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

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

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Example Questions

Example Question #1432 : Common Core Math: Grade 5

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

 

Possible Answers:

\(\displaystyle 36\)

\(\displaystyle 32\)

\(\displaystyle 28\)

\(\displaystyle 24\)

\(\displaystyle 20\)

Correct answer:

\(\displaystyle 32\)

Explanation:

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

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

\(\displaystyle \frac{8}{1}\times\frac{4}{1}=\frac{32}{1}=32\)

32

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

Sarah has \(\displaystyle 7\) gallons of milk. Each glass holds \(\displaystyle \frac{1}{4}\) 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 \(\displaystyle \frac{1}{4}\)s are in \(\displaystyle 7\) wholes? 

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

\(\displaystyle \frac{7}{1}\times\frac{4}{1}=\frac{28}{1}=28\)

28

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 \(\displaystyle \frac{1}{4}\) 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 \(\displaystyle \frac{1}{4}\)s are in \(\displaystyle 6\) wholes? 

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

\(\displaystyle \frac{6}{1}\times\frac{4}{1}=\frac{24}{1}=24\)

24

Example Question #601 : Numbers And Operations

Sarah has \(\displaystyle 2\) gallons of milk. Each glass holds \(\displaystyle \frac{1}{4}\) 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 \(\displaystyle \frac{1}{4}\)s are in \(\displaystyle 2\) wholes? 

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

\(\displaystyle \frac{2}{1}\times\frac{4}{1}=\frac{8}{1}=8\)

8

Example Question #121 : Fractions

Christa has \(\displaystyle 5\) gallons of milk. Each glass holds \(\displaystyle \frac{1}{4}\) 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 \(\displaystyle \frac{1}{4}\)s are in \(\displaystyle 5\) wholes? 

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

\(\displaystyle \frac{5}{1}\times\frac{4}{1}=\frac{20}{1}=20\)

20

Example Question #121 : Fractions

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

 

Possible Answers:

\(\displaystyle 24\)

\(\displaystyle 28\)

\(\displaystyle 16\)

\(\displaystyle 20\)

\(\displaystyle 32\)

Correct answer:

\(\displaystyle 16\)

Explanation:

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

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

\(\displaystyle \frac{4}{1}\times\frac{4}{1}=\frac{16}{1}=16\)

16

Example Question #11 : Interpret Division Of A Whole Number By A Unit Fraction: Ccss.Math.Content.5.Nf.B.7b

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

 

Possible Answers:

\(\displaystyle 6\)

\(\displaystyle 12\)

\(\displaystyle 7\)

\(\displaystyle 8\)

\(\displaystyle 9\)

Correct answer:

\(\displaystyle 12\)

Explanation:

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

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

\(\displaystyle \frac{3}{1}\times\frac{4}{1}=\frac{12}{1}=12\)

 12

Example Question #1431 : Common Core Math: Grade 5

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

 

Possible Answers:

\(\displaystyle 21\)

\(\displaystyle 12\)

\(\displaystyle 9\)

\(\displaystyle 18\)

\(\displaystyle 15\)

Correct answer:

\(\displaystyle 9\)

Explanation:

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

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

\(\displaystyle \frac{3}{1}\times\frac{3}{1}=\frac{9}{1}=9\)

9

Example Question #587 : Number & Operations With Fractions

Aubtin has \(\displaystyle 2\) gallons of soda. Each glass holds \(\displaystyle \frac{1}{3}\) 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 \(\displaystyle \frac{1}{3}\)s are in \(\displaystyle 2\) wholes? 

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

\(\displaystyle \frac{2}{1}\times\frac{3}{1}=\frac{6}{1}=6\)

6

Example Question #122 : Fractions

Armen has \(\displaystyle 4\) gallons of soda. Each glass holds \(\displaystyle \frac{1}{3}\) 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 \(\displaystyle \frac{1}{3}\)s are in \(\displaystyle 4\) wholes? 

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

\(\displaystyle \frac{4}{1}\times\frac{3}{1}=\frac{12}{1}=12\)

12

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