Scale the numerator and denominator together
Multiplying both parts of 1/7 by 2 gives 2/14; multiplying by 3 gives 3/21. 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 35. The scale factor is 35 ÷ 7 = 5. Multiply the numerator too: 1 × 5 = 5. Therefore 5/35 is the required representation.
The fraction 1/7 is already reduced. With integer numerators and denominators, any equivalent positive denominator must be a multiple of 7. A requested denominator that is not a multiple cannot be reached with an integer numerator.
Verify rather than compare rounded decimals
Cross-multiply 1/7 and 5/35: 1 × 35 = 35, and 7 × 5 = 35. Equal cross-products confirm exact equivalence.
Adding one to both parts would give 2/8, which is not equivalent: the cross-products 8 and 14 differ. Scaling is multiplication or division of both parts by the same nonzero factor, not equal addition.
LET’S WORK IT THROUGH
Rewrite 1/7 using a denominator of 28.
- Find the multiplier: 28 ÷ 7 = 4.
- Apply it to the numerator: 1 × 4 = 4.
- Reduce 4/28 by 4 to check the original fraction.
THE ANSWER4/28 is equivalent to 1/7.
YOUR TURN
A small check for understanding.
Is 6/42 equivalent to 1/7?
Reveal the answer
Yes. Both parts were multiplied by 6, and both cross-products equal 42.
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.