystyle \frac{9}{8}lb$

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

$\frac{1}{18}lb$ $\displaystyle \frac{1}{18}lb$

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

Correct answer:

$\frac{1}{18}lb$ $\displaystyle \frac{1}{18}lb$

Explanation:

We are splitting $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ into $\displaystyle 9$ equal groups, so we are dividing $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ by $\displaystyle 9$.

To solve $\frac{1}{2}\div9$ $\displaystyle \frac{1}{2}\div9$ we multiply by the reciprocal.

$\frac{1}{2}\times\frac{1}{9}=\frac{1}{18}$ $\displaystyle \frac{1}{2}\times\frac{1}{9}=\frac{1}{18}$

1 18

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Example Question #6 : Interpret Division Of A Unit Fraction By A Whole Number : Ccss.Math.Content.5.Nf.B.7a

Melissa has $\frac{1}{2}lb$ $\displaystyle \frac{1}{2}lb$ of gummy candies that she wants to divide evenly into $\displaystyle 8$ bags. How much will each bag of gummy candies weigh?

Possible Answers:

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

$\frac{16}{2}lb$ $\displaystyle \frac{16}{2}lb$

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

$\frac{1}{16}lb$ $\displaystyle \frac{1}{16}lb$

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

Correct answer:

$\frac{1}{16}lb$ $\displaystyle \frac{1}{16}lb$

Explanation:

We are splitting $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ into $\displaystyle 8$ equal groups, so we are dividing $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ by $\displaystyle 8$.

To solve $\frac{1}{2}\div8$ $\displaystyle \frac{1}{2}\div8$ we multiply by the reciprocal.

$\frac{1}{2}\times\frac{1}{8}=\frac{1}{16}$ $\displaystyle \frac{1}{2}\times\frac{1}{8}=\frac{1}{16}$

1 16

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Example Question #174 : How To Divide Fractions

Christine has $\frac{1}{2}lb$ $\displaystyle \frac{1}{2}lb$ of gummy candies that she wants to divide evenly into $\displaystyle 7$ bags. How much will each bag of gummy candies weigh?

Possible Answers:

$\frac{1}{14}lb$ $\displaystyle \frac{1}{14}lb$

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

$\frac{8}{7}lb$ $\displaystyle \frac{8}{7}lb$

$\frac{2}{7}lb$ $\displaystyle \frac{2}{7}lb$

$\frac{14}{2}lb$ $\displaystyle \frac{14}{2}lb$

Correct answer:

$\frac{1}{14}lb$ $\displaystyle \frac{1}{14}lb$

Explanation:

We are splitting $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ into $\displaystyle 7$ equal groups, so we are dividing $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ by $\displaystyle 7$.

To solve $\frac{1}{2}\div7$ $\displaystyle \frac{1}{2}\div7$ we multiply by the reciprocal.

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

1 14

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Common Core: 5th Grade Math : Common Core Math: Grade 5

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

All Common Core: 5th Grade Math Resources

Example Questions

Example Question #1311 : Ssat Middle Level Quantitative (Math)

Example Question #1 : Interpret Division Of A Unit Fraction By A Whole Number : Ccss.Math.Content.5.Nf.B.7a

Example Question #1 : Interpret Division Of A Unit Fraction By A Whole Number : Ccss.Math.Content.5.Nf.B.7a

Example Question #1231 : Ssat Middle Level Quantitative (Math)

Example Question #1232 : Ssat Middle Level Quantitative (Math)

Example Question #1233 : Ssat Middle Level Quantitative (Math)

Example Question #5 : Interpret Division Of A Unit Fraction By A Whole Number : Ccss.Math.Content.5.Nf.B.7a

Example Question #96 : How To Divide Fractions

Example Question #6 : Interpret Division Of A Unit Fraction By A Whole Number : Ccss.Math.Content.5.Nf.B.7a

Example Question #174 : How To Divide Fractions

All Common Core: 5th Grade Math Resources

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