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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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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 $\frac{2}{6}$ of an inch and a width of $\frac{4}{5}$ of an inch.

Possible Answers:

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

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

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

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

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

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:

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

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

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

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

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

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 #23 : 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:

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

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

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

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

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

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:

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

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

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

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

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

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:

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

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

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

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 $2\ ft\times 3\frac{3}{4}\ ft$ .

Correct answer:

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

Explanation:

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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 #21 : 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

Example Question #23 : 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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