Fractions and Decimals
A fraction represents a part of a whole. When comparing two fractions with like denominators, the fraction with the larger numerator is larger. When comparing two fractions with unlike denominators but same numerators, the fraction with the smaller denominator is the larger one.
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. Two fractions are multiplied by multiplying their numerators and denominators separately. A fraction acts as an operator ‘of ’. Example: 1/3 of 3 is 1/3 × 3 = 1. The product of two proper fractions is less than each of the fractions. The product of two improper fractions is greater than each of the fractions. When a proper fraction and an improper fraction are multiplied, the result obtained is greater than the proper fraction and less than the improper fraction.
A reciprocal of a fraction is obtained by inverting it upside down. Dividing a whole number by a fraction is equivalent to multiplying the number by the reciprocal of the fraction. While dividing a fraction by a whole number, multiply the fraction by the reciprocal of the whole number. To divide two fractions, multiply the first fraction by the reciprocal of the second fraction.
A decimal number is a number that contains a whole part and a decimal part which are separated by a decimal point. While multiplying a decimal number by 10, 100 and 1000 shift the decimal point one, two and three digits respectively towards right.
To multiply two decimal numbers, ignore the decimal points and multiply the numbers. Count the total number of digits after decimal point in multiplicand and multiplier and add them. Count the digits in the product equal to this sum from right and place the decimal point.
While dividing a decimal number by 10, 100 and 1000 shift the decimal point one, two and three digits respectively towards left to obtain the quotient.
Division of a decimal number by a whole number is done as division of a whole number by another whole number. Then place the decimal point in the quotient as in the decimal number.
Division of two decimal numbers:
i. Move the decimal point in the divisor to the right until it is a whole number.
ii. Move the decimal point in the dividend to the right by the same number of places as the decimal point was moved to make the divisor a whole number.
iii. Divide the new dividend by the new divisor.
Keywords: Place Value,