Write one quantity as a fraction or percentage of another in different units, write ratios in words and in notation, and turn a ratio into fractions and into an equation y = kx.
What you will learn
- Write one quantity as a fraction or a percentage of another, changing units first
- Simplify a ratio with three parts in different units
- Turn words, fractions and graphs into ratio notation in the right order
- Write a ratio as a fraction of the other part, of the whole, and as an equation y = kx
One quantity as a fraction of another
The amount after "of" goes on the bottom.
Put both amounts in the same unit first, then simplify.
- write 45 minutes as a fraction of 2 hours
- 2 hours = 120 minutes
- 45/120
- divide both by 15: 3/8
For a percentage, divide and then multiply by 100: 350 g as a percentage of 2.5 kg is 350 ÷ 2500 × 100 = 14%. Writing 350/2.5 compares grams with kilograms, which gives a nonsense answer.
To decide which of two fractions is greater, change both to decimals: 7/20 = 0.35 and 1/3 = 0.333..., so 7/20 is the greater fraction, even if its amount in minutes is smaller.
The rest of this lesson and its 10 practice questions are locked.
In this lesson
- One quantity as a fraction of another
- Ratio notation, in the right order
- A ratio as fractions and as a linear function
- A ratio and a perimeter
- Try it: Check with the ratio tool
10 practice questions, marked as you go; about 30 minutes in all.
Key terms
Same unit
In this unit: Ratio, gradients, similarity and growth
More ratio: one quantity as a fraction of another, ratio notation with units, ratios as linear functions, gradients as rates, similar shapes through length, area and volume ratios, and repeated percentage change.
- Fractions, ratio notation and linear functions
- Gradients as rates
- Similar shapes and scale factors
- Repeated proportional change