Equivalent Ratios and Simplifying Ratios

Warning: Your screen size is quite small for viewing this. Rotate your device into landscape mode if you can.

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

Illustration for Getting Started 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

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.

Teacher Notes

2:3 scaled up: multiply both parts by 2 to get 4:6, by 3 to get 6:9. Stress the SAME number multiplies both parts; point to bars keeping equal relative length.

10:15 simplified: ask what is the biggest number that divides both 10 and 15 before revealing 5. Gives 2:3, smallest whole numbers.

12:8 simplified: show the trap. Dividing by 2 gives 6:4, still simplifies further. Hunt for the largest common factor, 4, to finish in one step at 3:2.

9:6 simplified: both divide by 3, also 3:2. Land the surprise that 12:8 and 9:6 share one simplest form.

Revoice: simplest form is like a 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 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.

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

These are the practice questions — 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

123learn · Online learning platform

Unlock the full learning experience

You're previewing this lesson. Get full access to this lesson and hundreds more — each one ready to teach, with interactive activities, printable resources and pupil progress tracking built in.

Hundreds of curriculum-aligned lessons

Interactive activities in every lesson

Printable resources & progress tracking

Get started

Copyright Notice
This lesson is copyright of Coding Ireland 2017 - 2025. Unauthorised use, copying or distribution is not allowed.

Teacher Class Feed

1 - Getting Started ~4 mins

2 - Watch and Notice ~9 mins

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

Unlock the full learning experience

XP