Multiplication & Division of Fractions

Here we will learn the various methods for Multiplication and Division of Fractions.

Multiplication of Fractions

Multiplication of a fraction by a whole number :

  • To multiply a whole number with a proper or an improper fraction, we multiply the whole number with the numerator of the fraction, keeping the denominator same.e.g., 2 \times \frac{5}{3} =\frac {(2\times 5)}{3} = \frac{10}{3}
  • To multiply a mixed fraction to a whole number, first convert the mixed fraction to an improper fraction and then multiply.

Fraction as an operator ‘of ’

  • \frac {1}{2}\, of \,1 = \frac{1}{2} \times1 = \frac {1}{2}
  • \frac {1}{2}\, of\, 2 = \frac {1}{2} \times 2 = \frac {2}{2}  = 1
  • \frac {1}{2}\, of \,3 = \frac {1}{2} \times 3 = \frac {3}{2} = 1\frac {1}{2}
  • ‘of’ represents multiplication.

Multiplication of a Fraction by a Fraction :

  • We multiply two fractions as: \frac{Product\, of\, Numerators}{Product\, of \,Denominators}
  •  \frac {1}{2}\times \frac{5}{3} = \frac {1\times 5}{2\times 3} = \frac{5}{6}

  Value of the Product

  • The value of the product of two proper fractions is smaller than each of the two fractions.
  • The value of the product of two improper fractions is more than each of the two fractions
  • The product of a proper and an improper fraction is less than the improper fraction and greater than the proper fraction.

Division of Fractions

Reciprocal of a fraction

  • The non-zero numbers whose product with each other is 1, are called the reciprocals of each other.
  • The reciprocal of a fraction can be obtained by interchanging the numerator and denominator of the fraction or by inverting it.
  • So reciprocal of \frac{5}{9} is \frac{9}{5} and the reciprocal of \frac{9}{5} is \frac{5}{9}.

Division of a Whole Number by a Fraction

  • To divide a whole number by any fraction, multiply that whole number by the reciprocal of that fraction.
  • 3\div \frac{5}{2} = 3\times \frac{2}{5} = \frac {3\times 2}{5} = \frac{6}{5}
  • While dividing a whole number by a mixed fraction, first convert the mixed fraction into improper fraction and then solve it.

Division of a Fraction by a Whole Number

  • To divide a fraction by a whole number, multiply that fraction by the reciprocal of that whole number.
  • \frac{ 1}{2} \div 3 = \frac{1}{2} \times \frac {1}{3} = \frac{1}{6}
  • While dividing mixed fractions by whole numbers, convert the mixed fractions into improper fractions.

Division of a Fraction by Another Fraction

  • To divide a fraction by another fraction, multiply that fraction by the reciprocal of another fraction (divisor).
  • \frac{1}{2} \div \frac{2}{3} = \frac{1}{2} \times \frac{3}{2} = \frac{ 3}{4}
  • While dividing mixed fractions, convert the mixed fractions into improper fractions.
  • 3\frac{3}{4 }\div 2\frac{9}{8}=\frac{ 15}{4 }\div \frac{ 25}{8}  = \frac{ 15}{4} \times \frac{ 8}{25} = \frac{6}{5}

Time to think [ Division of fractions ]

1) Arrange the following in descending order:

(i)\,\frac{2}{9},\frac{2}{3},\frac{8}{21}

(ii)\,\frac{1}{5},\frac{3}{7},\frac{7}{10}

2) Represent pictorially :  2\times \frac{ 2}{5} = \frac{4}{5}

3) What is (i) 1/2 of 10?, (ii) 1/4 of 16?, (iii) 2/5 of 25?

4)(i) Will the reciprocal of a proper fraction be again a proper fraction?

(ii) Will the reciprocal of an improper fraction be again an improper fraction?

5) Find:

(i)\,\frac{3}{5} \div \frac{ 1}{2} \,(ii)\, \frac{ 1}{2} \div \frac {3}{5}\\  \(iii)\, 2\frac{1}{2} \div \frac{3}{5} \,(iv)\, 5\frac{1}{6} \div \frac{9}{ 2}

⏪ Fractions Decimals ⏩

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