Maths · Multiplying Fractions
Area Grid
Slide the coral band to and the teal band to . Where they cross is .
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Why this works
Cutting the square into 3 rows and 4 columns makes equal cells, and the two bands cross over of them. That is the whole reason you multiply the tops and multiply the bottoms: the tops count the rows and columns the overlap covers, and the bottoms count the rows and columns the square was cut into. cancels by 6 to , the same rectangle regrouped into bigger pieces. Notice the overlap is smaller than either band on its own - taking a fraction OF something always shrinks it, which is why adding the two fractions can never be the answer.
Helping a child through Area Grid
It runs in 3 steps
- 1. Build it. Slide the coral band to of the height and the teal band to of the width.
- 2. Cancel it. The overlap covers 6 of the 12 cells. Pull the simplify handle as far as it will go.
- 3. Without the square. The square is covered. What is ?
Hints, least revealing first
- of the HEIGHT and of the WIDTH. Drag one band at a time and watch the ruled cells change.
- The whole square is now cut into little cells, and the overlap covers of them.
- is not in its simplest form - both numbers divide by 6.
When they finish it: “The overlap IS the product.”
3 11+ skills this exercise practises
Each of these has its own page, with a worked example on it.
- Find a fraction of a quantityCalculate one unit or non-unit fraction of a quantity.
- Multiply fractionsMultiply two proper fractions and simplify the result when required.
- Recognise equivalent fractionsRecognise two fractions representing the same value.
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