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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 #1964 : Numbers And Operations

Olivia lives $\frac{6}{9}$ of a mile away from her friend's house. She walked $\frac{1}{3}$ of the way there and then stopped to get ice cream from an ice cream truck driving by. How far did she travel before she stopped to get ice cream?

Possible Answers:

$\frac{6}{27}\text{ of a mile}$

$\frac{7}{27}\text{ of a mile}$

$\frac{6}{26}\text{ of a mile}$

$\frac{7}{26}\text{ of a mile}$

$\frac{5}{26}\text{ of a mile}$

Correct answer:

$\frac{6}{27}\text{ of a mile}$

Explanation:

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of". $\frac{1}{3}$ of the way to her friends house she stopped.

We know that her friend lives $\frac{6}{9}$ of a mile away from her so we can set up our multiplication problem.

$\frac{1}{3}\times\frac{6}{9}$

We can set up a tiled area model to help us solve the problem.

We use the denominators for the dimensions of our area model, and we use the numerators to fill parts of the area model.

6 27

We make the area model by because those are the denominators of our fractions. We shade up and over , because those are the numerators of our fractions. Our answer is a fraction made up of the boxes that are shaded (the numerator) and the total tiles in the area model (the denominator).

$\frac{1}{3}\times\frac{6}{9}=\frac{6}{27}$

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Example Question #331 : Number & Operations With Fractions

Holly lives $\frac{6}{9}$ of a mile away from her friend's house. She walked $\frac{2}{3}$ of the way there and then stopped to get ice cream from an ice cream truck driving by. How far did she travel before she stopped to get ice cream?

Possible Answers:

$\frac{12}{27}\text{ of a mile}$

$\frac{8}{27}\text{ of a mile}$

$\frac{12}{26}\text{ of a mile}$

$\frac{4}{26}\text{ of a mile}$

$\frac{4}{27}\text{ of a mile}$

Correct answer:

$\frac{12}{27}\text{ of a mile}$

Explanation:

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of". $\frac{2}{3}$ of the way to her friends house she stopped.

We know that her friend lives $\frac{6}{9}$ of a mile away from her so we can set up our multiplication problem.

$\frac{2}{3}\times\frac{6}{9}$

We can set up a tiled area model to help us solve the problem.

We use the denominators for the dimensions of our area model, and we use the numerators to fill parts of the area model.

12 27

$\frac{2}{3}\times\frac{6}{9}=\frac{12}{27}$

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Example Question #1966 : Numbers And Operations

Virginia lives $\frac{5}{9}$ of a mile away from her friend's house. She walked $\frac{2}{3}$ of the way there and then stopped to get ice cream from an ice cream truck driving by. How far did she travel before she stopped to get ice cream?

Possible Answers:

$\frac{10}{27}\text{ of a mile}$

$\frac{7}{27}\text{ of a mile}$

$\frac{3}{26}\text{ of a mile}$

$\frac{7}{26}\text{ of a mile}$

$\frac{3}{27}\text{ of a mile}$

Correct answer:

$\frac{10}{27}\text{ of a mile}$

Explanation:

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of". $\frac{2}{3}$ of the way to her friends house she stopped.

We know that her friend lives $\frac{5}{9}$ of a mile away from her so we can set up our multiplication problem.

$\frac{2}{3}\times\frac{5}{9}$

We can set up a tiled area model to help us solve the problem.

We use the denominators for the dimensions of our area model, and we use the numerators to fill parts of the area model.

10 27

$\frac{2}{3}\times\frac{5}{9}=\frac{10}{27}$

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Example Question #1967 : Numbers And Operations

Kenzie lives $\frac{5}{9}$ of a mile away from her friend's house. She walked $\frac{1}{3}$ of the way there and then stopped to get ice cream from an ice cream truck driving by. How far did she travel before she stopped to get ice cream?

Possible Answers:

$\frac{7}{26}\text{ of a mile}$

$\frac{6}{27}\text{ of a mile}$

$\frac{6}{26}\text{ of a mile}$

$\frac{5}{27}\text{ of a mile}$

$\frac{4}{26}\text{ of a mile}$

Correct answer:

$\frac{5}{27}\text{ of a mile}$

Explanation:

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of". $\frac{1}{3}$ of the way to her friends house she stopped.

We know that her friend lives $\frac{5}{9}$ of a mile away from her so we can set up our multiplication problem.

$\frac{1}{3}\times\frac{5}{9}$

We can set up a tiled area model to help us solve the problem.

We use the denominators for the dimensions of our area model, and we use the numerators to fill parts of the area model.

5 27

$\frac{1}{3}\times\frac{5}{9}=\frac{5}{27}$

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Example Question #1968 : Numbers And Operations

Elsie lives $\frac{4}{9}$ of a mile away from her friend's house. She walked $\frac{1}{3}$ of the way there and then stopped to get ice cream from an ice cream truck driving by. How far did she travel before she stopped to get ice cream?

Possible Answers:

$\frac{3}{27}\text{ of a mile}$

$\frac{4}{28}\text{ of a mile}$

$\frac{5}{27}\text{ of a mile}$

$\frac{4}{27}\text{ of a mile}$

$\frac{3}{26}\text{ of a mile}$

Correct answer:

$\frac{4}{27}\text{ of a mile}$

Explanation:

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of". $\frac{1}{3}$ of the way to her friends house she stopped.

We know that her friend lives $\frac{4}{9}$ of a mile away from her so we can set up our multiplication problem.

$\frac{1}{3}\times\frac{4}{9}$

We can set up a tiled area model to help us solve the problem.

We use the denominators for the dimensions of our area model, and we use the numerators to fill parts of the area model.

4 27

$\frac{1}{3}\times\frac{4}{9}=\frac{4}{27}$

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Example Question #1961 : Numbers And Operations

Nina lives $\frac{4}{9}$ of a mile away from her friend's house. She walked $\frac{2}{3}$ of the way there and then stopped to get ice cream from an ice cream truck driving by. How far did she travel before she stopped to get ice cream?

Possible Answers:

$\frac{6}{27}\text{ of a mile}$

$\frac{8}{27}\text{ of a mile}$

$\frac{9}{27}\text{ of a mile}$

$\frac{9}{26}\text{ of a mile}$

$\frac{8}{25}\text{ of a mile}$

Correct answer:

$\frac{8}{27}\text{ of a mile}$

Explanation:

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of". $\frac{2}{3}$ of the way to her friends house she stopped.

We know that her friend lives $\frac{4}{9}$ of a mile away from her so we can set up our multiplication problem.

$\frac{2}{3}\times\frac{4}{9}$

We can set up a tiled area model to help us solve the problem.

We use the denominators for the dimensions of our area model, and we use the numerators to fill parts of the area model.

8 27

$\frac{2}{3}\times\frac{4}{9}=\frac{8}{27}$

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Example Question #331 : Number & Operations With Fractions

Sandra lives $\frac{3}{9}$ of a mile away from her friend's house. She walked $\frac{2}{3}$ of the way there and then stopped to get ice cream from an ice cream truck driving by. How far did she travel before she stopped to get ice cream?

Possible Answers:

$\frac{6}{27}\textup{ of a mile}$

$\frac{6}{26}\textup{ of a mile}$

$\frac{1}{27}\textup{ of a mile}$

$\frac{5}{26}\textup{ of a mile}$

$\frac{5}{27}\textup{ of a mile}$

Correct answer:

$\frac{6}{27}\textup{ of a mile}$

Explanation:

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of". $\frac{2}{3}$ of the way to her friends house she stopped.

We know that her friend lives $\frac{3}{9}$ of a mile away from her so we can set up our multiplication problem.

$\frac{2}{3}\times\frac{3}{9}$

We can set up a tiled area model to help us solve the problem.

We use the denominators for the dimensions of our area model, and we use the numerators to fill parts of the area model.

6 27

$\frac{2}{3}\times\frac{3}{9}=\frac{6}{27}$

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Example Question #101 : Operations With Fractions And Whole Numbers

Jean lives $\frac{3}{9}$ of a mile away from her friend's house. She walked $\frac{1}{3}$ of the way there and then stopped to get ice cream from an ice cream truck driving by. How far did she travel before she stopped to get ice cream?

Possible Answers:

$\frac{5}{26}\text{ of a mile}$

$\frac{3}{26}\text{ of a mile}$

$\frac{4}{26}\text{ of a mile}$

$\frac{3}{27}\text{ of a mile}$

$\frac{4}{27}\text{ of a mile}$

Correct answer:

$\frac{3}{27}\text{ of a mile}$

Explanation:

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of". $\frac{1}{3}$ of the way to her friends house she stopped.

We know that her friend lives $\frac{3}{9}$ of a mile away from her so we can set up our multiplication problem.

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

We can set up a tiled area model to help us solve the problem.

We use the denominators for the dimensions of our area model, and we use the numerators to fill parts of the area model.

3 27

$\frac{1}{3}\times\frac{3}{9}=\frac{3}{27}$

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Example Question #33 : Operations With Fractions And Whole Numbers

Jessica made gallons of punch. $\frac{1}{5}$ of the punch was water. How many gallons of water did she use to make the punch?

Possible Answers:

$\frac{2}{5}$

$\frac{4}{5}$

$\frac{3}{5}$

Correct answer:

$\frac{2}{5}$

Explanation:

A keyword in our question that gives us a clue that we are going to multiply to solve this problem is the word "of". $\frac{1}{5}$ of the punch is water.

We know that we have gallons of punch so we can set up our multiplication problem.

$\frac{1}{5}\times2$

2 5

$\frac{1}{5}\times2$ which means $\frac{1}{5}$ of each group of $2=\frac{2}{5}$

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Example Question #1 : Find The Area Of A Rectangle With Fractional Side Lengths By Tiling: Ccss.Math.Content.5.Nf.B.4b

By tiling a rectangle with unit squares, find the area of a rectangle with a length of $\frac{7}{9}$ of an inch and a width of $\frac{1}{2}$ of an inch.

Possible Answers:

$\frac{7}{11}\text{ of an inch}^2$

$\frac{5}{11}\text{ of an inch}^2$

$\frac{7}{18}\text{ of an inch}^2$

$\frac{8}{11}\text{ of an inch}^2$

$\frac{9}{18}\text{ of an inch}^2$

Correct answer:

$\frac{7}{18}\text{ of an inch}^2$

Explanation:

To set up a tiled area model to solve the problem, we use the denominators for the dimensions of our area model, and we use the numerators to fill parts of the area model.

7 18

$\frac{7}{18}$

Notice that we could have multiplied the numerators of our fractions and the denominators of our fraction to find our answer.

$7\times1=7$

$9\times2=18$

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All Common Core: 5th Grade Math Resources

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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 #1964 : Numbers And Operations

Example Question #331 : Number & Operations With Fractions

Example Question #1966 : Numbers And Operations

Example Question #1967 : Numbers And Operations

Example Question #1968 : Numbers And Operations

Example Question #1961 : Numbers And Operations

Example Question #331 : Number & Operations With Fractions

Example Question #101 : Operations With Fractions And Whole Numbers

Example Question #33 : Operations With Fractions And Whole Numbers

Example Question #1 : Find The Area Of A Rectangle With Fractional Side Lengths By Tiling: Ccss.Math.Content.5.Nf.B.4b

All Common Core: 5th Grade Math Resources

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