DIVIDING RATIONAL NUMBERS

To divide a rational number by another rational number, we have to multiply the dividend by the reciprocal of the divisor. 

The rules for the sign of quotient are summarized below.

Let p and q be rational numbers.

Example 1 : 

Divide 2/3 by -7/6.

Solution :

Step 1 :

Take the reciprocal of the second rational number.

-7/6 ----> reciprocal ----> -6/7

Step 2 : 

Multiply the first rational number 2/3 by -6/7.

(2/3) x (-6/7)  

Step 3 : Simplify

(2/1) x (-2/7)

Step 4 : Multiply 

(2/1) x (-2/7) = -4/7     Positive times negative equals     negative

So,

2/3 ÷ -7/6 = -4/7

Example 2 : 

Divide -2 by 8/3.

Solution :

Step 1 :

Take the reciprocal of the second rational number.

8/3 ----> reciprocal ----> 3/8

Step 2 : 

Multiply the first rational number 2 by 3/8.

(-2) x (3/8)  

Step 3 : Simplify

(-1) x (3/4)

Step 4 : Multiply 

(-1) x (3/4) = -3/4     Positive times negative equals negative

So,

-2 ÷ 8/3 = -3/4

Example 3 : 

Divide 9/5 by 3.

Solution :

Step 1 :

Take the reciprocal of the second rational number.

3 ----> reciprocal ----> 1/3

Step 2 : 

Multiply the first rational number 9/5 by 1/3.

(9/5) x (1/3)  

Step 3 : Simplify

(3/5) x (1/1)

Step 4 : Multiply 

(3/5) x (1/1) = 3/5      Positive times positive equals   positive

So,

9/5 ÷ 3 = 3/5

Example 4 :

How many quarters are in 8?

Solution :

One quarter = 1/4

Number of quarters in 8 :

= 8 ÷ (1/4)

Step 1 :

Take the reciprocal of the second rational number.

1/4 ----> reciprocal ----> 4

Step 2 : 

Multiply the first rational number 8 by 4.

8 x 4 = 32    Positive times positive equals positive

There are 32 quarters in 8.

Example 5 :

How many halves are in 7?

Solution :

One half = 1/2

Number of halves in 7 :

= 7 ÷ (1/2)

Step 1 :

Take the reciprocal of the second rational number.

1/2 ----> reciprocal ----> 2

Step 2 : 

Multiply the first rational number 7 by 2.

7 x 2 = 14    Positive times positive equals positive

There are 14 halves in 7.

Example 6 :

How many three-fourths are in 6?

Solution :

Three-fourth = 3/4

Number of three-fourths in 6 :

= 6 ÷ (3/4)

Step 1 :

Take the reciprocal of the second rational number.

3/4 ----> reciprocal ----> 4/3

Step 2 : 

Multiply the first rational number 6 by 4/3.

6 x (4/3)  

Step 3 : Simplify

2 x (4/1)

Step 4 : Multiply 

2 x (4/1) = 4     Positive times positive equals  positive

There are 4 three fourths in 6.

Example 7 :

How many one-fifths are in 10?

Solution :

One-fifth = 1/5

Number of one-fifths in 10 :

= 10 ÷ (1/5)

Step 1 :

Take the reciprocal of the second rational number.

1/5 ----> reciprocal ----> 5

Step 2 : 

Multiply the first rational number 10 by 5.

10 x 5 = 50    Positive times positive equals positive

There are 50 one-fifths in 10.

Example 8 : 

A diver needs to descend to a depth of 100 feet below sea level. She wants to do it in 5 equal descents. How far should she travel in each descent ?

Solution :

To find how far she should travel in each descent, we have to divide 100 by 5. 

Step 1 :

Take the reciprocal of the divisor 5.

5 ----> reciprocal ----> 1/5

Step 2 : 

Multiply 100 by 1/5

(100) x (1/5)  

Step 3 : Simplify

(20) x (1/1)

Step 4 : Multiply 

(20) x (1/1) = 20    

So, she should travel 20 feet in each descent.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.