## LetsPlayMaths.Com

WELCOME TO THE WORLD OF MATHEMATICS

# Class-7 Rational Numbers

Introduction to Rational Number

Positive Rational Number

Negative Rational Number

Properties of Rational Number

Comparison of Rational Number

Subtraction of Rational Number

Multiplication of Rational Number

Reciprocal of Rational Number

Division of Rational Number

Rational Numbers Test

Rational Number Worksheet

## Introduction to Rational Numbers

Rational number can be defined as a ratio or fraction (PQ) form where numerator and denominator are integer and denominator (Q) should not be equal to zero.

Example: 58 is an example of rational number as 5 and 8 are integers and 8 ≠ 0
In the same way -112, 9-2, -43-7 are also rational number.

## Positive Rational Number

When both the numerator and denominator are positive or negative integer then they are said to be Positive Rational Number. Let's see some examples.

Examples -25-13 (can be written as 2513), 1719 etc.

## Negative Rational Number

When one of the numerator or denominator is negative integer then they are said to be Negative Rational Number. Let's see some examples.

Example: -2527, 15-17 etc.

• If both the numerator and denominator of a rational number is either positive or negative, then multiplying −1 to numerator or denominator will convert the rational number to negative.
• If any of the numerator or denominator of a rational number is negative, then multiplying −1 to the negative part of the numerators or denominator will convert the rational number to positive.

Example: 35 = (3 × (-1))5 = -35

-615 = ((-6)×(-1))15 = 615

## Properties of Rational Number

1. Every integer is a rational number but every rational number is not an integer.

E.g. 79 is a rational number and 9 ≠ 0 but 79 not an integer.

E.g. -79 is a rational number and 9 ≠ 0 but -79 not an integer.

2. Every natural number and whole number is also an integer and so a rational number.

3. zero (0) is also a rational number but it is neither positive nor negative.

## Comparison of Rational Number

Before comparing the rational numbers, we must remember the following points:

1. Every positive rational number is greater than 0 and every negative number.

95 > 0, 95 > -32

2. Every negative rational number is less than 0 and every positive number.

-33 < 0, -53 < 1323

3. Zero is greater than every negative number and smaller than every positive number.

418 > 0 > -418

Example 1. Compare 57 and -25

Solution. As we know Every positive rational number is greater than every negative number.

57 > -25.

Example 2. Compare -12 and -54

Solution. Here both are negative rational number having different denominators. So, we have to make both the denominators same.

-12 = (-1×2)(2×2) = -24

Then compare the rational number of same denominators.

-24 > -54

-12 > -54

When the denominators are equal:

• By keeping the denominators same simply add the numerators.
• Simplify the result if possible.
Let's see some examples.

Example 1. Add 25 and 35

Solution. 25 + 35

= (2+3)5

= 55

= 1

Example 2. Add 59 and -49

Solution. 59 + -49

= {5+(-4)}9

= (5-4)9

= 19

When the denominators are unequal:

• Find out LCM of the denominators of the given rational numbers.
• Convert the given rational numbers to have LCM as the common denominator.
• Add the newly converted rational numbers by following the process of equal denominators
Let's see some examples.

Example 1. Add -45 and 72

Solution. -45 + 72

LCM of 5 and 2 is 10.

-45 = -4×25×2 = -810

72 = 7×52×5 = 3510

-810 + 3510

(-8+35)10 = 2710

## Subtraction of Rational Number

When the denominators are equal:

• By keeping the denominators same simply subtract the numerators.
• Simplify the result if possible.
Let's see some examples.

Example 1. Subtract 25 from 35

Solution. 3525

= (3-2)5

= 15

Example 2. Subtract -27 from 37

Solution. 37-27

= {3-(-2)}7

= (3+2)7

= 57

When the denominators are unequal:

• Find out LCM of the denominators of the given rational numbers.
• Convert the given rational numbers to have LCM as the common denominator.
• Subtract the newly converted rational numbers by following the process of equal denominators
Let's see some examples.

Example 1. Subtract 45 from 72

Solution. 7245

LCM of 5 and 2 is 10.

72 = 7×52×5 = 3510

45 = 4×25×2 = 810

Now, subtract 3510 from 810.

3510810

(35-8)10 = 2710

## Multiplication of Rational Number

• Multiply the numerators of given rational numbers and the product becomes numerator
• multiply the denominators of given rational numbers and the product becomes denominator of the result
• Simplify the result if possible
Let's consider ab and cd are two rational numbers.

ab x cd = (axc)(bxd)

Example 1. Multiply 45 and 27.

Solution. 45 × 27

= (4×2)(5×7)

= 835

Example 2. Multiply -59 and 35.

Solution. -59 × 35

= (-5×3)(9×5)

= -1545

= -13

## Reciprocal of Rational Number

When the product of two rational number is 1 then each one is called the reciprocal of other. In other words ab rational number reciprocal is ba.
Let's see some examples.

Example 1. Find the reciprocal of 45.

Solution. Reciprocal of 45 = 54

Example 2. Find the reciprocal of 7-9.

Solution. Reciprocal of 7-9 = -97

## Division of Rational Number

If PQ and RS are two rational number to be divided, then multiply PQ with reciprocal of RS i.e. SR.

Let's see some examples.

Example 1. Divide 45 by 25.

Solution. 45 ÷ 25

Reciprocal of 25 = 52

45 × 52 = 2

Example 2. Divide 37 by -514.

Solution. 37 ÷ -514

Reciprocal of -514 = 14-5 = -145

37 × -145 = -65

## Class-7 Rational Numbers Test

Rational Numbers - 1

Rational Numbers - 2

## Class-7 Rational Numbers Worksheet

Rational Numbers Worksheet - 1

Rational Numbers Worksheet - 2

Rational Numbers Worksheet - 3

Rational Numbers Worksheet - 4