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".
Apart from the stuff given above, if you want to know more about "Multiplicative inverses", please click here
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
MATH FOR KIDS
HCF and LCM word problems
Word problems on quadratic equations
Word problems on comparing rates
Ratio and proportion word problems
Converting repeating decimals in to fractions