Multiplicative inverses :
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).
If (a/b) is a rational number, then (b/a) is the multiplicative inverse or reciprocal of it.
Let us see some example problems based on the above concept.
Example 1 :
What is the multiplicative inverse of 9/11
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.
Example 2 :
What is the multiplicative inverse of -5
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.
Example 3 :
What is the multiplicative inverse of the mixed number 00 2 5/7
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.
Example 4 :
What is the multiplicative inverse of the sum of (2/5) and (7/10)
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
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)
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)
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".
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