Multiply by 25: think of a quarter of a hundred

Four lots of twenty-five make a hundred

To multiply by 25, multiply by 100 and divide by four. That works because 25 is one quarter of 100. For 28 × 25, a quarter of 2,800 is 700.

You can sometimes make the numbers smaller first. A quarter of 28 is 7, so 7 × 100 also gives 700. Choose the order that is easier to hold in your head.

Change the route, keep the value

Replace 25 with the equal amount 100 ÷ 4. Then 28 × 25 = (28 × 100) ÷ 4. You have changed how you calculate, not what you are calculating.

The National Centre for Excellence in the Teaching of Mathematics includes this strategy in its multiplication reasoning guidance. The examples below show how to choose a convenient route.

A quarter is half, then half again

For 36 × 25, halve 36 to get 18. Halve again to get 9. Multiply by 100 and the answer is 900.

You can reverse those stages: 36 × 100 = 3,600. Half is 1,800 and half again is 900. Both routes keep the exact same value.

This builds on doubling and halving. If you know that 25% means a quarter, you may also recognise the connection to mental percentages.

Seven does not divide evenly by four

Now try 7 × 25. Dividing seven by four first gives 1.75. That is valid, but you may prefer to multiply by 100 first.

Seven hundreds make 700. Half is 350; half again is 175. You never needed to hold a decimal result.

Do not turn 7 ÷ 4 into 1 and throw away the rest. The shortcut works only when you preserve the exact value at each step.

Choose your route

Work out 52 × 25. You could quarter 52 first or start with 5,200 and halve twice.

For another way to replace one multiplication with easier steps, revisit ten groups minus one group.