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Fractions help

Cross-cancelling

Cross-cancelling is a shortcut for multiplying fractions. Instead of simplifying at the end — after multiplying — you simplify before you start. This keeps the numbers smaller and the working easier. You do not have to use it. But when the numbers are big, it saves a lot of work.

What this looks like in the game

You tap a fish and see something like "Work out 4/9 × 3/8." The game expects a fully simplified answer. You can multiply first and simplify at the end — or you can cross-cancel first to make the numbers easier.

How cross-cancelling works

When you multiply two fractions, you times the top numbers and the bottom numbers. Before you do that, look diagonally across the two fractions. If a top number and a bottom number share a factor, you can divide both by that factor now — before multiplying.

You can cross-cancel in both directions if there are common factors in both pairs.

Worked example 1 — with cross-cancelling

Work out 4/9 × 3/8

Cross-cancel diagonally: 4 (top left) and 8 (bottom right)

Both divide by 4 → 4 becomes 1, 8 becomes 2

Cross-cancel: 3 (top right) and 9 (bottom left)

Both divide by 3 → 3 becomes 1, 9 becomes 3

Now multiply with the smaller numbers

1/3 × 1/2 = 1/6

Worked example 2 — without cross-cancelling

Work out 4/9 × 3/8 without cross-cancelling

Top: 4 × 3 = 12  ·  Bottom: 9 × 8 = 72

Simplify 12/72 (both divide by 12)

1/6 — same answer, but 72 is much harder to work with.

Cross-cancelling got you there more easily.

The most common mistake

Watch out for

Cross-cancelling with numbers that are in the same fraction — top and bottom of the same fraction — rather than diagonally across two fractions.

Wrong

In 4/9 × 3/8, trying to cancel the 4 and 9 because they are in the same fraction. That is simplifying one fraction — not cross-cancelling.

Right

Cross-cancel diagonally: 4 (top of first) with 8 (bottom of second), and 3 (top of second) with 9 (bottom of first).

The numbers you cancel must be in different fractions — one a top number, one a bottom number, from different fractions.

Which game stage uses this

Cross-cancelling is its own stage in FishyFractions — it is where the game rewards you for working cleverly, not just correctly. You will see these questions when you reach the shark and manta ray.

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