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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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Example Questions

Example Question #1 : Number & Operations With Fractions

$\frac{1}{7}+\frac{3}{14}=$ $\displaystyle \frac{1}{7}+\frac{3}{14}=$

Possible Answers:

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

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

$\frac{4}{14}$ $\displaystyle \frac{4}{14}$

$\frac{5}{14}$ $\displaystyle \frac{5}{14}$

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

Correct answer:

$\frac{5}{14}$ $\displaystyle \frac{5}{14}$

Explanation:

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Example Question #1 : Number & Operations With Fractions

Mary has a bag of marbles. She gives half of the marbles to her brother and a third of the marbles to her sister. What fraction of the original marbles does Mary have left?

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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Example Question #2 : Number & Operations With Fractions

Joe paited $\frac{3}{10}$ $\displaystyle \frac{3}{10}$ of the fence an Sara painted $\frac{1}{2}$ $\displaystyle \frac{1}{2}$. How much of the fence is painted?

Possible Answers:

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

$\frac{4}{5}$ $\displaystyle \frac{4}{5}$

$\frac{4}{12}$ $\displaystyle \frac{4}{12}$

$\frac{9}{10}$ $\displaystyle \frac{9}{10}$

$\frac{7}{10}$ $\displaystyle \frac{7}{10}$

Correct answer:

$\frac{4}{5}$ $\displaystyle \frac{4}{5}$

Explanation:

$\frac{3}{10}+\frac{1}{2}$ $\displaystyle \frac{3}{10}+\frac{1}{2}$

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

$\frac{1}{2}\times\frac{5}{5}=\frac{5}{10}$ $\displaystyle \frac{1}{2}\times\frac{5}{5}=\frac{5}{10}$

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.

$\frac{3}{10 }+\frac{5}{10}=\frac{8}{10}$ $\displaystyle \frac{3}{10 }+\frac{5}{10}=\frac{8}{10}$

$\frac{8}{10}$ $\displaystyle \frac{8}{10}$ can be reduced be dividing both sides by $\displaystyle 2$.

$\frac{8}{10} \div\frac{2}{2}=\frac{4}{5}$ $\displaystyle \frac{8}{10} \div\frac{2}{2}=\frac{4}{5}$

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Example Question #3 : Number & Operations With Fractions

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 of the house did they clean?

Possible Answers:

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

$\frac{12}{21}$ $\displaystyle \frac{12}{21}$

$\frac{11}{24}$ $\displaystyle \frac{11}{24}$

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

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

Correct answer:

$\frac{11}{24}$ $\displaystyle \frac{11}{24}$

Explanation:

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

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

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

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

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.

$\frac{3}{24}+\frac{8}{24}=\frac{11}{24}$ $\displaystyle \frac{3}{24}+\frac{8}{24}=\frac{11}{24}$

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Example Question #4 : Number & Operations With Fractions

Ben washed $\frac{3}{8}$ $\displaystyle \frac{3}{8}$ of the windows and Jen washed $\frac{1}{4}$ $\displaystyle \frac{1}{4}$. How much of the windows have they washed?

Possible Answers:

$\frac{5}{8}$ $\displaystyle \frac{5}{8}$

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

$\frac{4}{12}$ $\displaystyle \frac{4}{12}$

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

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

Correct answer:

$\frac{5}{8}$ $\displaystyle \frac{5}{8}$

Explanation:

$\frac{3}{8}+\frac{1}{4}$ $\displaystyle \frac{3}{8}+\frac{1}{4}$

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

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

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.

$\frac{3}{8}+\frac{2}8{=\frac{5}{8}}$ $\displaystyle \frac{3}{8}+\frac{2}8{=\frac{5}{8}}$

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Example Question #5 : Number & Operations With Fractions

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 of the popcorn have they eaten?

Possible Answers:

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

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

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

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

$\small \frac{13}{21}$ $\displaystyle \small \frac{13}{21}$

Correct answer:

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

Explanation:

$\small \frac{1}{7}+\frac{4}{14}$ $\displaystyle \small \frac{1}{7}+\frac{4}{14}$

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.

$\small \frac{2}{14}+\frac{4}{14}=\frac{6}{14}$ $\displaystyle \small \frac{2}{14}+\frac{4}{14}=\frac{6}{14}$

$\small \frac{6}{14}$ $\displaystyle \small \frac{6}{14}$ can be reduced by dividing $\small 2$ $\displaystyle \small 2$ by both sides.

$\small \frac{6}{14}\div\frac{2}{2}=\frac{3}{7}$ $\displaystyle \small \frac{6}{14}\div\frac{2}{2}=\frac{3}{7}$

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Example Question #6 : Number & Operations With Fractions

Jessica ate $\frac{1}{3}$ $\displaystyle \frac{1}{3}$ of the cake and Megan ate $\frac{1}{2}$ $\displaystyle \frac{1}{2}$. How much of the cake have they eaten?

Possible Answers:

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

$\frac{5}{8}$ $\displaystyle \frac{5}{8}$

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

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$

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

Correct answer:

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

Explanation:

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

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

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

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

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.

$\frac{2}{6}+\frac{3}{6}=\frac{5}{6}$ $\displaystyle \frac{2}{6}+\frac{3}{6}=\frac{5}{6}$

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Example Question #7 : Number & Operations With Fractions

Tim mowed $\frac{1}{7}$ $\displaystyle \frac{1}{7}$ of the yard and Tom mowed $\frac{1}{3}$ $\displaystyle \frac{1}{3}$. How much of the yard have they mowed?

Possible Answers:

$\frac{10}{21}$ $\displaystyle \frac{10}{21}$

$\frac{9}{21}$ $\displaystyle \frac{9}{21}$

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

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

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

Correct answer:

$\frac{10}{21}$ $\displaystyle \frac{10}{21}$

Explanation:

$\frac{1}{7}+\frac{1}{3}$ $\displaystyle \frac{1}{7}+\frac{1}{3}$

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

$\frac{1}{7}\times\frac{3}{3}=\frac{3}{21}$ $\displaystyle \frac{1}{7}\times\frac{3}{3}=\frac{3}{21}$

$\frac{1}{3}\times \frac{7}{7}=\frac{7}{21}$ $\displaystyle \frac{1}{3}\times \frac{7}{7}=\frac{7}{21}$

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.

$\frac{3}{21}+\frac{7}{21}=\frac{10}{21}$ $\displaystyle \frac{3}{21}+\frac{7}{21}=\frac{10}{21}$

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Example Question #1 : Number & Operations With Fractions

Shannon has painted $\frac{5}{8}$ $\displaystyle \frac{5}{8}$ of the house and Dan has paided $\frac{1}4{}$ $\displaystyle \frac{1}4{}$ of the house. How much of the house is painted?

Possible Answers:

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

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

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

$\frac{6}{12}$ $\displaystyle \frac{6}{12}$

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

Correct answer:

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

Explanation:

$\frac{5}{8}+\frac{1}{4}$ $\displaystyle \frac{5}{8}+\frac{1}{4}$

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

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

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.

$\frac{5}{8}+\frac{2}{8}=\frac{7}{8}$ $\displaystyle \frac{5}{8}+\frac{2}{8}=\frac{7}{8}$

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Example Question #4 : Number & Operations With Fractions

David ate $\frac{3}{12}$ $\displaystyle \frac{3}{12}$ of the pizza and Alison ate $\frac{1}{3}$ $\displaystyle \frac{1}{3}$ of the pizza. How much of the pizza did they eat?

Possible Answers:

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

$\frac{6}{12}$ $\displaystyle \frac{6}{12}$

$\frac{4}{15}$ $\displaystyle \frac{4}{15}$

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

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

Correct answer:

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

Explanation:

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

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

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

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.

$\frac{3}{12}+\frac{4}{12}=\frac{7}{12}$ $\displaystyle \frac{3}{12}+\frac{4}{12}=\frac{7}{12}$

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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 : Number & Operations With Fractions

Example Question #1 : Number & Operations With Fractions

Example Question #2 : Number & Operations With Fractions

Example Question #3 : Number & Operations With Fractions

Example Question #4 : Number & Operations With Fractions

Example Question #5 : Number & Operations With Fractions

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All Common Core: 5th Grade Math Resources

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