Picture a shop window with a sign: 25% OFF €60. Roughly how much money would that take off the price? Before we work it out the careful way, what does your gut say, and is there a shortcut hiding in that 25%?

Each percentage of an amount is built from equal parts. Each bar below is the whole amount, cut into equal parts. Before each part and each percentage appears, predict it in your head. Notice which part we find first, and how we build the percentage from it.

25% of €60. 25% is one quarter, so the bar is cut into 4 equal parts.

10% of €80. 10% is one tenth, so the bar is cut into 10 equal parts.

15% of €40. This bar is cut into 20 equal parts, so each part is 5%. Two parts make 10%, and one more part is the other 5%.

30% of 150. The bar is cut into 10 equal parts, so each part is 10%, and 30% is three of those parts.

75% of €40. 75% is three quarters: three of the 4 equal parts.

Find one equal part first: a quarter for 25%, a tenth for 10%. Then build the percentage from those parts.

Find a percentage by starting from 10%. First find 10% of €35, then build up to 20%. Predict each answer before you check it.