USING DIVISION TO SOLVE EQUATIONS

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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