Here, we explain Multiplication of fractions,reciprocal or multiplicative inverse andUse of the operation 'of'in a lucid way. We include solved examples and problems for practice with answers.

Product of fractions = (Product of their numerators)⁄(Product of their denominators)

Thus,

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

Solution :

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 31⁄4^{2} x 17⁄7 x 10^{2}⁄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

Solution :

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 = 6^{3}⁄1 x 9⁄2 x 23⁄4 x 19⁄2 x 1⁄57^{3} = 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

Solution :

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 = 8^{2}⁄1 x 11⁄4 x 101⁄11 x 20⁄7 x 1⁄120^{6}^{3} = 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)=

1,so,

the reciprocal of a⁄bis b⁄a.

Thus,

To write the reciprocal of a fraction, we interchangeits numerator and denominator.

Examples :

(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.

Find the value of 4 ^{5}⁄_{6} x 1 ^{5}⁄_{7} x5⁄29 x 4

Find the value of 3 ^{1}⁄_{3} x 2 ^{1}⁄_{3} x6⁄7 x 2

Find the value of 3 ^{1}⁄_{4} x 2 ^{1}⁄_{6} x12⁄26