Percentages (age 9+)
Know and use the vocabulary of ratio and proportion — ratio, proportion, percentage, scale, equivalent, unequal, relative size, part-to-part, part-to-whole, and out of — and understand the difference between ratio (comparing parts to parts) and proportion (comparing a part to the whole)
What a learner can do afterwards
- Explain the difference between a 'ratio' and a 'proportion' using a concrete example like mixing paint
- Use 'per cent' correctly and convert between fractions, decimals, and percentages in context
- Define 'scale factor' and use it to describe how a shape has been enlarged or reduced
The lesson
A ratio compares one part to another part. A proportion compares one part to the whole thing. They sound alike, but they answer different questions.
Mia's paint has 5 cups in total: 3 red and 2 yellow. The ratio of red to yellow is 3:2, a part-to-part comparison. But the proportion of red in the whole mix is 3 out of 5, which is 60 percent. That's a part-to-whole comparison.
A scale factor tells you how many times bigger or smaller a shape becomes. A scale factor of 2 doubles every length. A scale factor of one half shrinks every length by half.
The word 'per cent' means 'out of 100'. So 60% is the same as 60 out of 100, or 3 out of 5 in its simplest form. To change a fraction into a percentage, picture the whole split into 100 equal parts.
Ratio compares part to part, proportion compares part to whole, percent means out of 100, and scale factor shows how much a shape grew or shrank.
Watch it
Where it sits
Learn first
Nothing; this is a starting point.
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.