Multiplication of Fractions with Fractions

Multiplying Proper Fractions

Multiplication of proper fractions is simple, as we can directly multiply the numerator of one fraction with the other fraction and the denominator of one fraction with the other fraction. If required, we can simplify the resultant fractions into their lowest term.

For example, the multiplication of 5/9 and 2/3.

(5/9)×(2/3)= (5×2)/(9×3) = 10/27.

Multiplying Improper Fractions

We know that in an improper fraction, the numerator is greater than the denominator. While multiplying two improper fractions, it will also result in the improper fraction. For example, multiplying two improper fractions, such as 9/2 and 6/5, results in:

(9/2)×(6/5) = (9/1)×(3/5)= 27/5.

If required, we can convert the improper fraction into a mixed fraction.

Example 1: Solve ⅔×½

Solution: ⅔×½ = 2×1/3×2 = 2/6 = ⅓

Therefore, from the above example, we can observe, by multiplying two fractions we get a fraction number. This is a proper fraction.

Example 2: Multiply ⅘×⅞

Solution: ⅘×⅞ = 4×7 / 5×8 = 28/40

We can further simplify it as;

28/40 = 7/10

If we have to multiply three fractions, then the above formula remains the same.

Example 3: Multiply ¼×⅖×⅛

Solution: Multiplying the given fraction ¼×⅖×⅛, we get

Product = 1×2×1 / 4×5×8

= 2 / 160

= 1 / 80