Fractions and Percentages: Same Amount, New Name

Here is a number trick. One half can transform into fifty per cent... without changing its size at all! How? Because fractions and percentages are simply two different ways to describe the SAME part of a whole. Let's uncover the connection.

Per cent means out of one hundred. Picture a square made from one hundred equal little tiles. If twenty-five tiles are coloured, that is twenty-five out of one hundred, or twenty-five per cent. The percent sign is a reminder that the whole has been divided into one hundred EQUAL parts. Now divide that hundred-square into four equal blocks. Each block contains twenty-five tiles. So one block is one quarter of the whole, and it is also twenty-five per cent. One quarter and twenty-five per cent cover precisely the same area. Only the LABEL has changed. This gives you a useful pair to remember: one quarter equals twenty-five per cent. You can travel either way. But never just drop or add a percent sign. That sign means out of one hundred, so the number must match the scale. And check the pieces are equal - uneven pieces do NOT make true fractions.

Here's an example. Convert seventy-five per cent into its simplest fraction in this 11+ question. Start with the meaning of per cent. Seventy-five per cent means seventy-five out of one hundred, so write seventy-five over one hundred. We have converted the percentage sign into its proper SCALE. Now simplify. Split the hundred-square into four equal blocks. Each block has twenty-five tiles. Three of those four blocks are coloured, so seventy-five out of one hundred is three quarters. You can also divide the top and bottom numbers by twenty-five: seventy-five becomes three, and one hundred becomes four. Our answer is three quarters. Check it: three equal blocks out of four are coloured, and together they contain seventy-five tiles out of one hundred. Perfect. Therefore, seventy-five per cent equals three quarters. Notice that the amount never changed... only the way we named it.

Remember: per cent means out of one hundred. Match the same equal area, then simplify if you are writing a fraction. Never add or remove the sign without changing the scale. Same amount, different name - and now YOU can switch between them!