**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.

**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.

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