Maths Chapter 02: Fractions and Decimals

Class 07 Maths NCERT

Two fractions are multiplied by multiplying their numerators and denominators separately. The product of two proper fractions is less than each of the fractions that are multiplied.

The product of a proper and an improper fraction is less than the improper fraction and greater than the proper fraction. The product of two improper fractions is greater than the two fractions.

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

How to divide two fractions

  • While dividing a whole number by a fraction, we multiply the whole number with the reciprocal of that fraction.
  • While dividing a fraction by a whole number we multiply the fraction by the reciprocal of the whole number.
  • While dividing one fraction by another fraction, we multiply the first fraction by the reciprocal of the other.

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 = 0.35

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.

For example, 0.53 × 10 = 5.3, 0.53 × 100 = 53, 0.53 × 1000 = 530

How to divide decimal numbers

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 = 2.1

Here we consider only those divisions in which the remainder is zero.

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.

For example, , 23.9 ÷ 10 = 2.39,23.9 ÷ 100 = 0 .239, 23.9 ÷ 1000 = 0.0239

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. For example,, 2.4 ÷ 0.2 = 24 ÷ 2 = 12.