Simplifying Fractions
Divide numerator and denominator by their GCD.
Key idea
Divide numerator and denominator by their GCD.
In depth
To simplify, divide top and bottom by their GCD. The fraction is in lowest terms when the GCD is 1. The value does not change; only the representation does.
Worked example
18/24: GCD = 6, so 18/24 = 3/4.
Formula
Real-world uses
- Writing exam answers in lowest terms
- Reducing ratios on maps and in engineering drawings
Common mistake
Cancelling terms instead of factors. In (2+3)/(2+5) you cannot cancel the 2s.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Simplifying Fractions?
Divide numerator and denominator by their GCD. It is a topic at the intermediate level in Arithmetic & Number Sense.
What is the formula for Simplifying Fractions?
The key formula is 12/18 = 2/3.
Where is Simplifying Fractions used in real life?
Real-world examples: Writing exam answers in lowest terms; Reducing ratios on maps and in engineering drawings.
What should I learn before Simplifying Fractions?
Make sure you are comfortable with Equivalent Fractions, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Simplifying Fractions?
Cancelling terms instead of factors. In (2+3)/(2+5) you cannot cancel the 2s.
How can I practise Simplifying Fractions?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Simplifying Fractions?
Move on to Comparing Fractions next.
Related intermediate topics in Arithmetic & Number Sense
- Long Multiplication – Multiply by each digit of the multiplier, shift by place value, then add partial products.
- Long Division – Divide, multiply, subtract and bring down repeatedly to get the quotient.
- Factors and Multiples – Factors divide a number exactly; multiples are its products with whole numbers.
- Divisibility Rules – Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9.
- Prime Numbers – A prime has exactly two positive divisors: 1 and itself.
- Composite Numbers – Numbers greater than 1 with more than two factors.