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 onefourth 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 twofifth 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 twofifths of the threefourths 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:
If a b and c d are fractions with b, d ≠ 0, then a b x c d = ac bd 
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