# USING DIVISION TO SOLVE EQUATIONS

We can use division to solve equations which contain multiplication.

That is, when an equation contains multiplication, solve by dividing both sides of the equation by the same nonzero number.

## Division Property of Equality

Both sides of an equation can be divided by the same non zero number, and the two sides will remain equal.

Example 1 :

Solve the following equation and graph the solution on a number line.

9a = 54

Solution :

9a = 54

Since we are trying to solve for 'a', we have to get rid of '9' which is multiplied by a in the above equation.

To get rid of 9, we have to divide both sides of the equation by 9.

9a/9 = 54/9

a = 6 Example 2 :

Solve the following equation and and graph the solution on a number line.

Solution :

18 = 6d

Divide both sides by 6.

18/6 = 6d/6

3 = d Example 3 :

The product of two numbers is 20. If one number is 8, find the other number.

Solution :

Let x be the other number.

8x = 20

Divide both sides by 8.

8x/8 = 20/8

x = 2.5

The other number is 2.5.

Example 4 :

Three times of x is equal to four times of y. If the value of y is 6, find the value of x.

Solution :

Given : Three times of x is equal to four times of y.

3x = 4y

Substitute y = 6.

3x = 4(6)

3x = 24

Divide each both sides by 3.

3x/3 = 24/3

x = 8

Example 5 :

Deanna has a recipe for potato cakes that requires 12 eggs to make 3 batches of potato cakes. Represent the given situation as an equation.

Model the equation and find how many eggs are needed per batch.

Solution :

Write a word equation based on the situation. Rewrite the equation using a variable for the unknown quantity and the given values for the known quantities.

Let x represent the number of eggs needed per batch.

Then, we have Therefore, the equation 3x = 12 represents the given situation.

Let us model the equation 3x = 12 using algebra tiles. To find how many eggs are needed per batch, we have to solve for x.

To solve for x in the above model, we have to isolate x.

There are three x tiles, so draw circles to separate the tiles into 3 equal groups.

One group has been circled here. In the circled group above, we find one x on the left side and four 1 tiles on the right side.

So, the value of x is 4.

Hence, 4 eggs are needed per batch.

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