# Subtraction of Rational Numbers

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

What is Rational Numbers?

Is Every Rational Number a Natural Number?

Is Zero a Rational Number?

Is Every Rational Number an Integer?

Is Every Rational Number a Fraction?

Positive Rational Number

Negative Rational Number

Equivalent Rational Numbers

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

Representation of 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 Different Denominator

Subtraction of Rational Numbers

Properties of Subtraction of Rational Numbers

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

Division of Rational Numbers

Rational Expressions Involving Division

Properties of Division of Rational Numbers

To Find Rational Numbers

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