Equivalent Fractions
Multiply or divide numerator and denominator by the same non-zero number.
Key idea
Multiply or divide numerator and denominator by the same non-zero number.
In depth
Multiplying or dividing numerator and denominator by the same non-zero number does not change the value, because you are multiplying by 1 in disguise. This is how you convert to a common denominator.
Worked example
1/2 = 2/4 = 3/6 = 50/100.
Formula
Real-world uses
- Comparing discounts such as 1/4 off and 25% off
- Scaling a recipe up or down
Common mistake
Adding the same number to top and bottom. 1/2 and 2/3 are not equal.
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 Equivalent Fractions?
Multiply or divide numerator and denominator by the same non-zero number. It is a topic at the intermediate level in Arithmetic & Number Sense.
What is the formula for Equivalent Fractions?
The key formula is a/b = ka/kb.
Where is Equivalent Fractions used in real life?
Real-world examples: Comparing discounts such as 1/4 off and 25% off; Scaling a recipe up or down.
What should I learn before Equivalent Fractions?
Make sure you are comfortable with Fractions Basics, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Equivalent Fractions?
Adding the same number to top and bottom. 1/2 and 2/3 are not equal.
How can I practise Equivalent 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 Equivalent Fractions?
Move on to Simplifying 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.