Ratios and rates

A ratio compares two or more amounts of the same kind: 2 cups of rice to 3 cups of water, 4 leaders to 30 campers, 3 parts cement to 5 parts sand. A rate compares amounts of different kinds, like kilometres per hour or dollars per kilogram. In this topic you'll learn to write ratios, simplify them, and use them to share things out fairly. Ratios turn up in recipes, maps, building, sport and money, so you'll use these skills often.

What you'll learn

• 7.01 Identify ratios: writing ratios in the right order, part-to-part and part-to-whole ratios, changing to the same unit first, and telling a ratio from a rate.
• 7.02 Equivalent and simplified ratios: ratios that look different but compare the same way, writing ratios in simplest form, and scaling recipes and models up or down.
• 7.03 Find part or whole measures: sharing an amount in a given ratio, and working out the other part or the whole when you know one part.

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: three-part ratios, mixed units 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.