Simplify a ratio
Use one unit and whole-number terms. Here a and b are the terms, and h is their highest common factor. Divide every term by h
\[a:b=(a\div h):(b\div h)\]
- Common units Compare like quantities in the same unit
- Common form Clear decimal places or fraction denominators using the same multiplier for every term
- Final check Keep the term order. No common factor greater than one should remain
Common mistakes
Ignoring units
✕\(\displaystyle 1.6\text{ m}:72\text{ cm}=1.6:72\)✓\(\displaystyle 1.6\text{ m}:72\text{ cm}=160:72\)
The numbers must describe lengths in the same unitUnfinished simplest-form answer
✕\(\displaystyle \text{Final answer: }14:22\)✓\(\displaystyle \text{Final answer: }7:11\)
The earlier ratio is equivalent, but both terms still divide by twoDifficulty levels
introSimplify two whole-number terms
standardUse decimals, a third term or one unit conversion
challengeClear fractions or compare three lengths in mixed units
Questions about this topic
Can I simplify in more than one step?+
Yes. Each step must divide every term by the same common factor. Stop when no common factor greater than one remains
Do ratio terms keep their units?+
A ratio comparing like quantities is unitless after the quantities have been converted to a common unit
Can I use a calculator?+
A calculator is allowed unless a question is marked no calculator
Which year level and chapter is this?+
Year 9 Mathematics, chapter 1: Number and financial mathematics
In this chapter
Evaluate an integer expressionFactors, multiples, HCF, LCM and primesRound to decimal places or significant figuresEstimate an expression using rounded inputsConvert between fractions, mixed numbers and decimalsClassify real numbers and compare exact valuesAdd, subtract, multiply and divide fractions and mixed numbersWrite a ratio from countsWrite ratios in simplest formComplete equivalent ratiosUse a constant rateDivide a quantity in a given ratioDecide which option is the better valueConvert between fractions, decimals and percentagesFind a percentage of a quantityExpress one quantity as a percentage of another1F Percentages and money: Find the original amount from a percentageIncrease or decrease a quantity by a percentageFind percentage changePercentage error against a reference value1G Percentage change and percentage error: Find the original amount from a percentageProfit, mark-up and discountIncome and taxSimple interestCompound interest (optional extension)