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How do you subtract rational numbers Class 8?

Published in Rational Numbers 3 mins read

To subtract rational numbers, you add the opposite (additive inverse) of the number you're subtracting. This transforms the subtraction problem into an addition problem, which is often easier to manage.

Here's a breakdown of how to subtract rational numbers, suitable for a Class 8 understanding:

Understanding the Basics

  • Rational Numbers: Remember that rational numbers can be expressed as a fraction p/q, where p and q are integers, and q is not zero. Examples include 1/2, -3/4, 5 (which is 5/1), and -2.

  • Additive Inverse (Opposite): The additive inverse of a number is the number that, when added to the original number, results in zero. For example, the additive inverse of 3 is -3, and the additive inverse of -1/2 is 1/2.

Steps for Subtracting Rational Numbers

  1. Identify the Numbers: Determine the two rational numbers you need to subtract. Let's say you want to calculate a/b - c/d.

  2. Find the Additive Inverse: Find the additive inverse of the number you're subtracting (the subtrahend). In the example a/b - c/d, the additive inverse of c/d is -c/d.

  3. Rewrite as Addition: Change the subtraction problem to an addition problem by adding the additive inverse. So, a/b - c/d becomes a/b + (-c/d).

  4. Find a Common Denominator (if necessary): If the rational numbers do not have a common denominator, find the least common multiple (LCM) of the denominators and rewrite the fractions with the common denominator.

  5. Add the Numerators: Add the numerators of the fractions, keeping the common denominator.

  6. Simplify (if possible): Simplify the resulting fraction to its lowest terms.

Examples

Example 1: Subtracting with a Common Denominator

Calculate: 5/7 - 2/7

  • Additive inverse of 2/7 is -2/7.
  • Rewrite: 5/7 + (-2/7)
  • Add numerators: (5 + (-2)) / 7 = 3/7
  • Answer: 3/7

Example 2: Subtracting with Different Denominators

Calculate: 1/2 - 1/3

  • Additive inverse of 1/3 is -1/3.
  • Rewrite: 1/2 + (-1/3)
  • Find a common denominator: The LCM of 2 and 3 is 6.
  • Rewrite with common denominator: 3/6 + (-2/6)
  • Add numerators: (3 + (-2)) / 6 = 1/6
  • Answer: 1/6

Example 3: Subtracting a Negative Rational Number

Calculate: 1/4 - (-1/2)

  • Additive inverse of -1/2 is 1/2.
  • Rewrite: 1/4 + 1/2
  • Find a common denominator: The LCM of 4 and 2 is 4.
  • Rewrite with common denominator: 1/4 + 2/4
  • Add numerators: (1 + 2) / 4 = 3/4
  • Answer: 3/4

Key Takeaway

Subtracting rational numbers is essentially adding the opposite. By understanding the concept of additive inverses and following the steps above, you can confidently subtract any rational numbers.

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