Ratios and rates

A ratio compares amounts of the same kind, like 2 parts cordial to 9 parts water. A rate compares amounts of different kinds, like kilometres per hour or dollars per kilogram. In Year 7 you learned to write and simplify ratios. In this topic you'll use ratios and rates to read maps, work out speeds, pay and interest, and find the best value when you shop.

What you'll learn

• 3.01 Ratios: simplifying ratios with decimals, fractions and units, sharing an amount in a ratio, and finding the whole from one part.
• 3.02 Maps and scale: reading a map scale, changing map distances to real distances and back, and making scale drawings.
• 3.03 Rates: unit rates, changing the units of a rate, and speed, distance and time.
• 3.04 Financial rates: pay per hour and salaries, overtime, simple interest and exchange rates.
• 3.05 Best buys: unit prices, specials and choosing the best value.

Which level should I pick?

Every worksheet comes in three levels. Each one covers the same skills.

• Level 1 · Warm-up: smaller numbers and more help along the way. A good place to start.
• Level 2 · Core: the main worksheet for the lesson.
• Level 3 · Challenge: mixed units, ratios that change and problems with more steps, for when the Core level feels easy.

Not sure? Start with Level 2. If the first few questions feel tricky, drop to Level 1. If you finish quickly and get them right, try Level 3. Download the worksheet, print it, and write your answers in the boxes.

Practice tests

When you've finished the lessons, try the three practice tests. Each one is like the real topic test: 45 minutes, 40 marks, a section without a calculator and a section with one. Write your working under each question, then copy your final answers onto the answer sheet on the last page, just like you will in the real test.