Education

Operations on Fractions in Maths

In Mathematics, we have learned how to add and subtract integers in a simple way. Also, multiplication and division of integers are not a difficult task to do. But when it comes to fractions, we have to take care of certain things while performing mathematical operations on them. 

Before we learn how to do arithmetic operations on fractions, let us understand fractions first.

What are Fractions?

A fraction is a part of a whole. When we divide a whole into equal parts, then each part will represent the fraction. For example, if we divide a pizza into four equal pieces, then each piece of pizza will be equal to one-fourth of the whole pizza, i.e. ¼. 

In the same way, ½, ⅓, ⅕, ⅙, etc., are the examples of fractions. The fraction has two parts numerator and denominator. The upper part is called the numerator and the lower part is called the denominator. On a number line, the fraction can be expressed between any two integers. 

Fractions are also classified into different types such as unit fractions, proper fractions, improper fractions, mixed fractions. Apart from these, there are other types, such as like and unlike fractions, that play an important role in the addition and subtraction of fractions. 

Like fractions have the same denominator and unlike fractions have different denominators. For example, 3/2 and ½ are like fractions whereas ¾ and ⅚ are unlike. But on multiplying fractions or dividing them, we are not restricted to like and unlike fractions.

Now, we are going to explain how maths operations are performed on fractions with the help of examples in detail.

Arithmetic Operations on Fractions

Basically, there are four operations performed on these fractions:

  • Addition
  • Subtraction
  • Multiplication
  • Division

Addition and Subtraction of Fractions

When we add or subtract the fractions, we need to make sure that the denominators of the fractions are the same or equal. 

Same Denominators:

Example: Add ¾ and 7/4

⇒ ¾ + 7/4

Once we have checked that the denominators are the same, then we will keep the denominators of both the fractions, common, and add the numerators.

⇒ (3+7)/4

⇒ 11/4    (Answer)

In the same way, we can subtract the fractions, with the same denominators.

Example: Subtract ¼ from ¾.

⇒ ¾ – ¼ 

⇒ (3-1)/4

⇒ 2/4

⇒ ½    (Answer)

Different Denominators:

Now, if the denominators are different, then we need to rationalise the denominators first and then perform the required operations. Let us understand with examples.

Example: Add ⅔ and ¾. 

⇒ ⅔ + ¾ 

⇒ 8/12 + 9/12        [LCM of 3 and 4 is 12]

⇒ (8+9)/12

⇒ 17/12    [Answer]

Multiplication and Division of Fractions

When we multiply two or more fractions, then the numerators and denominators of the fractions are multiplied, respectively.

Example: Multiply ⅘ and ⅛

⇒ ⅘ x ⅛

⇒ (4×1)/(5 x 8)

⇒ 4/40

⇒ 1/10     [Answer]

In case of division of fractions, we need to find the reciprocal of the divisor first and then multiply with the dividend. Hence, there is only one step extra while dividing fractions as compared to multiplication.

Example: ⅘ ÷ ⅛

⇒ ⅘ x 8/1    [reciprocal of ⅛ is 8/1]

⇒ 32/5   [Answer]

Thus, we have learned how to add, subtract, multiply and divide the fractions with examples here. 

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