Number triangle

Number Triangles

Number triangles are a useful way of working out how to rearrange a multiplication or division sum.

This is important if you have to ‘fill in the gaps’, for example.

Let’s say the question sets out a bus stop method division sum with the dividend missing. In other words, something divided by 9 is 38. You could work it out ‘backwards’, but it would be much easier to put the values into a number triangle and rearrange it so that the something is simply 9 x 38.


If you draw an equilateral triangle and write the three values in the right corners, you can just put your finger over one of them to see what you have to do to work it out.

For example, if you know that a = bc (or a = b x c), then you should put a in the top corner of the triangle. That’s because the two other letters are now together at the bottom, forming bc. If you put your finger on the a, you just see bc—which is the formula for a.

It’s the same if you know what the formula for b or c is. All you need to do is put the b and the c in the bottom corners. The a has to go at the top because the formula for b is a over c (in other words, a divided by c), and the formula for c is a over b. That means if you put your finger over the b, you’ll get the formula for b, which is a over c.

The same goes for c. If you put your finger over the c, you’ll get the formula for c, which is a over b.

All that means that one triangle contains three formulas:

a = bc
b = a/c
c = a/b


Rearrange these sums by drawing a number triangle and work out what the question mark stands for. (In other words, turn them into division or multiplication sums that start with “? =” and then work out the answer.)

  1. 36 = 9 x ?
  2. 108 = ? x 3
  3. 4 = 24 ÷ ?
  4. 5 = ? ÷ 15
  5. 2.5 = 300 ÷ ?


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