Scale the numerator and denominator together
Multiplying both parts of 13/17 by 2 gives 26/34; multiplying by 3 gives 39/51. 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 85. The scale factor is 85 ÷ 17 = 5. Multiply the numerator too: 13 × 5 = 65. Therefore 65/85 is the required representation.
The fraction 13/17 is already reduced. With integer numerators and denominators, any equivalent positive denominator must be a multiple of 17. A requested denominator that is not a multiple cannot be reached with an integer numerator.
Verify rather than compare rounded decimals
Cross-multiply 13/17 and 65/85: 13 × 85 = 1105, and 17 × 65 = 1105. Equal cross-products confirm exact equivalence.
Adding one to both parts would give 14/18, which is not equivalent: the cross-products 234 and 238 differ. Scaling is multiplication or division of both parts by the same nonzero factor, not equal addition.
LET’S WORK IT THROUGH
Rewrite 13/17 using a denominator of 68.
- Find the multiplier: 68 ÷ 17 = 4.
- Apply it to the numerator: 13 × 4 = 52.
- Reduce 52/68 by 4 to check the original fraction.
THE ANSWER52/68 is equivalent to 13/17.
YOUR TURN
A small check for understanding.
Is 78/102 equivalent to 13/17?
Reveal the answer
Yes. Both parts were multiplied by 6, and both cross-products equal 1326.
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.