# USING MULTIPLICATION TO SOLVE EQUATIONS

## About "Using multiplication to solve equations"

Using multiplication to solve equations :

Multiplication and division equations are the equations which contain multiplication or division.

For example,

4x  =  16

y/2  =  6

We use multiplication to solve equations which contain division.

That is, when an equation contains division, solve by multiplying both sides of the equation by the same number.

## Using multiplication to solve equations - Examples

Example 1 :

Solve the equation x/5  =  10 and graph the solution on a number line.

Solution :

x/5  =  10

Since we are trying to solve for "x", we have to get rid of 5 which divides x in the above equation.

To get rid of 5, we have to multiply by 5 on both sides.

(x / 5) x 5  =  10 x 5

x  =  50

Graphing the solution on a number line

Example 2 :

Solve the equation 15  =  r/2 and graph the solution on a number line.

Solution :

15  =  r/2

Since we are trying to solve for "r", we have to get rid of 2 which divides r in the above equation.

To get rid of 2, we have to multiply by 2 on both sides.

15 x 2  =  (r/2) x 2

30  =  r

Graphing the solution on a number line

Example 3 :

Solve the equation y/9  =  1 and graph the solution on a number line.

Solution :

y/9  =  1

Since we are trying to solve for "y", we have to get rid of 9 which divides r in the above equation.

To get rid of 9, we have to multiply by 9 on both sides.

(y/9) x 9  =  1 x 9

y  =  9

Graphing the solution on a number line

Example 4 :

John had some candies. He shared the candies equally to his 3 kids. If each kid had received 7 candies, how many candies did John have ?

Solution :

Let "m' be the no. of candies that John initially .

According to the question, we have

m/3   =  7

Here 3 divides m. To get rid of 3, we have to multiply by 3 on both sides and solve the equation as explained below.

(m/3) x 3  =  7 x 3

m  =  21

Hence, John initially had 21 candies.

Example 5 :

The speed of John is 50 miles per hour. At the same rate, find the distance covered by John in 4.5 hours.

Solution :

Let "x' be the distance covered by John in 4.5 hours.

We know the formula for speed. That is

Speed  =  Distance / Time

Speed  =  x / 4.5

But, the speed is given 50 miles per hour.

Then, we have

x / 4.5  =  50

Here 4.5 divides x. To get rid of 4.5, we have to multiply by 4.5 on both sides and solve the equation as explained below.

(x/4.5) x 4.5  =  50 x 4.5

x  =  225

Hence, the distance covered by John in 4.5 hours is 225 miles.

After having gone through the stuff given above, we hope that the students would have understood "Using multiplication to solve equations".

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