Math · Stage 4
Compare fractions quickly by cross-multiplying
No need to find a common denominator the long way — multiply across the X and the bigger cross-product wins. a/b > c/d exactly when a×d > c×b.
✦ Math📘 Stage 4 · S4⏱ ~11 min🧒 Ages 8–9★ Free to start
I can compare two fractions quickly by cross-multiplying: a/b > c/d exactly when a×d > c×b.
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Kavi's X-Ray Fraction Trick ✖️
Kavi has to say which is bigger — 2/3 or 3/4 🍕. "The slow way is to rename both into twelfths," hoots Kavi, "but watch this ⚡!" Kavi draws a big X across the two fractions: 2 × 4 = 8 on one arm and 3 × 3 = 9 on the other. "Nine beats eight, so 3/4 is bigger — and I never found a common denominator at all!"
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What your child will learn
1Which is bigger — 2/3 or 3/4?Here is 2/3 drawn on a bar — two of three equal parts shaded. Next to it imagine 3/4. The pieces are different sizes, so you cannot just look. The slow fix is to rename both into twelfths (2/3 = 8/12, 3/4 = 9/12). We are about to do the same comparison in one quick step.
2Multiply across the XTo compare 2/3 and 3/4, draw an X. Multiply up the diagonals: the top of the first times the bottom of the second, and the top of the second times the bottom of the first. Write each product next to the fraction it came from. Tap each card.
3It IS the common denominator — just fasterCross-multiplying is not magic. Renaming 2/3 and 3/4 to the common bottom 12 gives 8/12 and 9/12, and you then compare the tops: 8 vs 9. Cross-multiplying jumps straight to those two tops without drawing the twelfths. Tap each card.
4Cross-multiply, then sort
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A peek inside
Which is bigger — 2/3 or 3/4? Use the cross-multiply X ✖️.
2 × 4 = 8 (beside 2/3), 3 × 3 = 9 (beside 3/4); 8 < 9
Try this at home: Cross-multiply to compare 1/2 and 3/5: 1 × 5 = __ · 3 × 2 = __ · so ___ is bigger
Ready to play and learn?
Start the free interactive lesson, or print the handout for screen-free play.
Part of Math · Stage 4 · S4 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.