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

## Example Questions

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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

A rectangular yard measures . Which of the following statements is TRUE?

The yard is a square.

A playground that measures has the same area as the rectangular yard.

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

The area of the yard is twice the area of a sandbox that measures .

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

The area of the yard is twice the area of a sandbox that measures .

Explanation:

### 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 until squares, find the area of a rectangle with a length of  of an inch and a width of  of an inch.

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.

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).

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

### Example Question #3 : Find The Area Of A Rectangle With Fractional Side Lengths By Tiling: Ccss.Math.Content.5.Nf.B.4b

By tiling a rectangle with until squares, find the area of a rectangle with a length of  of an inch and a width of  of an inch.

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.

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).

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

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

By tiling a rectangle with until squares, find the area of a rectangle with a length of  of an inch and a width of  of an inch.

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.

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).

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

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

By tiling a rectangle with until squares, find the area of a rectangle with a length of  of an inch and a width of  of an inch.

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.

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).

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

### Example Question #2 : Find The Area Of A Rectangle With Fractional Side Lengths By Tiling: Ccss.Math.Content.5.Nf.B.4b

By tiling a rectangle with until squares, find the area of a rectangle with a length of  of an inch and a width of  of an inch.

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.

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).

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

### Example Question #7 : Find The Area Of A Rectangle With Fractional Side Lengths By Tiling: Ccss.Math.Content.5.Nf.B.4b

By tiling a rectangle with until squares, find the area of a rectangle with a length of  of an inch  and a width of  of an inch.

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.

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).

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

### Example Question #3 : Find The Area Of A Rectangle With Fractional Side Lengths By Tiling: Ccss.Math.Content.5.Nf.B.4b

By tiling a rectangle with until squares, find the area of a rectangle with a length of  of an inch and a width of  of an inch.

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.

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).

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

### Example Question #9 : Find The Area Of A Rectangle With Fractional Side Lengths By Tiling: Ccss.Math.Content.5.Nf.B.4b

By tiling a rectangle with until squares, find the area of a rectangle with a length of  of an inch and a width of  of an inch.

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.

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).

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

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

By tiling a rectangle with until squares, find the area of a rectangle with a length of  of an inch and a width of  of an inch.

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.

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).

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

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