Scale both parts together
A fraction is a ratio of two numbers. Multiplying its numerator and denominator by the same nonzero factor preserves that ratio because you are multiplying by k/k, which equals one.
This is useful when a recipe changes size, a diagram is divided into smaller pieces, or two fractions need a common denominator before addition.
Test equivalence with cross-products
For nonzero denominators, a/b and c/d are equivalent exactly when ad = bc. This test avoids judging rounded decimals, which can make different fractions appear equal.
If a target denominator is a multiple of the original denominator, divide the target by the original to find the scale factor. Apply that factor to the numerator as well.
Keep the task separate from simplification
Generating equivalent fractions makes a family of representations. Simplifying chooses the member with relatively prime integer numerator and denominator. Neither operation changes the amount.
Adding the same number to both parts usually changes the fraction. For example, 1/2 and 2/3 are different even though both numerator and denominator increased by one.
LET’S WORK IT THROUGH
Write 3/7 with denominator 35.
- 35 ÷ 7 = 5.
- Multiply the numerator by the same factor: 3 × 5 = 15.
- Check 3 × 35 = 7 × 15 = 105.
THE ANSWER3/7 = 15/35.
YOUR TURN
A small check for understanding.
Are 8/12 and 10/15 equivalent?
Reveal the answer
Yes. Both simplify to 2/3, and both cross-products equal 120.
Now try your own numbers.
The equivalent fractions includes input guidance and the limits of its supported calculations. Use it alongside the method above.
Open Equivalent fractions ↗A note on precision: preserve exact fractions where possible and round numerical results at the end. Found an unclear step? Prepare a correction report.