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?
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