Scale the numerator and denominator together
Multiplying both parts of 8/9 by 2 gives 16/18; multiplying by 3 gives 24/27. 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 45. The scale factor is 45 ÷ 9 = 5. Multiply the numerator too: 8 × 5 = 40. Therefore 40/45 is the required representation.
The fraction 8/9 is already reduced. With integer numerators and denominators, any equivalent positive denominator must be a multiple of 9. A requested denominator that is not a multiple cannot be reached with an integer numerator.
Verify rather than compare rounded decimals
Cross-multiply 8/9 and 40/45: 8 × 45 = 360, and 9 × 40 = 360. Equal cross-products confirm exact equivalence.
Adding one to both parts would give 9/10, which is not equivalent: the cross-products 80 and 81 differ. Scaling is multiplication or division of both parts by the same nonzero factor, not equal addition.
LET’S WORK IT THROUGH
Rewrite 8/9 using a denominator of 36.
- Find the multiplier: 36 ÷ 9 = 4.
- Apply it to the numerator: 8 × 4 = 32.
- Reduce 32/36 by 4 to check the original fraction.
THE ANSWER32/36 is equivalent to 8/9.
YOUR TURN
A small check for understanding.
Is 48/54 equivalent to 8/9?
Reveal the answer
Yes. Both parts were multiplied by 6, and both cross-products equal 432.
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.