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Fractions help

Multiplying and dividing mixed numbers

Multiplying and dividing mixed numbers is the final stage of FishyFractions. It combines what you have already learned — converting mixed numbers, multiplying fractions, and dividing using the reciprocal — into one.

What this looks like in the game

You tap a fish and see something like "Work out 1 and 1/2 × 2 and 2/3." You drag tiles to build the answer. At this stage, the numbers are bigger and the steps are more involved — but every individual step is something you have already done.

How to multiply mixed numbers

Convert both mixed numbers to improper fractions.

Multiply across (times the tops, times the bottoms).

Simplify — or use cross-cancelling to simplify before multiplying.

Convert back to a mixed number if the answer is bigger than 1.

Worked example 1 — multiplying mixed numbers

Work out 1 and 1/2 × 2 and 2/3

Convert

1 and 1/2 → (1 × 2) + 1 = 3 → 3/2

2 and 2/3 → (2 × 3) + 2 = 8 → 8/3

Cross-cancel: 3 (top left) and 3 (bottom right) → both become 1. 8 (top right) and 2 (bottom left) → divide by 2 → 4 and 1.

1/1 × 4/1

Answer: 4

How to divide mixed numbers

Convert both mixed numbers to improper fractions.

Keep the first fraction, change ÷ to ×, flip the second fraction.

Multiply across.

Simplify.

Convert back to a mixed number if needed.

Worked example 2 — dividing mixed numbers

Work out 2 and 2/5 ÷ 1 and 1/5

Convert

2 and 2/5 → (2 × 5) + 2 = 12 → 12/5

1 and 1/5 → (1 × 5) + 1 = 6 → 6/5

Keep, change, flip

12/5 ÷ 6/5 → 12/5 × 5/6

Cross-cancel: 12 and 6 → divide by 6 → 2 and 1. The 5s cancel → both become 1.

2/1 × 1/1

Answer: 2

The most common mistake

Watch out for

Forgetting to convert to improper fractions before multiplying or dividing.

Wrong

1 and 1/2 × 2 and 2/3 → multiply whole parts (1 × 2 = 2) and fraction parts (1/2 × 2/3 = 1/3) separately → 2 and 1/3. Incorrect.

Right

Convert first: 3/2 × 8/3 = 4. The answer is 4, not 2 and 1/3.

Mixed numbers cannot be multiplied or divided directly. Always convert them to improper fractions first.

Which game stage uses this

This is the Master level — the final stage in FishyFractions. You will see these questions when the bioluminescent jellyfish appears.

← Cross-cancelling
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