Knowledge Organiser: Simplifying Ratios
Key Terms
- Ratio: A comparison of two or more quantities using the : notation
- HCF: Highest Common Factor: the largest number that divides all parts exactly
- Simplest form: A ratio where the numbers share no common factor other than 1
- Equivalent ratios: Ratios that represent the same relationship (e.g. 2:3 and 4:6)
- Unit conversion: Changing quantities to the same unit before simplifying
Must-Know Facts
- Convert all quantities to the same units BEFORE simplifying
- Divide ALL parts of the ratio by the HCF
- Keep simplifying until no common factor remains
- For decimals: multiply all parts by 10 (or 100) first to get whole numbers
- For fractions: multiply all parts by the LCM of the denominators
- Use the smallest unit to avoid decimals (pence not pounds; cm not m)
Key Methods
- Step 1: convert to same units
- Step 2: find HCF of all parts
- Step 3: divide every part by the HCF
- Step 4: check no further simplification is possible
- Shortcut: divide by 2, then 3, then 5 if the HCF is not obvious
Common Mistakes
- Not converting units first: 2 km : 500 m must become 2000 m : 500 m before simplifying, ratios must have the same units throughout
- Dividing by a small factor instead of the HCF: 12:18 ÷ 2 = 6:9 (still not fully simplified; use HCF = 6 to get 2:3 in one step)
- Reversing the ratio order: The order of a ratio matches the order of the quantities described: "boys to girls" is not the same as "girls to boys"
- Leaving decimals in a simplified ratio: If simplifying gives 1.5:2, multiply both by 2 to get 3:4, ratios must always use whole numbers