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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 #821 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Zach cleaned $\frac{1}{8}$ $\displaystyle \frac{1}{8}$ of the house and Alex cleaned $\frac{1}{3}$ $\displaystyle \frac{1}{3}$ of the house. How much more of the house did Alex clean?

Possible Answers:

$\frac{5}{24}$ $\displaystyle \frac{5}{24}$

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

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

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

$\frac{7}{24}$ $\displaystyle \frac{7}{24}$

Correct answer:

$\frac{5}{24}$ $\displaystyle \frac{5}{24}$

Explanation:

$\frac{1}{3}-\frac{1}{8}$ $\displaystyle \frac{1}{3}-\frac{1}{8}$

In order to solve this problem, we first need to make common denominators.

$\frac{1}{8}\times\frac{3}{3}=\frac{3}{24}$ $\displaystyle \frac{1}{8}\times\frac{3}{3}=\frac{3}{24}$

$\frac{1}{3}\times\frac{8}{8}=\frac{8}{24}$ $\displaystyle \frac{1}{3}\times\frac{8}{8}=\frac{8}{24}$ $\frac{1}{3}\times\frac{8}{8}=\frac{8}{24}$ $\displaystyle \frac{1}{3}\times\frac{8}{8}=\frac{8}{24}$ $\frac{1}{3}\times\frac{8}{8}=\frac{8}{24}$ $\displaystyle \frac{1}{3}\times\frac{8}{8}=\frac{8}{24}$ $\frac{1}{3}\times\frac{8}{8}=\frac{8}{24}$ $\displaystyle \frac{1}{3}\times\frac{8}{8}=\frac{8}{24}$

Now that we have common denominators, we can subtract the fractions. Remember, when we subtract fractions, the denominator stays the same, we only subtract the numerator.

$\frac{8}{24}-\frac{3}{24}=\frac{5}{24}$ $\displaystyle \frac{8}{24}-\frac{3}{24}=\frac{5}{24}$

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Example Question #31 : How To Subtract Fractions

Lily pulled $\frac{1}{9}$ $\displaystyle \frac{1}{9}$ of the weeds and Rose pulled $\frac{1}{3}$ $\displaystyle \frac{1}{3}$. How much more of the weeds did Rose pull?

Possible Answers:

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

$\frac{3}{5}$ $\displaystyle \frac{3}{5}$

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

$\frac{2}9{}$ $\displaystyle \frac{2}9{}$

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

Correct answer:

$\frac{2}9{}$ $\displaystyle \frac{2}9{}$

Explanation:

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

In order to solve this problem, we first need to make common denominators.

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

Now that we have common denominators, we can subtract the fractions. Remember, when we subtract fractions, the denominator stays the same, we only subtract the numerator.

$\frac{3}{9}-\frac{1}{9}=\frac{2}{9}$ $\displaystyle \frac{3}{9}-\frac{1}{9}=\frac{2}{9}$

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Example Question #823 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Sally drank $\frac{1}{12}$ $\displaystyle \frac{1}{12}$ of the milk and Sam drank $\frac{2}{3}$ $\displaystyle \frac{2}{3}$. How much more of the milk did Sam drink?

Possible Answers:

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

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

$\frac{7}{12}$ $\displaystyle \frac{7}{12}$

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

$\frac{5}{12}$ $\displaystyle \frac{5}{12}$

Correct answer:

$\frac{7}{12}$ $\displaystyle \frac{7}{12}$

Explanation:

$\frac{2}{3}-\frac{1}{12}$ $\displaystyle \frac{2}{3}-\frac{1}{12}$

In order to solve this problem, we first need to make common denominators.

$\frac{2}{3}\times\frac{4}{4}=\frac{8}{12}$ $\displaystyle \frac{2}{3}\times\frac{4}{4}=\frac{8}{12}$

Now that we have common denominators, we can subtract the fractions. Remember, when we subtract fractions, the denominator stays the same, we only subtract the numerator.

$\frac{8}{12}-\frac{1}{12}=\frac{7}{12}$ $\displaystyle \frac{8}{12}-\frac{1}{12}=\frac{7}{12}$

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Example Question #824 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Jake ate $\frac{1}{7}$ $\displaystyle \frac{1}{7}$ of the popcorn and Dave ate $\small \frac{4}{14}$ $\displaystyle \small \frac{4}{14}$ of the popcorn. How much more of the popcorn did Dave eat?

Possible Answers:

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

$\frac{9}{11}$ $\displaystyle \frac{9}{11}$

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

$\frac{5}6{}$ $\displaystyle \frac{5}6{}$

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

Correct answer:

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

Explanation:

$\frac{4}{14}-\frac{1}{7}$ $\displaystyle \frac{4}{14}-\frac{1}{7}$

In order to solve this problem, we first need to make common denominators.

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

Now that we have common denominators, we can add the fractions. Remember, when we add fractions, the denominator stays the same, we only add the numerator.

$\frac{4}{14}-\frac{2}{14}=\frac{2}{14}$ $\displaystyle \frac{4}{14}-\frac{2}{14}=\frac{2}{14}$

$\small \frac{2}{14}$ $\displaystyle \small \frac{2}{14}$ can be reduced by dividing $\small 2$ $\displaystyle \small 2$ by both sides.

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

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Example Question #21 : Number & Operations With Fractions

Sally drank $\frac{1}{12}$ $\displaystyle \frac{1}{12}$ of the milk and Sam drank $\frac{2}{3}$ $\displaystyle \frac{2}{3}$. What fraction of the milk did they drink?

Possible Answers:

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

$\frac{11}{15}$ $\displaystyle \frac{11}{15}$

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

$\frac{3}{15}$ $\displaystyle \frac{3}{15}$

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

Correct answer:

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

Explanation:

$\frac{1}{12}+\frac{2}{3}$ $\displaystyle \frac{1}{12}+\frac{2}{3}$

In order to solve this problem, we first need to make common denominators.

$\frac{2}{3}\times\frac{4}{4}=\frac{8}{12}$ $\displaystyle \frac{2}{3}\times\frac{4}{4}=\frac{8}{12}$

Now that we have common denominators, we can add the fractions. Remember, when we add fractions, the denominator stays the same, we only add the numerator.

$\frac{1}{12}+\frac{8}{12}=\frac{9}{12}$ $\displaystyle \frac{1}{12}+\frac{8}{12}=\frac{9}{12}$

$\frac{9}{12}$ $\displaystyle \frac{9}{12}$ can be reduced by dividing $\displaystyle 3$ by both sides.

$\frac{9}{12}\div \frac{3}{3}=\frac{3}{4}$ $\displaystyle \frac{9}{12}\div \frac{3}{3}=\frac{3}{4}$

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Example Question #287 : Fractions

Lily pulled $\frac{1}{9}$ $\displaystyle \frac{1}{9}$ of the weeds and Rose pulled $\frac{1}{3}$ $\displaystyle \frac{1}{3}$. What fraction of the weeds have they pulled?

Possible Answers:

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

$\frac{4}{9}$ $\displaystyle \frac{4}{9}$

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

$\frac{8}{15}$ $\displaystyle \frac{8}{15}$

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

Correct answer:

$\frac{4}{9}$ $\displaystyle \frac{4}{9}$

Explanation:

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

In order to solve this problem, we first need to make common denominators.

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

Now that we have common denominators, we can add the fractions. Remember, when we add fractions, the denominator stays the same, we only add the numerator.

$\frac{1}{9}+\frac{3}{9}=\frac{4}{9}$ $\displaystyle \frac{1}{9}+\frac{3}{9}=\frac{4}{9}$

Report an Error

Example Question #1 : Solve Word Problems Involving Division Of Whole Numbers Leading To Answers In The Form Of Fractions Or Mixed Numbers: Ccss.Math.Content.5.Nf.B.3

If you bake 374 cookies for your class of 50 people, how many cookies does each student get?

Possible Answers:

Between 6 and 7 cookies

Between 9 and 10 cookies

Between 7 and 8 cookies

Between 10 and 11 cookies

Between 8 and 9 cookies

Correct answer:

Between 7 and 8 cookies

Explanation:

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Example Question #2 : Solve Word Problems Involving Division Of Whole Numbers Leading To Answers In The Form Of Fractions Or Mixed Numbers: Ccss.Math.Content.5.Nf.B.3

$\small 4$ $\displaystyle \small 4$ people are sharing a $\small 23$ $\displaystyle \small 23$ pound bag of peanuts. How much will each person get? Select the answer with the pair of numbers that the answer will be between.

Possible Answers:

$\displaystyle 5$ and $\small 6$ $\displaystyle \small 6$

$\small 3$ $\displaystyle \small 3$ and $\small 4$ $\displaystyle \small 4$

$\small 6$ $\displaystyle \small 6$ and $\small 7$ $\displaystyle \small 7$

$\small 2$ $\displaystyle \small 2$ and $\small 3$ $\displaystyle \small 3$

$\small 4$ $\displaystyle \small 4$ and $\small 5$ $\displaystyle \small 5$

Correct answer:

$\displaystyle 5$ and $\small 6$ $\displaystyle \small 6$

Explanation:

We can think of this problem as an improper fraction and solve for the mixed number.

$\small \frac{23}{4}=5\frac{3}4{}$ $\displaystyle \small \frac{23}{4}=5\frac{3}4{}$

$\small 4$ $\displaystyle \small 4$ can go into $\small 23$ $\displaystyle \small 23$ only $\small 5$ $\displaystyle \small 5$ times with $\small \frac{3}{4}$ $\displaystyle \small \frac{3}{4}$ left over.

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Example Question #22 : Number & Operations With Fractions

$\small 6$ $\displaystyle \small 6$ people are sharing a $\small \small 37$ $\displaystyle \small \small 37$ pound bag of peanuts. How much will each person get? Select the answer with the pair of numbers that the answer will be between.

Possible Answers:

$\small 7$ $\displaystyle \small 7$ and $\small 8$ $\displaystyle \small 8$

$\small 8$ $\displaystyle \small 8$ and $\small 9$ $\displaystyle \small 9$

$\small 5$ $\displaystyle \small 5$ and $\small 6$ $\displaystyle \small 6$

$\small 4$ $\displaystyle \small 4$ and $\small 5$ $\displaystyle \small 5$

$\small 6$ $\displaystyle \small 6$ and $\small 7$ $\displaystyle \small 7$

Correct answer:

$\small 6$ $\displaystyle \small 6$ and $\small 7$ $\displaystyle \small 7$

Explanation:

We can think of this problem as an improper fraction and solve for the mixed number.

$\small \frac{37}{6}=6\frac{1}{6}$ $\displaystyle \small \frac{37}{6}=6\frac{1}{6}$

$\small 6$ $\displaystyle \small 6$ can go into $\small 37$ $\displaystyle \small 37$ only $\small 6$ $\displaystyle \small 6$ times with $\small \frac{1}{6}$ $\displaystyle \small \frac{1}{6}$ left over.

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Example Question #23 : Number & Operations With Fractions

$\small 5$ $\displaystyle \small 5$ people are sharing a $\small 43$ $\displaystyle \small 43$ pound bag of peanuts. How much will each person get? Select the answer with the pair of numbers that the answer will be between.

Possible Answers:

$\small 10$ $\displaystyle \small 10$ and $\small 11$ $\displaystyle \small 11$

$\small 12$ $\displaystyle \small 12$ and $\small 13$ $\displaystyle \small 13$

$\small 11$ $\displaystyle \small 11$ and $\small 12$ $\displaystyle \small 12$

$\small 8$ $\displaystyle \small 8$ and $\small 9$ $\displaystyle \small 9$

$\small 9$ $\displaystyle \small 9$ and $\displaystyle 10$

Correct answer:

$\small 8$ $\displaystyle \small 8$ and $\small 9$ $\displaystyle \small 9$

Explanation:

We can think of this problem as an improper fraction and solve for the mixed number.

$\small \frac{43}{5}=8\frac{3}{5}$ $\displaystyle \small \frac{43}{5}=8\frac{3}{5}$

$\small 5$ $\displaystyle \small 5$ can go into $\small 43$ $\displaystyle \small 43$ only $\small 8$ $\displaystyle \small 8$ times with $\small \frac{3}{5}$ $\displaystyle \small \frac{3}{5}$ left over.

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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 #821 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Example Question #31 : How To Subtract Fractions

Example Question #823 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Example Question #824 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Example Question #21 : Number & Operations With Fractions

Example Question #287 : Fractions

Example Question #1 : Solve Word Problems Involving Division Of Whole Numbers Leading To Answers In The Form Of Fractions Or Mixed Numbers: Ccss.Math.Content.5.Nf.B.3

Example Question #2 : Solve Word Problems Involving Division Of Whole Numbers Leading To Answers In The Form Of Fractions Or Mixed Numbers: Ccss.Math.Content.5.Nf.B.3

Example Question #22 : Number & Operations With Fractions

Example Question #23 : Number & Operations With Fractions

All Common Core: 5th Grade Math Resources

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