Multiplication and Division of Fractions

Multiplication and Division of Fractions

Multiplication of Fractions

Multiplication of a fraction by a whole number

In multiplication of a fraction by a whole number we use the process of repeated addition.

For example,                  

process of repeated addition
In short method, we multiply the numerator by a whole number and keep the denominator as it is.

For example,

Multiplication of a fraction by a whole number

Multiplication of a fraction by a fraction

In multiplication of a fraction by a fraction, we divide the same whole object into two fractions. The common shaded part is the product of the fractions.

For example,

Multiplication of a fraction by a fraction

In short method, we follow the following steps to multiply the fractions:

a. If there is a mixed fraction, change it to improper fraction.

b. Numerators and denominators should be cancelled by common factors.

c. Numerators and denominators are multiplied.

d. If the product is an improper fraction, change it to a mixed fraction.

For example,

Multiplication of a fraction by a fraction

Division of Fractions

Division of a fraction by a fraction

In division of a fraction by a fraction or when we divide a fraction by another fraction, we multiply the dividend fraction with the reciprocal of its divisor fraction.

The reciprocal of a fraction is the fraction obtained by interchanging its numerator and denominator.

For example:

reciprocal of a fraction

So, we simply change the divide (÷) sign into multiply (×) sign and interchange the numerator and denominator of the divisor. Then, we multiply the fractions.

For example,

Division of a fraction by a fraction
             

Workout Examples


Example 1: Multiply

Example 2: Multiply

Example 3: Multiply

Example 4: Divide

Example 5: Divide

Example 6: Simplify

 

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