Equivalent Fractions
Different fractions can name the same amount.
About this topic
Equivalent fractions look different but name the same amount, such as 1/2, 2/4 and 50/100. You create one by multiplying or dividing both the numerator and denominator by the same non-zero number, which is really multiplying by a form of 1.
Simplifying a fraction means dividing by the GCD until no more common factors remain. Equivalent fractions are the key to comparing fractions and to adding or subtracting them, because you must first rewrite them over a common denominator. For instance, 2/3 and 8/12 are equal, since multiplying top and bottom of 2/3 by 4 gives 8/12.
A visual helps: a rectangle split into 2 columns with 1 shaded shows 1/2. Cut each column into two rows and 2 of 4 boxes are shaded, which shows 2/4. The shaded area never changed, only how we sliced it. To test two fractions, cross-multiply: 3/5 and 9/15 are equal because 3 × 15 = 5 × 9 = 45. Recipes use equivalence when you swap a half cup for two quarter cups.
A common error is adding the same number to the top and bottom, as in turning 1/2 into 3/4. That changes the value. Only multiplication or division keeps it the same. Writing a fraction in lowest terms makes answers easy to compare and is usually expected in a final answer.
Key ideas
- Multiply top and bottom by the same number
- Divide both by their GCD to simplify
- Equivalent fractions have the same decimal
Quick check
Use cases: where Equivalent Fractions helps
- Homework: review the key idea behind Equivalent Fractions before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Equivalent Fractions without notes.
- Visual learning: play with the interactive lab to see how Equivalent Fractions changes when you adjust its inputs.
- Teaching a friend: explain Equivalent Fractions in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Equivalent Fractions?
Different fractions can name the same amount.
What will I learn in Equivalent Fractions?
Multiply top and bottom by the same number. Divide both by their GCD to simplify. Equivalent fractions have the same decimal.
Is Equivalent Fractions part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Equivalent Fractions lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Equivalent Fractions?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.