The Distributive Property for 7th Grade: Using a rectangle

Calculate the area of the rectangle below using the distributive property.

The area of the rectangle is equal to the length multiplied by the width.

We begin by writing the exercise according to the existing data:

$7\times(4+5)$

We then solve the exercise by using the distributive property, that is, we multiply 7 by each of the terms inside of the parentheses:

$(7\times4)+(7\times5)=$

Lastly we solve the exercise inside of the parentheses and obtain the following:

$28+35=63$

63

Calculate the area of the rectangle below using the distributive property.

The area of a rectangle is equal to its length multiplied by the width.

We begin by writing the following exercise using the data shown in the figure:

$(3+2)\times(9+4)=$

We solve the exercise using the distributive property.

That is:

We multiply the first term of the left parenthesis by the first term of the right parenthesis.

We then multiply the first term of the left parenthesis by the second term of the right parenthesis.

Now we multiply the second term of the left parenthesis by the first term of the left parenthesis.

Finally, we multiply the second term of the left parenthesis by the second term of the right parenthesis.

In the following way:

$(3\times9)+(3\times4)+(2\times9)+(2\times4)=$

We solve each of the exercises within the parentheses:

$27+12+18+8=$

Lastly we solve the exercise from left to right:

$27+12=39$

$39+18=57$

$57+8=65$

65

Given the rectangular area 78 cm².

Find X

We know that the area of a rectangle is equal to its length multiplied by its width.

We begin by writing an equation with the available data.

$78=3\times(x+7)$

We then use the distributive property to solve the equation.

That is, we multiply each of the terms inside of the parentheses by 3:

$78=3\times x+3\times7$

$78=3x+21$

We move 21 to the other side and use the appropriate sign:

$78-21=3x$

$57=3x$

Lastly we divide both sides by 3:

$\frac{57}{3}=\frac{3x}{3}$

$x=19$

$19$

Look at the rectangle in the figure.

What is its area?

We know that the area of a rectangle is equal to its length multiplied by its width.

We begin by writing an equation with the available data.

$(4x+x^2)\times(3x+8+5x)$

Next we use the distributive property to solve the equation.

$(4x\times3x)+(4x\times8)+(4x\times5x)+(x^2\times3x)+(x^2\times8)+(x^2\times5x)=$

We then solve each of the exercises within the parentheses:

$12x^2+32x+20x^2+3x^3+16x^2+5x^3=$

Finally we add up all the coefficients of X squared and all the coefficients of X cubed and we obtain the following:

$48x^2+8x^3+32x$

$8x^3+28x^2+44x$

Which expressions represent the area of the rectangle in the drawing?

1. $56x$

2. $9(3x^2+5x)$

3. $x(3x+5)+9(3x+5)$

4. $32x+x^2$

5. $3x^2+45$

6. $3x^2+32x+45$

3, 6

Gerard plans to paint a fence 7X meters high and 30X+4 meters long.

Gerardo paints at a rate of 7 m² per half an hour.

Choose the expression that represents the time it takes for Gerardo to paint one side of the fence.

$15x^2+2x$ hours