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., 2×5/3 =(2×5)/3 = 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 ’
- 1/2 of 1 = 1/2 × 1 = 1/2
- 1/2 of 2 = 1/2 × 2 = 2/2 = 1
- 1/2 of 3 = 1/2 × 3 = 3/2 = 11/2
- ‘of’ represents multiplication.
Multiplication of a Fraction by a Fraction :
- we multiply two fractions as:
- 1/2×5/3 = 1×5/2×3 = 5/6
- 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 5/9 is 9/5 and the reciprocal of 9/5 is 5/9.
Division of Whole Number by a Fraction
- To divide a whole number by any fraction, multiply that whole number by the reciprocal of that fraction.
- 3÷5/2 = 3×2/5 = 3×2/5 = 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.
- 1/2 ÷ 3 = 1/2 × 1/3 = 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).
- 1/2 ÷ 2/3 = 1/2 × 3/2 = 3/4
- While dividing mixed fractions by a fractions, convert the mixed fractions into improper fractions.
- 33/4 ÷ 29/8 = 15/4 ÷ 25/8 = 15/4 × 8/25 = 6/5
Time to think :
1)Arrange the following in descending order:(i) 2∕9, 2∕3, 8∕21 (ii) 1∕5, 3∕7, 7∕10
2)Represent pictorially : 2×2/5 = 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) 3/5÷1/2 (ii) 1/2÷3/5 (iii) 2 1/2 ÷3/5 (iv) 5 1/6÷9/2
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