Swapping the Numbers in a Percentage

Teaches that a% of b is the same as b% of a, because both are a × b ÷ 100, and how swapping the numbers can make a percentage easy to work out.

Print handout

Your first print is free, with no sign-in. Then 10 sheets a month with a free account. Prints on Letter paper, or print on A4.

What is on a handout

The big idea: the rule, in a few short sentences.
Watch me: worked examples, each with why it changes as it does.
Watch out: the mistakes children often make, struck through beside the right answer.
Try it together: a few items or problems to do as a class, with an answer key.
On your own: the practice sheet that comes next.

Ask students to work out 8% of 50 the long way and as 50% of 8, then compare. Writing both as 8 × 50 ÷ 100 shows why the swap always works.
Read the big idea aloud, then work through Watch me together, saying why each one changes.
Ask the class to find the mistake in each Watch out before you show the answer.
Do Try it together as a class, check it with the answer key, then hand out the practice sheet.

After the handout, in this order: the main practice sheet first, then more practice, then quick checks.