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Simplifying Fractions
A fraction is in simplest form when the top and bottom have no common factor except 1. To simplify, divide both by their greatest common factor (GCF).
For: Grade 4 to 6 students and anyone who needs a refresher.
The rules
- Find the greatest common factor of the numerator and denominator.
- Divide both by the GCF.
- If you are not sure of the GCF, divide by any common factor and repeat until none is left.
- An improper fraction can be simplified, then written as a mixed number if you like.
Worked examples
Example 1: Simplify 18/24
- Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
- The greatest common factor is 6.
- 18 ÷ 6 = 3 and 24 ÷ 6 = 4.
Answer: 3/4
Example 2: Simplify 45/60
- Both end in 0 or 5, so divide by 5: 9/12.
- 9 and 12 share 3: divide by 3 to get 3/4.
Answer: 3/4
Example 3: Simplify 28/8 and write it as a mixed number
- The GCF of 28 and 8 is 4: 28/8 = 7/2.
- 7 ÷ 2 = 3 remainder 1.
Answer: 7/2 = 3 1/2
Practice problems
- 10/15
- 16/40
- 21/28
- 36/48
- 27/6
Show answers
- 2/3
- 2/5
- 3/4
- 3/4
- 9/2 = 4 1/2
Frequently asked questions
How do you know a fraction is fully simplified?
When the only whole number that divides both the top and the bottom is 1.
Does simplifying change the value of a fraction?
No. A simplified fraction is equivalent to the original; it just uses smaller numbers.
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