Scale the numerator and denominator together
Multiplying both parts of 11/13 by 2 gives 22/26; multiplying by 3 gives 33/39. These fractions have the same value because the extra factor is 2/2 or 3/3, both equal to one.
The numerator counts selected parts and the denominator describes their size relative to the whole. If you make each part smaller by subdividing it, the selected count must grow by the same factor.
Choose a denominator for the problem
Suppose a worksheet asks for denominator 65. The scale factor is 65 ÷ 13 = 5. Multiply the numerator too: 11 × 5 = 55. Therefore 55/65 is the required representation.
The fraction 11/13 is already reduced. With integer numerators and denominators, any equivalent positive denominator must be a multiple of 13. A requested denominator that is not a multiple cannot be reached with an integer numerator.
Verify rather than compare rounded decimals
Cross-multiply 11/13 and 55/65: 11 × 65 = 715, and 13 × 55 = 715. Equal cross-products confirm exact equivalence.
Adding one to both parts would give 12/14, which is not equivalent: the cross-products 154 and 156 differ. Scaling is multiplication or division of both parts by the same nonzero factor, not equal addition.
LET’S WORK IT THROUGH
Rewrite 11/13 using a denominator of 52.
- Find the multiplier: 52 ÷ 13 = 4.
- Apply it to the numerator: 11 × 4 = 44.
- Reduce 44/52 by 4 to check the original fraction.
THE ANSWER44/52 is equivalent to 11/13.
YOUR TURN
A small check for understanding.
Is 66/78 equivalent to 11/13?
Reveal the answer
Yes. Both parts were multiplied by 6, and both cross-products equal 858.
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.