The Distributive Property for 7th Grade: Opening parentheses

$(3+20)\times(12+4)=$

Simplify this expression paying attention to the order of arithmetic operations. Exponentiation precedes multiplication whilst division precedes addition and subtraction. Parentheses precede all of the above.

Therefore, let's first start by simplifying the expressions within the parentheses. Then we can proceed to perform the multiplication between them:

$(3+20)\cdot(12+4)=\\ 23\cdot16=\\ 368$Therefore, the correct answer is option A.

368

$(35+4)\times(10+5)=$

We begin by opening the parentheses using the extended distributive property to create a long addition exercise:

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

We 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:

$(35\times10)+(35\times5)+(4\times10)+(4\times5)=$

We solve each of the exercises within parentheses:

$350+175+40+20=$

We solve the exercise from left to right:

$350+175=525$

$525+40=565$

$565+20=585$

585

Which expression is the exercise 14X3equal to?

We begin by breaking down the 14 into a subtraction exercise:

$(15-1)\times3=$

Next we multiply each of the numbers inside of the parentheses by 3:

$(15\times3)-(1\times3)=$

We can already discard option A and option D since the solution must contain 15x3.

Lastly we solve the parenthesis on the right side of the equation and obtain the following:

$15\times3-3$

Therefore, the answer is C.

15X3 and we subtract 3

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

$(a+3a)\times(5+2)=112$

Calculate a a

We begin by solving the two exercises inside of the parentheses:

$4a\times7=112$

We then divide each of the sections by 4:

$\frac{4a\times7}{4}=\frac{112}{4}$

In the fraction on the left side we simplify by 4 and in the fraction on the right side we divide by 4:

$a\times7=28$

Remember that:

$a\times7=a7$

Lastly we divide both sections by 7:

$\frac{a7}{7}=\frac{28}{7}$

$a=4$

4

$(7x+3)\times(10+4)=238$

We begin by solving the addition exercise in the right parenthesis:

$(7x+3)+14=238$

We then multiply each of the terms inside of the parentheses by 14:

$(14\times7x)+(14\times3)=238$

Following this we solve each of the exercises inside of the parentheses:

$98x+42=238$

We move the sections whilst retaining the appropriate sign:

$98x=238-42$

$98x=196$

Finally we divide the two parts by 98:

$\frac{98}{98}x=\frac{196}{98}$

$x=2$

2

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