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Common Core: 5th Grade Math : Find the Area of a Rectangle with Fractional Side Lengths by Tiling: CCSS.Math.Content.5.NF.B.4b

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

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All Common Core: 5th Grade Math Resources

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Example Questions

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

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).

$\frac{8}{30}$

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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Example Question #21 : 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 $\frac{5}{9}$ of an inch and a width of $\frac{1}{2}$ of an inch.

Possible Answers:

$\frac{5}{18}\text{ of an inch}^2$

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

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

$\frac{6}{18}\text{ of an inch}^2$

$\frac{5}{28}\text{ of an inch}^2$

Correct answer:

$\frac{5}{18}\text{ of an inch}^2$

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.

5 18

$\frac{5}{18}$

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

$5\times1=5$

$9\times2=18$

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Example Question #22 : 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 $\frac{3}{8}$ of an inch and a width of $\frac{3}{9}$ of an inch.

Possible Answers:

$\frac{9}{72}\text{ of an inch}^2$

$\frac{1}{72}\text{ of an inch}^2$

$\frac{6}{17}\text{ of an inch}^2$

$\frac{9}{17}\text{ of an inch}^2$

$\frac{5}{72}\text{ of an inch}^2$

Correct answer:

$\frac{9}{72}\text{ of an inch}^2$

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 72

$\frac{9}{72}$

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

$3\times3=9$

$8\times9=72$

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Example Question #24 : 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 $\frac{8}{9}$ of an inch and a width of $\frac{1}{2}$ of an inch.

Possible Answers:

$\frac{8}{18}\text{ of an inch}^2$

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

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

$\frac{9}{11}\text{ of an inch}^2$

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

Correct answer:

$\frac{8}{18}\text{ of an inch}^2$

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.

8 18

$\frac{8}{18}$

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

$8\times1=8$

$9\times2=18$

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Example Question #21 : Find The Area Of A Rectangle With Fractional Side Lengths By Tiling: Ccss.Math.Content.5.Nf.B.4b

A rectangular yard measures $4\ ft\times 7\frac{1}{2}\ ft$ . Which of the following statements is TRUE?

Possible Answers:

Increasing both the width and length of the yard by the same amount will not change the area.

The yard's area is the same as the yard's perimeter.

The yard is half the area of a playground that measures $6 ft \times 10 ft$

The area of the yard is twice the area of a sandbox that measures $2\ ft\times 3\frac{3}{4}\ ft$ .

A playground that measures $9\ ft\times 3\ ft$ has the same area as the rectangular yard.

Correct answer:

The yard is half the area of a playground that measures $6 ft \times 10 ft$

Explanation:

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All Common Core: 5th Grade Math Resources

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Common Core: 5th Grade Math : Find the Area of a Rectangle with Fractional Side Lengths by Tiling: CCSS.Math.Content.5.NF.B.4b

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

All Common Core: 5th Grade Math Resources

Example Questions

Example Question #1212 : Common Core Math: Grade 5

Example Question #21 : Find The Area Of A Rectangle With Fractional Side Lengths By Tiling: Ccss.Math.Content.5.Nf.B.4b

Example Question #22 : Find The Area Of A Rectangle With Fractional Side Lengths By Tiling: Ccss.Math.Content.5.Nf.B.4b

Example Question #24 : Find The Area Of A Rectangle With Fractional Side Lengths By Tiling: Ccss.Math.Content.5.Nf.B.4b

Example Question #21 : 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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