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Common Core: 5th Grade Math : Number & Operations with Fractions

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

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All Common Core: 5th Grade Math Resources

7 Diagnostic Tests 225 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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

Sarah has $\displaystyle 8$ gallons of milk. Each glass holds $\frac{1}{4}$ $\displaystyle \frac{1}{4}$ of a gallon. How many glasses can she fill?

Possible Answers:

$\displaystyle 20$

$\displaystyle 32$

$\displaystyle 28$

$\displaystyle 24$

$\displaystyle 36$

Correct answer:

$\displaystyle 32$

Explanation:

Think: How many $\frac{1}{4}$ $\displaystyle \frac{1}{4}$s are in $\displaystyle 8$ wholes?

To solve $8\div\frac{1}{4}$ $\displaystyle 8\div\frac{1}{4}$ we multiply by the reciprocal

$\frac{8}{1}\times\frac{4}{1}=\frac{32}{1}=32$ $\displaystyle \frac{8}{1}\times\frac{4}{1}=\frac{32}{1}=32$

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Example Question #1261 : Ssat Middle Level Quantitative (Math)

Sarah has $\displaystyle 7$ gallons of milk. Each glass holds $\frac{1}{4}$ $\displaystyle \frac{1}{4}$ of a gallon. How many glasses can she fill?

Possible Answers:

$\displaystyle 32$

$\displaystyle 28$

$\displaystyle 30$

$\displaystyle 16$

$\displaystyle 24$

Correct answer:

$\displaystyle 28$

Explanation:

Think: How many $\frac{1}{4}$ $\displaystyle \frac{1}{4}$s are in $\displaystyle 7$ wholes?

To solve $7\div\frac{1}{4}$ $\displaystyle 7\div\frac{1}{4}$ we multiply by the reciprocal

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

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Example Question #2 : Interpret Division Of A Whole Number By A Unit Fraction: Ccss.Math.Content.5.Nf.B.7b

Kaitlyn has $\displaystyle 6$ gallons of milk. Each glass holds $\frac{1}{4}$ $\displaystyle \frac{1}{4}$ of a gallon. How many glasses can she fill?

Possible Answers:

$\displaystyle 24$

$\displaystyle 20$

$\displaystyle 16$

$\displaystyle 8$

$\displaystyle 4$

Correct answer:

$\displaystyle 24$

Explanation:

Think: How many $\frac{1}{4}$ $\displaystyle \frac{1}{4}$s are in $\displaystyle 6$ wholes?

To solve $6\div\frac{1}{4}$ $\displaystyle 6\div\frac{1}{4}$ we multiply by the reciprocal

$\frac{6}{1}\times\frac{4}{1}=\frac{24}{1}=24$ $\displaystyle \frac{6}{1}\times\frac{4}{1}=\frac{24}{1}=24$

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Example Question #601 : Numbers And Operations

Sarah has $\displaystyle 2$ gallons of milk. Each glass holds $\frac{1}{4}$ $\displaystyle \frac{1}{4}$ of a gallon. How many glasses can she fill?

Possible Answers:

$\displaystyle 16$

$\displaystyle 12$

$\displaystyle 20$

$\displaystyle 8$

$\displaystyle 24$

Correct answer:

$\displaystyle 8$

Explanation:

Think: How many $\frac{1}{4}$ $\displaystyle \frac{1}{4}$s are in $\displaystyle 2$ wholes?

To solve $2\div\frac{1}{4}$ $\displaystyle 2\div\frac{1}{4}$ we multiply by the reciprocal

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

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Example Question #121 : Fractions

Christa has $\displaystyle 5$ gallons of milk. Each glass holds $\frac{1}{4}$ $\displaystyle \frac{1}{4}$ of a gallon. How many glasses can she fill?

Possible Answers:

$\displaystyle 5$

$\displaystyle 25$

$\displaystyle 10$

$\displaystyle 20$

$\displaystyle 15$

Correct answer:

$\displaystyle 20$

Explanation:

Think: How many $\frac{1}{4}$ $\displaystyle \frac{1}{4}$s are in $\displaystyle 5$ wholes?

To solve $5\div\frac{1}{4}$ $\displaystyle 5\div\frac{1}{4}$ we multiply by the reciprocal

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

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Example Question #601 : Numbers And Operations

Julie has $\displaystyle 4$ gallons of milk. Each glass holds $\frac{1}{4}$ $\displaystyle \frac{1}{4}$ of a gallon. How many glasses can she fill?

Possible Answers:

$\displaystyle 16$

$\displaystyle 32$

$\displaystyle 24$

$\displaystyle 20$

$\displaystyle 28$

Correct answer:

$\displaystyle 16$

Explanation:

Think: How many $\frac{1}{4}$ $\displaystyle \frac{1}{4}$s are in $\displaystyle 4$ wholes?

To solve $4\div\frac{1}{4}$ $\displaystyle 4\div\frac{1}{4}$ we multiply by the reciprocal

$\frac{4}{1}\times\frac{4}{1}=\frac{16}{1}=16$ $\displaystyle \frac{4}{1}\times\frac{4}{1}=\frac{16}{1}=16$

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Example Question #602 : Numbers And Operations

Sarah has $\displaystyle 3$ gallons of milk. Each glass holds $\frac{1}{4}$ $\displaystyle \frac{1}{4}$ of a gallon. How many glasses can she fill?

Possible Answers:

$\displaystyle 8$

$\displaystyle 7$

$\displaystyle 9$

$\displaystyle 12$

$\displaystyle 6$

Correct answer:

$\displaystyle 12$

Explanation:

Think: How many $\frac{1}{4}$ $\displaystyle \frac{1}{4}$s are in $\displaystyle 3$ wholes?

To solve $3\div\frac{1}{4}$ $\displaystyle 3\div\frac{1}{4}$ we multiply by the reciprocal

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

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Example Question #603 : Numbers And Operations

Aubtin has $\displaystyle 3$ gallons of soda. Each glass holds $\frac{1}{3}$ $\displaystyle \frac{1}{3}$ of a gallon. How many glasses can he fill?

Possible Answers:

$\displaystyle 12$

$\displaystyle 21$

$\displaystyle 18$

$\displaystyle 15$

$\displaystyle 9$

Correct answer:

$\displaystyle 9$

Explanation:

Think: How many $\frac{1}{3}$ $\displaystyle \frac{1}{3}$s are in $\displaystyle 3$ wholes?

To solve $3\div\frac{1}{3}$ $\displaystyle 3\div\frac{1}{3}$ we multiply by the reciprocal

$\frac{3}{1}\times\frac{3}{1}=\frac{9}{1}=9$ $\displaystyle \frac{3}{1}\times\frac{3}{1}=\frac{9}{1}=9$

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Example Question #587 : Number & Operations With Fractions

Aubtin has $\displaystyle 2$ gallons of soda. Each glass holds $\frac{1}{3}$ $\displaystyle \frac{1}{3}$ of a gallon. How many glasses can he fill?

Possible Answers:

$\displaystyle 6$

$\displaystyle 12$

$\displaystyle 18$

$\displaystyle 21$

$\displaystyle 9$

Correct answer:

$\displaystyle 6$

Explanation:

Think: How many $\frac{1}{3}$ $\displaystyle \frac{1}{3}$s are in $\displaystyle 2$ wholes?

To solve $2\div\frac{1}{3}$ $\displaystyle 2\div\frac{1}{3}$ we multiply by the reciprocal

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

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Example Question #122 : Fractions

Armen has $\displaystyle 4$ gallons of soda. Each glass holds $\frac{1}{3}$ $\displaystyle \frac{1}{3}$ of a gallon. How many glasses can he fill?

Possible Answers:

$\displaystyle 9$

$\displaystyle 6$

$\displaystyle 12$

$\displaystyle 21$

$\displaystyle 18$

Correct answer:

$\displaystyle 12$

Explanation:

Think: How many $\frac{1}{3}$ $\displaystyle \frac{1}{3}$s are in $\displaystyle 4$ wholes?

To solve $4\div\frac{1}{3}$ $\displaystyle 4\div\frac{1}{3}$ we multiply by the reciprocal

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

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Common Core: 5th Grade Math : Number & Operations with Fractions

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

All Common Core: 5th Grade Math Resources

Example Questions

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

Example Question #1261 : Ssat Middle Level Quantitative (Math)

Example Question #2 : Interpret Division Of A Whole Number By A Unit Fraction: Ccss.Math.Content.5.Nf.B.7b

Example Question #601 : Numbers And Operations

Example Question #121 : Fractions

Example Question #601 : Numbers And Operations

Example Question #602 : Numbers And Operations

Example Question #603 : Numbers And Operations

Example Question #587 : Number & Operations With Fractions

Example Question #122 : Fractions

All Common Core: 5th Grade Math Resources

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