Use a constant rate
Here A is an amount, q is its quantity and r is the amount per unit of quantity. The subscript “new” identifies the requested pair. Keep the rate’s units visible
- Unit rate Divide the known amount by the known quantity \(\displaystyle r=\frac{A}{q}\)
- New total Multiply the rate by the new quantity \(\displaystyle A_{\text{new}}=rq_{\text{new}}\)
- New quantity Divide a given total by the rate \(\displaystyle q_{\text{new}}=\frac{A_{\text{new}}}{r}\)
Common mistakes
Using the rate backwards
✕\(\displaystyle \text{Time}=\frac{14}{9}\times42\)✓\(\displaystyle \text{Time}=\frac{9}{14}\times42\)
Posters per minute and minutes per poster are reciprocal rates. Choose the direction needed by the calculationRounding too early
✕\(\displaystyle \text{Time}=0.64\times42=26.88\)✓\(\displaystyle \text{Time}=\frac{9}{14}\times42=27\)
A rounded intermediate rate changes the result. Keep the exact fraction until the endDifficulty levels
introScale a quantity forward at a simple constant rate
standardUse decimal rates or find a quantity from a total
challengeKeep an exact fractional rate, convert time units or combine two rates
Questions about this topic
How do I choose multiplication or division?+
Multiply a rate by a quantity to find a total. Divide the total by the rate to recover a quantity
Does a fixed fee allow direct proportion?+
A non-zero fixed fee means the total price is not directly proportional to the quantity
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)