Equivalent Ratios and Simplifying Ratios

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1 Getting Started
2 Watch and Notice
3 Try It Together
4 Write the Simplest Form in Your Copy
5 Class Challenge
6 What Did We Notice?
7 What's Next
Pupil practice

1 - Getting Started ~4 mins

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.

Teacher Notes

Take three hands-up answers for each side, then say 'let's find out' without confirming. Give five seconds of quiet think-time before any hands go up.

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~9 mins

Illustration for Watch and Notice

2:3 scaled up to 4:6 and 6:9

Watch the ratio bars. We start with two parts and three parts. When we multiply both parts by 2 we get 4:6, and when we multiply both parts by 3 we get 6:9. The bars stay the same length compared to each other every time, so it is still the same comparison.

10:15 simplified to 2:3

Now the other way. Ten parts to fifteen parts looks big, but both parts divide by 5. That gives us 2:3, the smallest whole numbers that still show the same comparison.

12:8 simplified to 3:2

Twelve to eight both divide by 4, leaving 3:2. But watch what happens if we only divide by 2: we get 6:4, and 6:4 can still go smaller. So we look for the biggest number that divides both 12 and 8 at once. That biggest number is called the largest common factor, and using it gets us to the simplest form in one step.

9:6 simplified to 3:2

Nine to six both divide by 3, also leaving 3:2. Two different-looking ratios, the same simplest form.

Teacher Notes

Walk each example aloud, one at a time.

2:3 → 4:6 → 6:9 — stress that the SAME number multiplies both parts. Point to how the two bars keep the same relative length.
10:15 → 2:3 — ask 'what is the biggest number that divides into both 10 and 15?' before revealing the 5.
12:8 → 3:2 — show the trap on the board: dividing by 2 gives 6:4, which still simplifies, so we hunt for the largest common factor (4) to finish in one step.
9:6 and 12:8 — land the surprise that two different ratios share one simplest form. Revoice: 'so the simplest form is like the fraction's lowest terms.'

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try It Together ~8 mins

Today we work through these together on the board. First we scale 1:4 up to 2:8 and then to 3:12. Then, on the same tool, we go the other way and simplify 8:12. If we divide both parts by 2 we get 4:6, but ask yourself: can it go smaller? Yes, so 4:6 is not finished. The largest number that divides both 8 and 12 is 4, and dividing by 4 gives 2:3 in one step. We will say out loud each time what number we are multiplying or dividing both parts by.

Scale and simplify ratios

Teacher Notes

This round is for talking it through together — pupils take turns at the board and the class agrees or corrects out loud.

For 1:4, have one pupil multiply both parts by 2 (2:8), then another by 3 (3:12). Ask the class to read each new ratio aloud. Then reset the explore tool to 8:12 for the simplifying half. Ask 'what divides into both?' — accept 2 (giving 4:6) but push to find the largest common factor 4 (giving 2:3); on the board show that 4:6 still simplifies, so 4 was the number to use. If time allows, run one more quick turn simplifying 6:8 (largest common factor 2, giving 3:4). Watch for pupils who change only one part.

+15 XP

4 - Write the Simplest Form in Your Copy ~3 mins

COPYBOOK MOMENT

In your maths copy, write each of these ratios and beside it write its simplest form. Then circle the number you divided both parts by.

6:9
15:10
24:18

Teacher Notes

Walk the room glancing at whether pupils divided BOTH parts by the same number — this is whole-class copybook practice, not marking. The circled common factor is the quick check: 6:9 by 3, 15:10 by 5, 24:18 by 6.

+10 XP

5 - Class Challenge ~8 mins

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.

Simplify and find equivalents

Teacher Notes

This round is the practice bank — pupils take turns at the board, check each answer, and the class confirms before moving on. Keep the board work brisk rather than over-explaining.

The simplifying questions test finding the largest common factor (6:9 by 3, 15:10 by 5, 24:18 by 6). The three equivalents of 2:5 are made by multiplying both parts by the same number: ×2 gives 4:10, ×3 gives 6:15, ×4 gives 8:20. Ask the class to confirm each equivalent by checking it simplifies back to 2:5.

+15 XP

6 - What Did We Notice? ~2 mins

MATHS TALK

How is simplifying a ratio like simplifying a fraction? What is the same about what we do, and what is different?

Teacher Notes

Listen for pupils linking 'divide both parts by the largest common factor' to lowest terms in fractions. Revoice a strong answer: 'so a ratio behaves just like the top and bottom of a fraction — same operation on both.' Head off the misconception that you can divide one part only.

+10 XP

7 - What's Next ~3 mins

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.

Coming up

Next we will use these skills to share a quantity in a given ratio, like splitting a prize or a packet of sweets fairly between two people.

Teacher Notes

Recap the two directions in one sentence: scale up by multiplying, simplify by dividing. Flag that the next lesson builds on simplifying to share amounts fairly.

+5 XP

Pupil practice

Module 4 · Ratio and Proportion Measures

Lesson 41 · Equivalent Ratios and Simplifying Ratios

Download Activity Book page (PDF)

End of lesson

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Teacher Class Feed

1 - Getting Started ~4 mins

2 - Watch and Notice ~9 mins

2:3 scaled up to 4:6 and 6:9

10:15 simplified to 2:3

12:8 simplified to 3:2

9:6 simplified to 3:2

3 - Try It Together ~8 mins

Scale and simplify ratios

4 - Write the Simplest Form in Your Copy ~3 mins

5 - Class Challenge ~8 mins

Simplify and find equivalents

6 - What Did We Notice? ~2 mins

7 - What's Next ~3 mins

Today you learned

Coming up

Unlock the full learning experience

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