# MULTIPLICATIVE INVERSES WORKSHEET

Multiplicative inverses worksheet :

Here we are going to see some practice questions on multiplicative inverse.

What is multiplicative inverse ?

For every rational number a/b, a ≠ 0, there exists a rational number c/d such that (a/b) x (c/d)  =  1. Then c/d is called the multiplicative inverse of (a/b).

That is,

If (a/b) is a rational number, then (b/a) is the multiplicative inverse or reciprocal of it.

• The reciprocal of 2 is 1/2
• The multiplicative inverse of (-3/5) is (-5/3)
• 0 has no reciprocal.
• 1 and – 1 are the only rational numbers which are their own reciprocals.

Let us see some practice questions based on the above concept.

(1)  What is the multiplicative inverse of 9/11

(2)  What is the multiplicative inverse of -5

(3)  What is the multiplicative inverse of the mixed number 00 2  5/7

(4)  What is the multiplicative inverse of the sum of (2/5) and (7/10)

(5)  What is the multiplicative inverse of the product of (5/21) x (7/20)

## Multiplicative inverses worksheet - Solution

Question 1 :

What is the multiplicative inverse of 9/11

Solution :

Since the given number is a fraction,

Let us consider the given fraction as (a/b)

Multiplicative inverse of (a/b) is (b/a)

Hence multiplicative inverse of 9/11 is 11/9.

Question 2 :

What is the multiplicative inverse of -5

Solution :

Since the given number is integer,

Let us consider the given number as "x"

Multiplicative inverse of x is (1/x)

Hence multiplicative inverse of -5 is -1/5.

Question 3 :

What is the multiplicative inverse of the mixed number 00 2  5/7

Solution :

Since the given number is mixed fraction, first we have to convert it as improper fraction.

2  5/7  =  [(2x7)+5]/7  =  (14+5)/7  =  19/7

From this we need to find the multiplicative inverse of the fraction 19/7.

Multiplicative inverse of the fraction in the form (a/b) is (b/a)

Hence multiplicative inverse of 19/7 is 7/19.

Question 4 :

What is the multiplicative inverse of the sum of (2/5) and (7/10)

Solution :

From the given question, we come to know that first we have to add the above fractions and find the multiplicative inverse for the answer.

(2/5) + (7/10)  =  (2/5) + (7/10)

L.C.M of 5 and 10 is 10.

=  (2/5) x (2/2) + (7/10)

=  (4/10) + (7/10)

=  (4 + 7)/10

=  11/10

By combining the above fractions, we get 11/10. Since the answer is in the form (a/b), (b/a) will be its reciprocal.

Hence the multiplicative inverse of 11/10 is 10/11.

Example 5 :

What is the multiplicative inverse of the product of (5/21) x (7/20)

Solution :

From the given question, we come to know that first we have to simplify the above fractions and find the multiplicative inverse for the answer.

=  (5/21) x (7/20)

=  (1/3) x (1/4)

=  (1/12)

By combining the above fractions, we get 1/12.Since 1/12 is in the form a/b, b/a will be its multiplicative inverse.

Hence multiplicative inverse of 1/12 is 12/1. That is 12.

After having gone through the stuff given above, we hope that the students would have understood "Multiplicative inverses worksheet".

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