Rates and Ratios — NSW Year 8 Maths
Equivalent ratios, simplifying, sharing in a ratio and rates such as L/min and $/h, taken further than in Year 7. Six subtopics and 120 practice questions, each with a fully worked solution, aligned to NESA outcome MA4-RAT-C-01.
Rates and Ratios in NSW Year 8
A ratio compares two or more amounts of the same kind, while a rate compares different kinds of quantity, such as dollars per hour or litres per minute. Year 8 builds on Year 7 ratios with harder numbers and situations: decimal and fraction terms, ratios with three or four parts, pronumerals, map scales, unit changes inside a rate, and problems where a ratio changes after people join, leave or swap.
The six subtopics below start with equivalent ratios and simplifying, move on to dividing a quantity in a ratio and ratio word problems, then finish with rates and rate problems such as best buys. Rates and Ratios is one of the 14 topics in NSW Year 8 Maths and sits in the Number and Algebra strand (NESA outcome MA4‑RAT‑C‑01). These skills are used again straight away for map scales, speed and travel graphs in Time and Travel, and in Stage 5 they lead to direct and inverse variation.
Subtopics
Rates and Ratios: common questions
What are equivalent ratios in Year 8 maths?
Equivalent ratios make the same comparison because every term has been multiplied or divided by the same number. \(4:6\), \(2:3\) and \(10:15\) are all equivalent, and \(2:3\) is the simplest form.
How do you divide a quantity in a given ratio?
Add the terms to count the parts altogether, divide the quantity by that count to get one part, then multiply. To share $90 in the ratio \(2:3:4\) there are 9 parts, so one part is $10 and the shares are $20, $30 and $40.
How do you change km/h to m/s?
Divide by 3.6, because 1 km/h is 1000 metres in 3600 seconds. So 72 km/h is \(72 \div 3.6 = 20\) m/s, and multiplying by 3.6 changes m/s back to km/h.
Which NESA outcome covers rates and ratios?
Ratios and rates sit in Stage 4 of the NSW Mathematics K–10 Syllabus (2022) under outcome MA4‑RAT‑C‑01. They are introduced in Year 7, and Year 8 takes them further with harder ratios, unit changes for rates and best buys.
What comes after rates and ratios in Year 8?
Ratios and rates come straight back in Time and Travel, for map scales, speed and travel graphs. In Stage 5 they lead to direct and inverse variation and to graphs that show rates of change.