Equivalent Fractions and Comparing Rational Numbers

Key points

• Multiply or divide the numerator and denominator by the same non-zero number: the value does not change.
• To compare, make the denominators equal (use the LCM), then compare numerators.
• Cross-multiplication: for a/b and c/d (b, d > 0), compare a × d with b × c.
• For negatives the order flips: −3/4 > −5/6 (nearer to 0).

Same amount, different names

Rahul eats 1 of 2 slices; Priya eats 4 of 8 slices of the same pizza. They ate the same amount: 1/2 and 4/8 are equivalent fractions.

p/q = (p × m)/(q × m) for any non-zero m

Comparing two rational numbers

• Write both with a positive denominator.
• Find the LCM of the denominators.
• Rewrite both with the LCM as denominator.
• Compare the numerators.

3/4 vs 5/6: LCM(4, 6) = 12, so 3/4 = 9/12 and 5/6 = 10/12. Since 10 > 9, 5/6 > 3/4.

The negative twist

For negative numbers the order reverses. −3/4 = −0.75 sits to the right of −5/6 ≈ −0.83 on the number line, nearer to 0, so −3/4 > −5/6.

Try it yourself

Goal: Turn any two fractions into the same-sized pieces and see which is bigger, on bars and on a number line.

• Set the two fractions with the + and − buttons (numerators may be negative).
• Press 'Same pieces' to re-cut both bars into LCM pieces.
• Read the verdict and check where both fractions sit on the number line.
• Try −3/4 against −5/6 to see the order flip.

Open the simulation full screen

Quick quiz

5 questions. Choose an answer for each, then submit to see your score and the explanations.