Fractions and Types

If a fraction is written in the form of a/b, then a and b are the parts of the fraction, where a is called a numerator and b is called the denominator.

For example,

Suppose ⅖ is a fraction, then 2 is the numerator and 5 is the denominator.

There are three main types of fractions which are proper fractions, improper fractions, and mixed fractions. Below is a brief explanation on each of the types.

Proper fractions

When the numerator of a fraction is less than the denominator.

Example: ½, ⅗, 7/9

Improper fractions

When the numerator is greater than the denominator

Example: 3/2, 5/4, 8/3

Mixed Fraction

The combination of a whole number and a fraction. It is also called a mixed number.

Example: 13/4 =  3 ¼ 

21/5 =  4 ⅕ 

How to Multiply Fractions?

Multiplying fractions is defined as the product of a fraction with a fraction or with an integer or with the variables. The procedure to multiply the fractions are:

• Multiply the numerator with numerator
• Multiply the denominator with the denominator
• Simplify the fractions, if required

For example,

3/2 and ⅓ are the two fractions

The multiplication of two fractions is given by:

(3/2)× (⅓) = [3×1]/[2×3]

(3/2)× (⅓) = 3/6

Now, simplify the fraction, we get ½

Therefore, the multiplication of two fractions 3/2 and ⅓ is ½. 

Simply, we can write the formula for multiplication of fraction as;

If “a/b” and “p/q are the multiplicand and multiplier, then the product of (a/b) and (p/q) is given by “ap/bq”

Thus, 

The product of Fraction = Product of Numerator/Product of Denominator

Dividing Fractions

When we divide the fraction by another fraction, we convert the latter into reciprocal and then multiply with the former fraction. Learn dividing fractions in detail at BYJU’S.

Example: ⅔ ÷ ¾

Solution: Convert ¾ into its reciprocal, to get 4/3.

Now multiply ⅔ by 4/3

⇒ ⅔ x 4/3 

⇒ (2×4)/(3×3)

⇒ 8/9.

Simplification of Fractions

In multiplying fractions, we generally multiply the top numbers (numerators) with each other, and the bottom numbers (denominators) with each other. To make the fractional multiplication simpler, we can reduce the fraction by cancelling off the common factors. It means that you can cancel out the common factors from one side of the fraction, which is duplicated on the other side of the fractional part.

For example, (4/9) and (3/16) are the two fractions.

(4/9) can be written as (2×2)/(3×3)

(3/16) can be written as (1×3)/(2×2×2×2)

Therefore, 49×316=2×23×3×1×32×2×2×2

Now, cancel out the common factors, we get49×316=13×14

Now, we can multiply numerator with numerator and denominator with denominator.

(4/9) × (3/16)= 1/12

In case, if the fraction has no common factors, then we should directly multiply the numerators and denominators to get the product of the fractions.