Fraction models – compare, add, multiply and divide

What it shows

Fractions are shown as equal parts of a bar, a circle or a grid. On Compare & add, both wholes are cut into the same number of pieces, the lowest common multiple of the denominators, so comparing and adding become counting. Multiply uses an area model: a rectangle a/b tall and c/d wide covers a × c of the b × d cells in each unit square. Divide uses the measurement model and asks how many c/d pieces fit into a/b; the count, including a part piece, equals a/b × d/c. Each step is simplified and shown as a mixed number.

How to use

Choose a screen with the tabs. On Compare & add, tap the model parts to change the numerators and use denom − and denom +. On the other screens, use num −, num + and the denominator buttons; on Multiply you can also drag across the grid. Fraction of an amount has its own − and + buttons for the amount. On Divide, predict how many pieces fit before reading the answer, then check it against the reciprocal.

Parameters you can change

• First numerator 0–12
• First denominator 1–12
• Second numerator 0–12
• Second denominator 1–12
• Model type Bar, Circle
• Screen Compare & add, Multiply, Fraction of an amount, Divide
• Amount (Fraction of an amount screen) 1–60

Questions to explore

1. Why is 1/3 + 1/4 not equal to 2/7, as the shaded pieces of the models show?
2. Why is the product of two fractions less than 1 smaller than each of them?
3. On Divide, why does 2/3 ÷ 1/6 give 4, and how does this match multiplying by 6?