Ratios, Rates and Time — NSW Year 7 Maths
Comparing amounts with ratios, working with rates such as km/h and $/kg, and everyday time skills. Fourteen subtopics and 280 practice questions, each with a fully worked solution, aligned to NESA outcome MA4-RAT-C-01.
Ratios, Rates and Time in NSW Year 7
A ratio compares amounts measured in the same unit, such as 3 cups of flour to 2 cups of milk, while a rate compares different units, such as 60 km/h or $4.50 per kilogram. In Year 7, students write and simplify ratios, share amounts using a ratio, convert rates between units, compare unit prices to find the best buy, and read travel graphs to work out speeds.
The fourteen subtopics below start with ratios and harder ratio problems, move on to rates, rate problems and best buys, then revise time from primary school (time calculations, 24-hour time, time differences and time problems) alongside travel graphs and timetables. Ratios, Rates and Time is one of the 13 topics in NSW Year 7 Maths and sits in the Number and Algebra strand (NESA outcome MA4‑RAT‑C‑01; the time subtopics are revision with no Stage 4 outcome of their own). In Stage 5, ratios and rates lead on to direct and inverse variation and graphs of rates of change.
Subtopics
Ratios, Rates and Time: common questions
What is the difference between a ratio and a rate?
A ratio compares quantities in the same unit, such as 4 cm to 10 cm, and is written without units as \(2:5\). A rate compares quantities with different units, like 150 km in 3 hours, which simplifies to 50 km/h.
How do you share an amount in a ratio?
Add the terms to count the parts altogether, divide the amount by that number to get one part, then multiply. To share $40 in the ratio \(3:5\) there are 8 parts, so one part is $5 and the shares are $15 and $25.
What is a common mistake with time calculations?
Treating an hour as if it had 100 minutes. 2.5 hours is 2 hours 30 minutes, not 2 hours 50 minutes, and when you subtract times you borrow 60 minutes, not 100.
Which NESA outcome covers ratios and rates?
Ratios, rates and distance–time graphs sit in Stage 4 of the NSW Mathematics K–10 Syllabus (2022) under outcome MA4‑RAT‑C‑01, usually taught in Year 7. The other time and timetable subtopics revise primary-school skills.
What comes after ratios and rates?
Ratios and rates keep appearing in scale, measurement and money problems. In Stage 5 they lead to direct and inverse variation and to graphs that show rates of change, and reading travel graphs is good preparation for linear relationships on the number plane.