## 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.,
• 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 ’

• ‘of’ represents multiplication.

### Multiplication of a Fraction by a Fraction :

• We multiply two fractions as:
•

#### 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 is and the reciprocal of is .

### 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.
• 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.
• 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).
• While dividing mixed fractions, convert the mixed fractions into improper fractions.

#### Time to think [ Division of fractions ]

1) Arrange the following in descending order:

2) Represent pictorially :

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: