What Have We Discussed ?

1.We have learnt how to multiply fractions. Two fractions are multiplied by multiplying their numerators and denominators seperately and writing the product as productofnumeratorsproductofdenominators. For example: 23 × 57 = 2 × 53 × 7 =

2. A fraction acts as an operator ‘of’. For example: 12 of 2 is 12 × 2 =

3. (a) The product of two proper fractions is lessmore than each of the fractions that are multiplied.

(b) The product of a proper and an impropermixed fraction is lessmore than the improper fraction and greaterlesser than the proper fraction.

(c) The product of two imporper fractions is greaterlesser than the two fractions.

4. A of a fraction is obtained by inverting it upside down.

5. We have seen how to divide two fractions:

(a) While dividing a whole number by a fraction, we multiply the whole number with the of that fraction.

For example: 2 ÷ 35 = 2 × 53 =

(b) While dividing a fraction by a whole number, we multiply the fraction by the reciprocal of the whole numberfraction.

For example: 23 ÷ 7 = 23 × 17 =

(c) While dividing one fraction by another fraction, we multiply the first fraction by the reciprocal of the other. So 23 ÷ 57 = 23 × 75 =

6. We also learnt how to multiply two decimal numbers. While multiplying two decimal numbers, first multiply them as whole numbers. Count the number of digits to the right of the decimal point in both the decimal numbers. Add the number of digits counted. Put the decimal point in the product by counting the digits from its rightmost place. The count should be the sum obtained earlier.

For example: 0.5 × 0.7 =

7. To multiply a decimal number by 10, 100 or 1000, we move the decimal point in the number to the right by as many places as there are zeros over 1. Thus, 0.53 × 10 = , 0.53 × 100 = , 0.53 × 1000 =

8. We have seen how to divide decimal numbers.

(a) To divide a decimal number by a whole number, we first divide them as whole numbers. Then place the decimal point in the quotient as in the decimal number.

For example: 8.4 ÷ 4 =

Note: That here we consider only those divisions in which the remainder is zero.

(b) To divide a decimal number by 10, 100 or 1000, shift the digits in the decimal number to the left by as many places as there are zeros over 1, to get the quotient.

So, 23.9 ÷ 10 = , 23.9 ÷ 100 = , 23.9 ÷ 1000 = .

(c) While dividing two decimal numbers, first shift the decimal point to the right by equal number of places in both, to convert the divisor to a whole number. Then divide. Thus, 2.4 ÷ 0.2 = 24 ÷ 2 = .