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Myriora Maths › Maths foundations › Chapter 12: Ratio and proportion

When the ratio changes

Ages 9–11Chapter 12 · Lesson 6

In this lesson

Your turn

Jo and Kim have stickers in the ratio five to three. Jo gives Kim four stickers, and now they have the same. How many did Jo have at the start?

Show the answer

Five to three is eight parts. One to one is also eight parts: four to four. Jo went from five parts to four, so one part is four stickers. Jo had five parts: twenty stickers!

The common mistake

Here's a question that catches lots of people. The ratio was three to two, and after Amy gives six marbles, it's one to one. Some people say Amy lost two parts, because three take away one is two. But the parts have changed size! Make the totals match first: six to four becomes five to five. Amy lost one part.

Try it at home

Give some counters away between two piles and talk about what happens to the total and the ratio.

Read the whole lesson

Hello, and welcome to Myriora Maths! Amy and Ben share their marbles in the ratio three to two. Then Amy gives Ben six marbles, and now they have the same. How many did each of them have at the start? Let's crack it.

Here's the key idea. When Amy gives marbles to Ben, the total doesn't change. No marbles are made, and none are lost.

Before, the ratio is three to two: five parts. After, it's one to one: two parts. The parts aren't the same size! So make both ratios have ten parts. Three to two is six to four. And one to one is five to five.

Now compare Amy. She had six parts, and now she has five. She gave away one part, and that was six marbles. So one part is six marbles.

Amy had six parts: six times six is thirty-six marbles. Ben had four parts: twenty-four marbles. Check: Amy gives six away and has thirty, and Ben has thirty too. The same!

Let's try one together. Ali and Sam have ten marbles each. Ali gives Sam two marbles. What is the new ratio? Say it out loud!

Ali has eight, and Sam has twelve. Eight to twelve simplifies to two to three!

Here's a question that catches lots of people. The ratio was three to two, and after Amy gives six marbles, it's one to one. Some people say Amy lost two parts, because three take away one is two. But the parts have changed size! Make the totals match first: six to four becomes five to five. Amy lost one part.

Your turn! Jo and Kim have stickers in the ratio five to three. Jo gives Kim four stickers, and now they have the same. How many did Jo have at the start? Pick the right card. You've got twenty seconds, or pause the video. Go!

Time's up! Five to three is eight parts. One to one is also eight parts: four to four. Jo went from five parts to four, so one part is four stickers. Jo had five parts: twenty stickers!

Quick review. When things are given or swapped, the total stays the same. Make the ratios before and after have the same number of parts. Compare one person's parts to find what one part is worth. Then multiply, and check. See you next time!