# OPERATIONS ON RATIONAL NUMBERS

Adding Rational Numbers with Same Denominator :

To add two or more rational numbers with same denominator, we have to take the denominator once in common and add the numerators.

Example :

Simplify :  + .

Adding Rational Numbers with Different Denominators :

To add two or more rational numbers with different denominators, we have to follow the steps given below.

Step 1 :

Find the least common multiple of the denominators.

Step 2 :

Make the denominators same using least common multiple and multiplication.

Step 3 :

Take the denominator once in common and add the numerators.

Example :

Simplify : ¼ + .

Least common multiple of (4, 6)  =  12

Multiply the numerator and denominator of the first rational number by 3 to get the denominator 12.

Multiply the numerator and denominator of the second rational number by 2 to get the denominator 12.

## Subtracting Rational Numbers

Subtracting Rational Numbers with Same Denominator :

To subtract two rational numbers with same denominator, we have to take the denominator once in common and subtract the numerators.

Example :

Simplify : ⅖ .

Subtracting Rational Numbers with Different Denominators :

To subtract two rational numbers with different denominators, we have to follow the steps given below.

Step 1 :

Find the least common multiple of the denominators.

Step 2 :

Make the denominators same using least common multiple and multiplication.

Step 3 :

Take the denominator once in common and subtract the numerators.

Example :

Simplify :  - .

Least common multiple of (6, 8)  =  24

Multiply the numerator and denominator of the first rational number by 4 to get the denominator 24.

Multiply the numerator and denominator of the second rational number by 3 to get the denominator 24.

## Multiplying Rational Numbers

To multiply two or more rational numbers, we have to follow the steps given below.

Step 1 :

Simply any numerator with any denominator as much as possible.

Step 2 :

After simplification in step 1, multiply the numerator by numerator and denominator by denominator.

Example :

Simplify : x ¹⁸⁄₂₅.

## Dividing Rational Numbers

To divide two rational numbers, we have to follow the steps given below.

Step 1 :

Change the division as multiplication and take the reciprocal for the second rational number.

Step 2 :

Simply any numerator with any denominator as much as possible.

Step 2 :

After simplification in step 2, multiply the numerator by numerator and denominator by denominator.

Example :

Simplify : ⅔ ÷ ⁸⁄₁₅.

## Distributive Property

(i) Distributive Property of Multiplication Over Addition :

Multiplication of rational numbers is distributive over addition.

Example :

Simplify :  x ( + ).

(ii) Distributive Property of Multiplication Over Subtraction :

Multiplication of rational numbers is distributive over subtraction.

Example :

Simplify : x ( - ).

## Converting Mixed Number to Improper Fraction

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