Generating equivalent fractions
I can make equivalent fractions by multiplying or dividing the numerator and denominator by the same non-zero number.
Learn
A recipe needs 2/3 cup, but your measuring cup only shows twelfths. How many twelfths do you need?
Multiplying the numerator and denominator by the same number splits every part into smaller equal pieces. The amount stays the same.
Example: 2/3 × 4/4 = 8/12. Each third became 4 twelfths, so 2 thirds became 8 twelfths.
Dividing both by a common factor joins pieces back together. 6/9 ÷ 3/3 = 2/3. This is called simplifying.
A fraction is in simplest form when the numerator and denominator have no common factor other than 1. You can never multiply or divide by zero here.
Worked examples
Scaling up
- To go from 3 to 12, multiply by 4.
- Multiply the numerator by 4 too: 2 × 4 = 8.
- 2/3 = 8/12.
Simplifying
- Look at 12/18. Both 12 and 18 are divisible by 6.
- 12 ÷ 6 = 2 and 18 ÷ 6 = 3.
- 12/18 = 2/3, and 2 and 3 share no other factor.
Explore
Start at 2/3. Double the denominator and numerator to 4/6, then 8/12. The shaded length stays the same.
Guided practice
Use the hints as much as you like. You can try each question as many times as you need.
0 of 2 solved
Fill in the missing numerator: 2/3 = ?/12. Type the full fraction.
Write 6/9 in simplest form.
Independent practice
Answers are checked exactly — equivalent fractions count unless a question asks for a particular form.
0 of 4 solved
Write 3/5 with a denominator of 15.
Write 10/15 in simplest form.
Write 18/24 in simplest form.
Which step keeps a fraction equivalent?
Common mistakes
Adding the same number to the top and bottom (1/2 → 3/4).
Why it happens: Adding does not split parts evenly, so the amount changes.
What to do: Only multiply or divide both numbers by the same non-zero number.
Stopping too early when simplifying (12/18 → 6/9).
Why it happens: 6 and 9 still share a factor of 3.
What to do: Keep dividing until the only common factor is 1, or use the greatest common factor at once.
Lesson check
Three practice questions to check your understanding. Hints and retries are allowed, so this counts as practice — not mastery.
0 of 3 solved
Write 3/4 with a denominator of 20.
Write 14/21 in simplest form.
Write 8/12 in simplest form.
Show mastery on your own
Ready? Answer 4 new questions with no hints and one try each. This is the only way a lesson is marked as mastered.
Start mastery check