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Class 6 — Ratio & Proportion

Ratio and proportion: the mix that must not change

A recipe is a ratio that people can taste. Double the lemons but not the sugar and the drink goes sour — and customers stop coming back. This is where a Class 6 student meets ratio as something with consequences rather than colons.

Ratio is a relationship, not a quantity

One lemon to two spoons of sugar is written 1 : 2. It does not tell you how much lemonade you are making. It tells you the relationship that has to survive whatever quantity you make.

That is the part children miss. They can compute 1 : 2 and still not see why 5 lemons needs 10 spoons rather than 6.

Proportion is keeping the ratio while the size changes

Making five times as much? Multiply both sides by five. The ratio 1 : 2 becomes 5 : 10, which is the same relationship at a bigger scale.

Change one side only and you have not scaled the recipe — you have invented a new and probably worse one.

A worked example from a real day

Recipe1 lemon : 2 spoons sugar
Glasses planned today18
Lemons needed18
Sugar needed
both sides scale together
18 × 2 = 36 spoons
Taste score that day92 / 100

The day the same shopkeeper used 18 lemons and only 24 spoons, the taste score fell to 61 and sales dropped by a third — with no change in price or weather. The ratio was the only thing that moved.

Try it: scale the recipe without ruining the taste

One lemon to two spoons of sugar. Keep the ratio, change the batch.
5 lemons · 10 spoons
the ratio stays 1 : 2 however big the batch gets

Practice

A recipe uses 2 lemons for every 3 spoons of sugar. How much sugar for 8 lemons?
Show the answer
12 spoons
8 ÷ 2 = 4, so the recipe is scaled 4 times. 3 × 4 = 12 spoons.
Are the ratios 3 : 4 and 9 : 12 in proportion?
Show the answer
Yes
9 ÷ 3 = 3 and 12 ÷ 4 = 3. Both sides scaled by the same number, so the relationship is unchanged.
A cart mixes ice and lemonade in the ratio 1 : 5. For 30 glasses of mixture, how much is ice?
Show the answer
5 parts of 30 = 5 glasses of ice
1 + 5 = 6 parts in total. 30 ÷ 6 = 5 per part. Ice is 1 part = 5.

Learn it by running one

In Lemonade Empire your child runs a lemonade cart and uses this exact concept to decide what to buy and what to charge. Free, no signup, plays in a browser.

▶ Play Lemonade Empire free

Common questions

What is the difference between ratio and proportion?
A ratio compares two quantities. A proportion says two ratios are equal — it is what lets you scale a recipe up or down without changing how it tastes.
Why does my child get ratio questions wrong even after learning the rule?
Usually they scale one side and not the other. It is hard to see the mistake on paper. It is very easy to see when the drink is too sour and nobody buys it.

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