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Subtracting Fractions

Overview

Slicing the pie.

What is it?

Finding the difference between two fractional parts.

History

Ancient Egyptians used complex tables for this because they only liked fractions with a 1 on top (Unit Fractions).

Key Idea

You can't subtract Apples from Oranges. Make the Bottoms Match.

Practice This Topic

Concept Guide

Plain English: To subtract slices of pizza, the slices must be the same size. You can't subtract a 'half' from a 'quarter' directly. You have to turn the half into two quarters first.

Real-world example: Cooking. You have 3/4 cup of flour, you use 1/2 cup. How much is left?

How to do it

  1. Check the denominators (bottoms).
  2. If different, find a Common Denominator (multiply them).
  3. Subtract the numerators (tops) ONLY.
  4. Keep the denominator the same.
  5. Simplify if possible.
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Common Pitfall

Subtracting the bottoms! 3/4 - 1/4 is NOT 2/0. The bottom number just stays the same.

Word Problem
"You have 3/4 of a tank of gas. You use 1/4. What is left?"
Reasoning: Bottoms match (4). Subtract tops: 3 - 1 = 2. Result: 2/4. Simplify to 1/2.

Practice Examples

Common Denom
3 1 2 1 - - - = - = - 4 4 4 2
Bottoms stay 4.