The numerator and denominator are separate cards feeding a fraction card. Change either and the reduced fraction, the mixed number, the decimal and the bar diagram all update. 8/12 becomes 2/3; 7/3 becomes 2 and 1/3.
How to read this board
A fraction card reads its first connection as the numerator and its second as the denominator. So the cards named "Numerator" and "Denominator" are only number cards — what makes a fraction is the way they are wired.
The bar diagram is what does the work. It splits a bar into as many parts as the denominator and fills as many as the numerator, so 8/12 and 2/3 fill the same length, and reducing turns out to be "smaller digits, same amount".
Where it trips you up
The places that are easy to get wrong, next to how to check each one on the board.
| Where it trips you up | Why that happens | How the board shows it |
|---|---|---|
| Forgetting to reduce | Reducing means dividing top and bottom by the same number to reach a simpler form of the same size. It happens after the arithmetic, so following the arithmetic alone leaves it out. | Leave 8 over 12 in place and the card shows 2/3 large with 8/12 small beside it. Both are visible at once. |
| Improper and mixed forms | Being told 7/3 and 2 1/3 are the same number does not help if you only memorised the conversion; you stall on which one to answer with. | Set the numerator to 7 and the denominator to 3. The improper fraction, the mixed number and the decimal (2.333…) all appear, so all three can be seen as one number. |
| Why unlike denominators cannot be added | The procedure is easy to remember, the reason is not. | Put a bar diagram with denominator 3 next to one with denominator 4. The cells are different widths, which is exactly why they cannot be added as they stand. |
| A fraction is also a division | Schools teach fractions and division as separate topics, so the link does not form. | The fraction card also holds 8/12 as the value 0.666…. Reference it from another card and it enters the arithmetic as a plain number. |
| A bigger denominator means smaller pieces | It runs against the instinct that a bigger number means more. | Raise the denominator from 3 to 12. The bar divides into finer cells and each one shrinks. |
| When the denominator is zero | Knowing "you cannot divide by zero" as a rule does not always fire when it turns up in fraction form. | Set the denominator to 0 and the card shows ÷0 with no value. Everything downstream stops calculating too. |
8/12, 2/3, 0.666… and the filled length of the bar are the same value in different clothes. The board shows all four at once so that, when you change a digit, you can see what moves and what does not.
Try this
- Bring the numerator up to the denominator — set 2/3 to 3/3 and the bar fills completely: the value is 1. That is the boundary where a fraction passes one.
- Make the numerator larger than the denominator — the mixed number appears. 7/3 reads as 2 and 1/3, and the bar fills one whole and starts the next.
- Double both numbers — 2/3 becomes 4/6 and the filled length does not change. You have run reducing backwards.