MULTIPLICATION AND DIVISION EQUATIONS

Example 1 :

Solve for x :  8x = 56.

Solution :

8x  =  56

Since we are trying to solve for "x", we have to get rid of 8 which is multiplied by "x".

To get rid of 8, we have to divide by 8 on both sides. 

8x / 8  =  56/8

x  =  7

Hence, the value of "x" is 7.

Example 2 :

Solve for y :  y/4 = 7.

Solution :

y / 4  =  7

Since we are trying to solve for "y", we have to get rid of 4 which divides y in the above equation.

To get rid of 4, we have to multiply by 4 on both sides. 

(y / 4) x 4  =  7 x 4

y  =  28

Hence, the value of "y" is 28.

Example 3 :

When 7 is multiplied by a number, we get 42. Find the number. 

Solution :

Let "x' be the required number. 

According to the question, we have

7x  =  42

Here, 7 is multiplied by x. To get rid of 7, we have to divide by 7 on both sides and solve the equation as explained below. . 

7x / 7  =  42/7 

x  =  6

Hence, the value of "x" is 6.

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

Solution :

Let "x' be the other number. 

According to the question, we have

8x   =  20

Here, 8 is multiplied by x. To get rid of 8, we have to divide by 8 on both sides and solve the equation as explained below. . 

8x / 8  =  20/8 

x  =  2.5

Hence, the other number is 2.5.

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