Ratio a:b Notation
This topic covers 4 learning steps, guiding your child from the basics through to confident problem-solving. Each step includes a worked example and adaptive practice questions.
What Your Child Will Learn
- Write Ratios
Express relationships in a:b notation - Simplify Ratios
Simplify ratios by dividing both parts - Equivalent Ratios
Scale ratios up and down - Ratio Problems
Solve problems using ratio notation
Common Mistakes
- Writing ratios in the wrong order (e.g. writing "boys to girls as 3:5" when there are 5 boys and 3 girls)
The order of a ratio MUST match the order of the words. "Boys to girls = 5:3" is different from "girls to boys = 3:5." Always read the question carefully to check which comes first. - Not simplifying ratios fully (e.g. leaving 6:9 instead of simplifying to 2:3)
Find the highest common factor (HCF) of both numbers and divide: the HCF of 6 and 9 is 3, so 6:9 = 2:3. A ratio is in simplest form when the only common factor is 1.
Tips for Parents
- Practise reading ratio notation: "3:5 is read as three to five." Make sure your child knows the colon (:) means "to."
- Link ratios to fractions: "In a ratio of 3:5, there are 8 parts total, so 3/8 is the first quantity and 5/8 is the second."
- Use real items: "In this bag there are 4 red beads and 6 blue beads. The ratio of red to blue is 4:6, which simplifies to 2:3."
- Play "simplify the ratio" as a quick-fire game: give a ratio and see how fast your child can simplify it.
Key Words
- Ratio notation — The way ratios are written using a colon — 3:4 means "3 to 4."
- Colon (:) — The symbol used between numbers in a ratio — read as "to."
- Simplest form — A ratio where both numbers share no common factor other than 1 — 2:3 is in simplest form.
- Equivalent ratios — Ratios that represent the same relationship — 2:3, 4:6, and 6:9 are all equivalent.
- Highest common factor (HCF) — The largest number that divides into both parts of the ratio — used to simplify.
Where This Fits
Before this topic: Children should understand basic ratio concepts, simplify fractions, and find common factors.
After this topic: Ratio notation leads to solving complex ratio and proportion problems, using scale factors in maps and models, and algebraic ratio work in secondary school.
How MathCraft Teaches This
In MathCraft, Ratio a:b Notation is taught through the Number & Fractions adventure track. Your child follows guided lessons with friendly characters, works through examples step by step, then practises with questions that adapt to their level.
The adaptive engine tracks mastery across all 4 steps, revisiting concepts your child finds tricky and advancing when they're ready. Parents can see detailed progress in the Parent Dashboard.
Practise Ratio a:b Notation with MathCraft
Step-by-step lessons, worked examples, and adaptive practice — all wrapped in an adventure game your child will love.
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