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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 #1201 : Common Core Math: Grade 5

By tiling a rectangle with unit squares, find the area of a rectangle with a length of $\frac{4}{9}$ of an inch and a width of $\frac{1}{2}$ of an inch.

Possible Answers:

$\frac{4}{18}\text{ of an inch}^2$

$\frac{3}{10}\text{ of an inch}^2$

$\frac{1}{18}\text{ of an inch}^2$

$\frac{3}{11}\text{ of an inch}^2$

$\frac{4}{11}\text{ of an inch}^2$

Correct answer:

$\frac{4}{18}\text{ of an inch}^2$

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.

4 18

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).

$\frac{4}{18}$

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

$4\times1=4$

$9\times2=18$

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Example Question #351 : Number & Operations With Fractions

By tiling a rectangle with unit squares, find the area of a rectangle with a length of $\frac{3}{4}$ of an inch and a width of $\frac{3}{8}$ of an inch.

Possible Answers:

$\frac{6}{30}\text{ of an inch}^2$

$\frac{9}{30}\text{ of an inch}^2$

$\frac{5}{30}\text{ of an inch}^2$

$\frac{9}{32}\text{ of an inch}^2$

$\frac{6}{32}\text{ of an inch}^2$

Correct answer:

$\frac{9}{32}\text{ of an inch}^2$

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.

9 32

$\frac{9}{32}$

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

$3\times3=9$

$4\times8=32$

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Example Question #1203 : Common Core Math: Grade 5

By tiling a rectangle with unit squares, find the area of a rectangle with a length of $\frac{3}{7}$ of an inch and a width of $\frac{3}{4}$ of an inch.

Possible Answers:

$\frac{9}{28}\text{ of an inch}^2$

$\frac{9}{25}\text{ of an inch}^2$

$\frac{14}{28}\text{ of an inch}^2$

$\frac{6}{28}\text{ of an inch}^2$

$\frac{8}{25}\text{ of an inch}^2$

Correct answer:

$\frac{9}{28}\text{ of an inch}^2$

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.

9 28

$\frac{9}{28}$

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

$3\times3=9$

$7\times4=28$

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Example Question #1204 : Common Core Math: Grade 5

By tiling a rectangle with unit squares, find the area of a rectangle with a length of $\frac{2}{4}$ of an inch and a width of $\frac{1}{7}$ of an inch.

Possible Answers:

$\frac{3}{28}\text{ of an inch}^2$

$\frac{3}{20}\text{ of an inch}^2$

$\frac{1}{28}\text{ of an inch}^2$

$\frac{2}{28}\text{ of an inch}^2$

$\frac{1}{20}\text{ of an inch}^2$

Correct answer:

$\frac{2}{28}\text{ of an inch}^2$

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.

2 28

$\frac{2}{28}$

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

$2\times1=2$

$4\times7=28$

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Example Question #1205 : Common Core Math: Grade 5

By tiling a rectangle with unit squares, find the area of a rectangle with a length of $\frac{2}{3}$ of an inch and a width of $\frac{1}{2}$ of an inch.

Possible Answers:

$\frac{1}{6}\text{ of an inch}^2$

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

$\frac{3}{5}\text{ of an inch}^2$

$\frac{2}{6}\text{ of an inch}^2$

$\frac{3}{6}\text{ of an inch}^2$

Correct answer:

$\frac{2}{6}\text{ of an inch}^2$

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.

2 6

$\frac{2}{6}$

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

$1\times2=2$

$3\times2=6$

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Example Question #1206 : Common Core Math: Grade 5

By tiling a rectangle with unit squares, find the area of a rectangle with a length of $\frac{2}{4}$ of an inch and a width of $\frac{4}{7}$ of an inch.

Possible Answers:

$\frac{8}{24}\text{ of an inch}^2$

$\frac{4}{24}\text{ of an inch}^2$

$\frac{6}{24}\text{ of an inch}^2$

$\frac{5}{20}\text{ of an inch}^2$

$\frac{8}{28}\text{ of an inch}^2$

Correct answer:

$\frac{8}{28}\text{ of an inch}^2$

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.

8 28 2

$\frac{8}{28}$

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

$2\times4=8$

$4\times7=28$

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Example Question #1207 : Common Core Math: Grade 5

By tiling a rectangle with unit squares, find the area of a rectangle with a length of $\frac{5}{6}$ of an inch and a width of $\frac{3}{8}$ of an inch.

Possible Answers:

$\frac{8}{48}\text{ of an inch}^2$

$\frac{15}{16}\text{ of an inch}^2$

$\frac{18}{48}\text{ of an inch}^2$

$\frac{15}{48}\text{ of an inch}^2$

$\frac{8}{16}\text{ of an inch}^2$

Correct answer:

$\frac{15}{48}\text{ of an inch}^2$

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.

15 48

$\frac{15}{48}$

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

$5\times3=15$

$6\times8=48$

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Example Question #1208 : Common Core Math: Grade 5

By tiling a rectangle with unit squares, find the area of a rectangle with a length of $\frac{8}{9}$ of an inch and a width of $\frac{2}{3}$ of an inch.

Possible Answers:

$\frac{14}{28}\text{ of an inch}^2$

$\frac{10}{29}\text{ of an inch}^2$

$\frac{16}{27}\text{ of an inch}^2$

$\frac{16}{29}\text{ of an inch}^2$

$\frac{10}{27}\text{ of an inch}^2$

Correct answer:

$\frac{16}{27}\text{ of an inch}^2$

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.

16 27

$\frac{16}{27}$

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

$8\times2=16$

$9\times3=27$

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Example Question #1211 : Common Core Math: Grade 5

By tiling a rectangle with unit squares, find the area of a rectangle with a length of $\frac{6}{8}$ of an inch and a width of $\frac{1}{2}$ of an inch.

Possible Answers:

$\frac{6}{12}\text{ of an inch}^2$

$\frac{6}{16}\text{ of an inch}^2$

$\frac{1}{16}\text{ of an inch}^2$

$\frac{7}{16}\text{ of an inch}^2$

$\frac{7}{10}\text{ of an inch}^2$

Correct answer:

$\frac{6}{16}\text{ of an inch}^2$

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.

6 16 2

$\frac{6}{16}$

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

$6\times1=6$

$8\times2=16$

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Example Question #1212 : Common Core Math: Grade 5

By tiling a rectangle with unit squares, find the area of a rectangle with a length of $\frac{2}{6}$ of an inch and a width of $\frac{4}{5}$ of an inch.

Possible Answers:

$\frac{9}{30}\text{ of an inch}^2$

$\frac{8}{35}\text{ of an inch}^2$

$\frac{8}{30}\text{ of an inch}^2$

$\frac{9}{35}\text{ of an inch}^2$

$\frac{6}{11}\text{ of an inch}^2$

Correct answer:

$\frac{8}{30}\text{ of an inch}^2$

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.

8 30

$\frac{8}{30}$

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

$2\times4=8$

$6\times5=30$

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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 #1201 : Common Core Math: Grade 5

Example Question #351 : Number & Operations With Fractions

Example Question #1203 : Common Core Math: Grade 5

Example Question #1204 : Common Core Math: Grade 5

Example Question #1205 : Common Core Math: Grade 5

Example Question #1206 : Common Core Math: Grade 5

Example Question #1207 : Common Core Math: Grade 5

Example Question #1208 : Common Core Math: Grade 5

Example Question #1211 : Common Core Math: Grade 5

Example Question #1212 : Common Core Math: Grade 5

All Common Core: 5th Grade Math Resources

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