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
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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