wunder beta🍋 Modeling with Ratio and Proportion
From lemonade to maps to mixing paint, ratios show how amounts go together. Learn to read a ratio, scale it up fairly, and solve real-world problems.
What you’ll learn
- What Is a Ratio?Read and write a ratio such as 2 : 3, and find the total number of parts.A ratio compares amounts in order: 2 : 3 means for every 2 parts lemon there are 3 parts water. It tells a small story about how amounts go together. Adding the parts (2 + 3 = 5) gives the number of parts in the whole.
- Keeping It ProportionalScale a ratio up by multiplying both parts by the same number to make equivalent ratios.Proportion keeps a recipe true at any size. The golden rule is to multiply both parts by the same number: 2 : 3 doubled is 4 : 6, tripled is 6 : 9. These are equivalent ratios — different sizes of the same mix, all tasting the same.
- Ratio in the Real WorldRecognise ratios in real situations and judge whether two ratios describe the same mix.Ratios model recipes, mixing paint, map scales and fair sharing. To check whether two ratios are the same, see if both parts were multiplied by one number: 4 : 6 and 6 : 9 match 2 : 3, but 3 : 2 (flipped) and 4 : 5 do not.
Questions this course answers
The ratio 2 : 3 (lemon : water) means…
A ratio compares parts in order: 2 : 3 means for every 2 parts lemon there are 3 parts water.
In the mix 2 : 3, how many parts are there altogether?
Add the parts: 2 + 3 = 5 parts in the whole jug.
If you double the ratio 2 : 3, what do you get?
Multiply both parts by 2: 2 × 2 = 4 and 3 × 2 = 6, giving 4 : 6.
What is the golden rule for keeping a ratio proportional?
A ratio stays the same only if you multiply (or divide) both parts by the same number.
Which ratio is the SAME mix as 2 : 3?
6 : 9 comes from multiplying both parts of 2 : 3 by 3, so it is an equivalent ratio.
Why is 3 : 2 a DIFFERENT mix from 2 : 3?
In 3 : 2 the lemon part is now bigger than the water part, so the taste changes — order matters.
Grounded in trusted sources
- BBC Bitesize — ratio and proportion
- Khan Academy — intro to ratios
- NRICH — proportional reasoning
Every Wunder lesson is built from real, reputable sources — never invented.
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