If two numbers are reciprocal to each other, then its product will be equal to 1.
For example :
Reciprocal of a is 1/a.
Reciprocal of a/b is b/a.
Reciprocal of -a is -1/a
Reciprocal of -a/b is -b/a.
Reciprocal of (a/b)n is (b/a)n
Reciprocal of (-a/b)n is (-b/a)n
Reciprocal of (a/b)-n is (b/a)n
Reciprocal of (-a/b)-n is (-b/a)n
Example 1 :
State the reciprocal of:
a) 3/4 b) 2/7 c) 4 d) -1/2 e) -2
f) 5/8 g) -5/2 h) -1 i) 0
Solution :
a) Reciprocal of 3/4 is 4/3.
b) Reciprocal of 2/7 is 7/2.
c) Reciprocal of 4 is 1/4.
d) Reciprocal of -1/2 is -2/1 that is -2.
e) Reciprocal of -2 is -1/2
f) Reciprocal of 5/8 is 8/5.
g) Reciprocal of -5/2 is -2/5.
h) Reciprocal of -1 is -1.
i) Reciprocal of 0 is undefined.
Example 2 :
4/7 of a number is 84. Find the number.
Solution :
4/7 of a number = 84 ----(1)
By finding 7/4 of the number, we can find that number.
Multiplying (1) by 7/4 on both sides.
(7/4) x (4/7) of a number = (7/4) x 84
Number = 7 x 21 ==> 147
So, the required number is 147.
Example 3 :
Find the quotient of 1/3 and 3/4.
Solution :
Let a = 1/3 and b = 3/4
To find the quotient of a and b, we have to divide a by b.
= (1/3) / (3/4)
If two fractions are divided, keep the first fraction as it is and change the division sign as multiplication and write the reciprocal of the second fraction.
= (1/3) x (4/3)
= 4/9
Example 4 :
Find the reciprocal of 5 and 7/8.
Solution :
Product of 5 and 7/8 = 5 x (7/8)
= 35/8
Reciprocal of 35/8 is 8/35.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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