Math · Stage 6

Use factor and divisibility tricks to simplify fractions and ratios

Spot a shared factor at a glance — the divisibility tricks (2, 3, 4, 5, 6, 9, 10) tell you what divides both numbers — then divide top and bottom (or both sides of a ratio) by it until nothing else fits.

✦ Math📘 Stage 6 · S6⏱ ~12 min🧒 Ages 10–12★ Free to start

I can use factor and divisibility tricks to simplify fractions and ratios.

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Kavi Splits the Treasure ⚖️

Kavi finds 18 gold coins and 24 silver coins. "Instead of counting them one by one, I look for a number that divides both," Kavi hoots. Both are even, both have digit-sums that share a 3 — so 6 divides each. Divide and the pile becomes a clean 3 : 4. Same trick turns a messy fraction into its simplest form.

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What your child will learn

1Spot a shared factor without dividingBefore you simplify anything, you need to know what divides both numbers. These quick tricks let you tell at a glance — no long division needed. Tap a row.

2Same amount, fewer piecesHere 6 of 8 equal parts are shaded — that is 6/8. Both 6 and 8 are even, so 2 divides both. Group the parts in twos and the same shaded amount reads as 3/4. Tap parts to rebuild it and watch the readout simplify.

3Divide top and bottom until nothing fitsFind a common factor with the tricks, divide top and bottom by it, and repeat until the only common factor left is 1 (then it is in simplest form). Dividing by the HCF in one go is the shortcut. Tap a row.

4A ratio is just a fraction on its sideTo simplify a ratio, divide both sides by a common factor — exactly like a fraction. Keep going until the two numbers are coprime. Tap a row.

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A peek inside

Simplify 18/24 to its simplest form.

Both even and both digit-sums share a 3, so 6 divides both (the HCF). 18÷6=3, 24÷6=4. 3 and 4 are coprime.

Try this at home: Use a trick — does the number divide both? Is 24 divisible by 3? · Is 35 divisible by 5? · Is 42 divisible by 4?

Ready to play and learn?

Start the free interactive lesson, or print the handout for screen-free play.

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Part of Math · Stage 6 · S6 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.