Product of fractions = (Product of their numerators)⁄(Product of their denominators)
a⁄b xc⁄d = (a x
c)⁄ (bx d)
Note : Every natural number is a fraction with denominator 1. 1 = 1⁄1; 2 = 2⁄1; 3 = 3⁄1; 4 = 4⁄1; etc.
Solved Example 1 of Multiplying Fractions
Find the value of
5 4⁄5 x 1 2⁄5 x7 3⁄4 x2 3⁄7 x 10⁄7
5 4⁄5 x 1 2⁄5 x7 3⁄4 x2 3⁄7 x 10⁄17 = (5 x 5 + 4)⁄5 x (1 x 5 + 2)⁄5 x (7 x 4 + 3)⁄4x (2 x 7 + 3)⁄7 x 10⁄17 = 29⁄5 x 7⁄5 x 31⁄4 x 17⁄7 x 10⁄17
Here 17 and 7 in the Nr and Dr get cancelled. These are shown by striking them off. 5 in the Dr goes 2 times in 10 in the Nr. This is shown by striking 5 off and writing 2 in the place of striked off 10. This 2 in the place of 10 in Nr goes 2 times in the place of 4 in Dr. These are again shown by striking off 2 in the Nr and writing 2 in the place of striked off 4 in Dr.
= 29⁄5 x 7⁄5 x 31⁄42 x 17⁄7 x 102⁄17 = 29⁄5 x 31⁄2 = (29 x 31 )⁄(5 x 2) = 899⁄10 = 89 9⁄10. Ans.
Find the value of 6 x 4 1⁄2 x 5 3⁄4 x9 1⁄2 xx 1⁄57
6 x 4 1⁄2 x 5 3⁄4 x9 1⁄2 x1⁄57 = 6⁄1 x (4 x 2 + 1)⁄2 x (5 x 4 + 3)⁄4 x (9 x 2 + 1)⁄2x 1⁄57 = 6⁄1 x 9⁄2 x 23⁄4 x 19⁄2 x 1⁄57 = 63⁄1 x 9⁄2 x 23⁄4 x 19⁄2 x 1⁄573 = 9⁄2 x 23⁄4 = (9 x 23)⁄(2 x 4) = 207⁄8 = 25 7⁄8. Ans.
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Find the value of 8 x 2 3⁄4 x 9 2⁄11 x2 6⁄7 x 1⁄120
8 x 2 3⁄4 x 9 2⁄11 x2 6⁄7 x 1⁄120 = 8⁄1 x (2 x 4 + 3)⁄4 x (9 x 11 + 2)⁄11 x (2 x 7 + 6)⁄7x 1⁄120 = 8⁄1 x 11⁄4 x 101⁄11 x 20⁄7 x 1⁄120 = 82⁄1 x 11⁄4 x 101⁄11 x 20⁄7 x 1⁄12063 = 101⁄(7 x 3) = 101⁄21 = 4 17⁄21. Ans.
Reciprocal or Multiplicative Inverse of a Fraction : Multiplying Fractions
If two fractions are such that their product is 1, then each is called the reciprocal of the other.
Since a⁄b xb⁄a = (a x
b)⁄ (bx a)=
the reciprocal of a⁄bis b⁄a.
To write the reciprocal of a fraction, we interchangeits numerator and denominator.
(i) reciprcal of 2⁄3 is 3⁄2.
(ii) reciprcal of 1⁄7 is 7⁄1.
(iii) reciprcal of 8 is 1⁄8.
(iv) reciprcal of 6 4⁄5 = reciprcal of (6 x 5 + 4)⁄5 = reciprcal of 34⁄5 = 5⁄34.
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Exercise on Multiplying Fractions
Solve the following problems on Multiplying Fractions.