We will learn about subtraction of rational numbers. If a/b and c/d are two rational numbers, then subtracting c/d from a/b means adding additive inverse (negative) of c/d to a/b. The subtracting of c/d from a/b is written as a/b - c/d.

Thus, we have

a/b - c/d = a/b + (-c/d), [Since additive inverse of c/d is -c/d]

How to solve subtraction of two rational numbers?

The examples will illustrate the procedure to solve subtraction of rational numbers.

**1.** Subtract 2/5
from 4/7

**Solution: **

The additive inverse of 2/5 is -2/5

Therefore, 4/7 - 2/5 = 4/7 + (-2/5)

⇒ 4/7 - 2/5 = 4 × 5/7 × 5 + (-2) × 7/5 × 7

= 20/35 + -14/35

= 20 + (-14)/35

= 6/35

Therefore, 4/7 - 2/5 = 6/35

**2.** Subtract -6/7 from -5/8.

**Solution: **

The additive inverse of -6/7 is 6/7

Therefore, -5/8 - (-6/7) = -5/8 + 6/7, [Since, -(-6/7) = 6/7)]

⇒ -5/8 - (-6/7) = -5 × 7/8 × 7 + 6 × 8/7 × 8

⇒ -5/8 - (-6/7) = -35/56 + 48/56

⇒ -5/8 - (-6/7) = -35 + 48/56

⇒ -5/8 - (-6/7) = 13/56

Therefore, -5/8 - (-6/7) = 13/56

**3.** Subtract -4/9
from 2/5

**Solution:**

The additive inverse of -4/9 is 4/9.

Therefore, 2/5 - (-4/9) = 2/5 + 4/9, [Since, -(-4/9) = 4/9)]

⇒ 2/5 - (-4/9) = 2 × 9/5 × 9 + 4 × 5/9 × 5

⇒ 2/5 - (-4/9) = 18/45 + 20/45

⇒ 2/5 - (-4/9) = 18 + 20/45

Therefore, 2/5 - (-4/9) = 38/45

**4.** The sum of two rational numbers is
-3/5. If one of the number is -9/20, find the other.

**Solution:**

Sum other number = -3/5, One number = -9/20

Therefore, the other number = Sum of the two rational numbers - One of the given rational number.

= -3/5 - (-9/20)

= -3/5 + 9/20, [Since - (-9/20) = 9/20]

= (-3) × 4 + 9 × 1/20

= -12 + 9/20

= -3/20

Therefore, the required rational number is -3/20.

**5.** Which rational number should be
added to -7/11 so as to get 4/7?

**Solution: **

Su of the given number and the required rational number = 4/7.

Given rational number = -7/11.

Therefore, the required number = Sum - Given number

= 4/7 + 7/11

= 4 × 11/7 ×11 + 7 × 7/11 × 7

= 44/77 + 49/77

= 44 + 49/77

= 93/77

Thus, the rational number 93/77 should be added to -7/11 so as to get 4/7.

**6.** What should be subtracted from
-4/5 so as to get 6/15?

**Solution:**

Difference of the given rational number and the required rational number = 6/15.

Given rational number = -4/5.

Therefore the required rational number = -4/5 - 6/15

= -4/5 + -6/15

= (-4) × 3/5 × 3 + -6/15

= -12/15 + -6/15

= (-12) + (-6)/15

= -18/15

= -6/5

Thus, the rational number -6/5 subtracted from -4/5 so as to get 6/15.

● **Rational Numbers**

Introduction of Rational Numbers

Is Every Rational Number a Natural Number?

Is Every Rational Number an Integer?

Is Every Rational Number a Fraction?

Equivalent form of Rational Numbers

Rational Number in Different Forms

Properties of Rational Numbers

Lowest form of a Rational Number

Standard form of a Rational Number

Equality of Rational Numbers using Standard Form

Equality of Rational Numbers with Common Denominator

Equality of Rational Numbers using Cross Multiplication

Comparison of Rational Numbers

Rational Numbers in Ascending Order

Rational Numbers in Descending Order

Representation of Rational Numbers on the Number Line

Rational Numbers on the Number Line

Addition of Rational Number with Same Denominator

Addition of Rational Number with Different Denominator

Properties of Addition of Rational Numbers

Subtraction of Rational Number with Same Denominator

Subtraction of Rational Number with Different Denominator

Subtraction of Rational Numbers

Properties of Subtraction of Rational Numbers

Rational Expressions Involving Addition and Subtraction

Simplify Rational Expressions Involving the Sum or Difference

Multiplication of Rational Numbers

Properties of Multiplication of Rational Numbers

Rational Expressions Involving Addition, Subtraction and Multiplication

Reciprocal of a Rational Number

Rational Expressions Involving Division

Properties of Division of Rational Numbers

Rational Numbers between Two Rational Numbers

**8th Grade Math Practice**

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● **Rational Numbers - Worksheets**

Worksheet on Equivalent Rational Numbers

Worksheet on Lowest form of a Rational Number

Worksheet on Standard form of a Rational Number

Worksheet on Equality of Rational Numbers

Worksheet on Comparison of Rational Numbers

Worksheet on Representation of Rational Number on a Number Line

Worksheet on Adding Rational Numbers

Worksheet on Properties of Addition of Rational Numbers

Worksheet on Subtracting Rational Numbers

Worksheet on Addition and
Subtraction of Rational Number

Worksheet on Rational Expressions Involving Sum and Difference

Worksheet on Multiplication of Rational Number

Worksheet on Properties of Multiplication of Rational Numbers

Worksheet on Division of Rational Numbers

Worksheet on Properties of Division of Rational Numbers

Worksheet on Finding Rational Numbers between Two Rational Numbers

Worksheet on Word Problems on Rational Numbers

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