Multiplying Fractions - Definition with Examples

Multiplying Fractions

A fraction is a part of a whole.

An apple pie cut into 4 equal slices and one slice is kept apart as shown.

Here, the apple pie is cut into 4 equal parts and each part represents one-fourth of the pie. How much apple pie would be there in 5 such pieces?

It would be the product of 5 × 1 4 . We can evaluate the multiplication as repeated addition also, and it is easier. 

5 × 1 4 = 1 4 + 1 4 + 1 4 + 1 4 + 1 4 = 5 4  

We can also convert this into a mixed number, 5 4  = 1 1 4 . Therefore, 5 pieces of the pie will have one and a quarter of apple pie.

But the repeated addition is not always an easier method, especially when the multiplier is also a fraction.

Consider the product 2 5 × 3 4 .

The fraction 3 4 can be represented as shown:

Now, the required product is the two-fifth of this shaded part.

To find that, you need to divide these three shaded part into 5 equal parts. An easier way to do this is to divide each of these 4 parts into 5 equal parts.

Now, the two-fifths of the three-fourths are the two shaded parts from each of these three parts, that is, 6 shaded parts out of 20 as shown.

Another way of representing this geometrically is:

In the fraction representing the product, the whole is divided into 20 equal parts and the shaded parts common to both the factors is the denominator, and 6 represents the numerator of the product.

Algebraically the rule to multiply two fractions is:

Step 1: Multiply the numerators of the factor fractions.

Step 2: Multiply the denominators.

Step 3: Simplify the product if required.

Example: 

5 6 x 3 8 = 5 × 3 6 × 8 = 15 48

Here, 3 is a common factor of the numerator and the denominator. So, to simplify the fraction, divide both numerator and denominator by 3.

15 ÷ 3 48 ÷ 3 = 5 6

Thus, 5 6 x 3 8 = 5 16 .

The rule is: