# Rational Number

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A rational number is a number which can be expressed as a fraction. A rational number can be expressed as P/q form. Where p and q are integers. The condition for the rational number is the denominator cannot be equal to zero i.e.q ≠ 0. The rational numbers question can be solved or simplified using different mathematical properties such as multiplicative property, associative property, additive inverse multiplicative inverse and many more.

Example 1: Solve the given rational numbers 2/3 (1/3 + 5/6).

Solution: Given in the question is 2/3 (1/3 + 5/6).

First add the two rational numbers 1/3 and 5/6.

Here we need the LCM of 3 and 6 which is 6.

Therefore the common denominator is 6.

Hence the sum of the fractions is 2/3 + 5/6 = 7/6.

Now the sum of the two rational numbers is multiplied to the rational number 2/3.

This gives (2/3) * (7/6) = 14/18.

Simplifying the rational number gives 7/9

Hence solution is 7/9.

Example 2: Solve the given rational numbers 5/4 (2/5 + 1/10).

Solution: Given in the question is 5/4 (2/5 + 1/10).

First add the two rational numbers 2/5 and 1/10.

Here we need the LCM of 5 and 10 which is 10.

Therefore the common denominator is 10.

Hence the sum of the fractions is 4/10 + 1/10 = 5/10.

Now the sum of the two rational numbers is multiplied to the rational number 5/4.

This gives (5/4) * (5/10) = 25/40.

Simplifying the rational number gives 5/8

Hence solution is 5/8.