Subtracting Fractions with Unlike Denominators
Subtracting Fractions with Unlike Denominators: The LCD & Butterfly Method
Why You Cannot Subtract Fractions Without Equal Slice Sizes
If you have 3 fourth-slices of a pizza (3/4) and a friend asks for 1 third-slice (1/3), you cannot simply take away 1 sliceโbecause your slices are fourths and their slice is a third!
To make the trade fair, you must slice your pizza into twelfths (12): your 3/4 becomes 9 twelfths, and their 1/3 is worth 4 twelfths. Now you simply subtract: 9 - 4 = 5 twelfths (5/12) remaining!
The 3-Step Recipe for Subtracting Any Fractions
Find the smallest multiple shared by both denominators (e.g. for 4 and 3, LCD = 12).
Multiply top and bottom of each fraction by the matching factor: 3/4 ร 3/3 = 9/12 and 1/3 ร 4/4 = 4/12.
Subtract top numbers: 9 - 4 = 5. Keep the denominator 12. Reduce to simplest terms!
How it works: Cross-multiply diagonally (a ร d) and (b ร c). Subtract the second diagonal from the first for your new numerator (ad - bc), and multiply the bottom numbers (b ร d) for the denominator!
Live Step-by-Step Subtraction Visualizer
Select any subtraction scenario below to see how different denominators are resized into identical common units:
The slice sizes are fourths vs thirds. You cannot take away 1 third from 3 fourths directly. We must slice both into equal twelfths!
3 Mistakes That Cost Students Marks on Fraction Subtraction
Writing 3/4 - 1/2 = 2/2 = 1. This breaks physical reality! 3/4 minus 1/2 is 1/4. Always find the LCD first (3/4 - 2/4 = 1/4).
Writing 5/6 - 1/6 = 4/0. Denominators represent the fixed slice size and NEVER subtract. 5 sixths minus 1 sixth is 4/6 = 2/3!
Leaving an answer like 2/6 or 4/10 without simplifying to 1/3 or 2/5. Always check if top and bottom divide by a common factor!
Test Your Understanding in 60 Seconds
Select your answers and click "Check Answers" to test your mastery:
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| Problem Type | Original | Equivalent (LCD) | Difference | Simplest Form |
|---|---|---|---|---|
| Co-Prime Denominators | 3/4 - 1/3 | 9/12 - 4/12 | 5/12 | 5/12 |
| Requires Reducing | 5/6 - 1/2 | 5/6 - 3/6 | 2/6 | 1/3 |
| Factor Multiple | 7/8 - 1/4 | 7/8 - 2/8 | 5/8 | 5/8 |
(aรd) - (bรc) for top. Multiply bottoms (bรd) for bottom!Need Practice Worksheets for This Topic?
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