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# Fractions Multiplication and Division

Multiplication of Fractions:

Steps for multiplication of fraction:-

1. First break the numerators and denominators of the fractions to its prime factors.

2. Look for common factors between numerators and denominators in fraction , cancel out common terms.

3. Then we multiply numerators of the fractions to get new numerator and denominators of fraction to get new denominator.

4. Reduce the resulting fraction, if possible.

Example-

1).Simplify $\frac{3}{7}$ X $\frac{10}{4}$

$\frac{3}{7} X \frac{10}{4} = \frac{3}{7} X \frac{5 X 2}{2 X 2} = \frac{3 X 5}{7 X 2} = \frac{15}{14} = 1\frac{1}{14}$

2). Simplify $\frac{3}{8}$ X $\frac{4}{9}$

$\frac{3}{8} X \frac{4}{9} = \frac{3 }{2 X 2 X 2}X \frac{2 X 2}{3 X 3} = \frac{1}{2 X 3} = \frac{1}{6}$

## Multiplication and Division of Mixed Fractions

Multiplication and division of mixed fractions, we need to convert them into improper fractions. And divide and multiply as stated earlier.

Example :

1. Simplify $\frac{3}{8} X 2\frac{2}{9}$

$2\frac{2}{9} = \frac{2 X 9 + 2}{9} = \frac{20}{9}$

$\frac{3}{8} X 2\frac{2}{9} = \frac{3}{8} X \frac{20}{9} = \frac{3 X 5 X 2 X 2}{2 X 2 X 2 X 3 X 3} = \frac{5}{2 X 3} = \frac{5}{6}$

2). Simplify $2\frac{5}{8} \div 1\frac{2}{5}$

$2\frac{5}{8} \div 1\frac{2}{5} = \frac{2 X 8 + 5}{8} \div \frac{1 X 5 + 2}{5} = \frac{21}{8} \div \frac{7}{5} = \frac{21}{8} X \frac{5}{7} = \frac{3 X 7}{2 X 2 X 2} X \frac{5}{ 7} = \frac{3 X 5}{2 X 2 X 2} = \frac{15}{8} = 1\frac{7}{8}$

## Multiplication and Division of Algebraic Expressions

Multiplication and division of Algebraic expression is similar to normal Multiplication and division. But in this case we have to be careful about constraint and condition.

In multiplication none of the denominators should be zero.

In division all denominators and also the numerators of second term shouldn’t be zero.

Example:

1). Simplify $\frac{a + 3}{b}$ . $\frac{b^5}{3a + 9}$

$\frac{a + 3}{b}$ . $\frac{b^5}{3a + 9}$ = $\frac{a + 3}{b}$ . $\frac{b^5}{3(a + 3)}$ = $\frac{b^4}{3}$