# Multiplication of Rational Numbers

## Key Questions

• You simply multiply the nominators (top) and the denominators (bottom):

a/b * c/d = (a*c)/(b*d

After this, you might have to simplify if asked to do so.
Here's an example:

$\frac{5}{8} \cdot \frac{4}{7}$

Following our rule, we should first multiply the nominators:
$5 \cdot 4 = 20$

After this, we should multiply the denominators:
$8 \cdot 7 = 56$

And then we should divide both these numbers:
$\frac{5}{8} \cdot \frac{4}{7} = \frac{5 \cdot 4}{8 \cdot 7} = \frac{20}{56}$

If you're asked to simplify this answer to the lowest terms, you should divide both the nominator and denominator by 4 (in this case), because that's the GCD of the two numbers.

$\frac{20}{56} = \frac{5}{14}$

• For multiplying and dividing the rules are same. If both numbers are positive then the answer will be positive, if both numbers are negative then the answer will again be positive. If one number is positive and one is negative then the answer will be negative.

$+ + = +$
$- - = +$
$+ - = -$
$- + = -$

• You only need to multiply the numerators and denominators separately: if you have a/b and c/d two fractions, their product will simply be ac/bd.

For example, if you have to multiply 2/3 and 4/7, the result will be 24/37=8/21