Multiplication and Division of Common Fractions

When multiplying or dividing fractions, we do NOT change the denominators to be common as in the case when adding or subtracting fractions. Multiplication and division of fractions are quite straightforward to do.

When multiplying fractions, you can follow two methods. The first method is that you multiply all the numerators with each other and multiply all the denominators with each other (“top multiply by top and bottom multiply by bottom”). Then, you should simplify the fraction – write an equivalent fraction by dividing the numerator and denominator with the highest common factor (HCF). In the second method, we will make use of the HCF much earlier. You can immediately look for values that can ‘cancel out’. Just remember to multiply all the numerators and all the denominators at the end to get to the final answer.

For the division of fractions, we can follow the trick of changing the division sign to a multiplication sign and “flip the fraction that follows”. We are actually multiplying with the reciprocal. Once the fraction is flipped, you handle the calculation as a multiplication calculation and follow either of the two methods discussed earlier.