Here are two ratios: 2:3 and 4:6. Are they telling us the same thing, or something different? Hands up if you think they are the same. Hands up if you think they are different. Now hold that thought, because by the end of today you will be able to prove who's right.

The ratio bars show the same comparison written different ways, first scaled up, then simplified down. Watch how the bars keep the same relative lengths even when the numbers change. Keep an eye out for two different-looking ratios that turn out to share one simplest form.

Today we work through these together on the board. First we scale 1:4 up by multiplying both parts by 2, and then by 3. Then, on the same tool, we go the other way and simplify 8:12. Try dividing both parts by 2, but ask yourself: can it go smaller? Find the largest number that divides both 8 and 12, and divide by that to finish in one step. We will say out loud each time what number we are multiplying or dividing both parts by.

Today we work through these on the board, getting trickier as we go: simplify 6:9, then 15:10, then 24:18. After that, build three ratios equivalent to 2:5 by multiplying both parts by 2, by 3, and by 4 in turn. Check each one by simplifying it back to 2:5.

Today you learned

• Multiplying or dividing both parts of a ratio by the same number makes an equivalent ratio.
• The simplest form uses the smallest whole numbers, found by dividing both parts by their largest common factor.
• Simplifying a ratio works just like reducing a fraction to lowest terms.