Ratio, Proportion & Compound Measures
Solve harder ratio and proportion problems and use compound measures such as speed and density.
Overview
Year 9 brings ratio and proportion together with compound measures — quantities made from two others, such as speed (distance ÷ time) and density (mass ÷ volume). Students solve multi-step ratio problems and rearrange compound-measure formulae. These appear constantly at IGCSE and in science.
What You Will Learn
- Solve multi-step problems involving ratio and proportion
- Understand speed as distance divided by time
- Understand density as mass divided by volume
- Rearrange a compound-measure formula to find any quantity
- Convert between units within a compound measure
Key Vocabulary
Common Mistakes to Avoid
- Dividing the quantities the wrong way round (e.g. time ÷ distance for speed)
- Mixing units, such as minutes and hours, without converting
- Forgetting to rearrange the formula when the unknown is not on top
- Misreading a ratio problem and sharing in the wrong order
What Comes Next
At IGCSE this becomes the rates, speed–distance–time, and density work in the Number topic, plus proportion expressed as an equation.
Frequently Asked Questions
What is a compound measure?
A compound measure combines two different quantities into one. Speed combines distance and time (speed = distance ÷ time), and density combines mass and volume (density = mass ÷ volume).
How do I find the time taken from speed and distance?
Rearrange speed = distance ÷ time to get time = distance ÷ speed. For a journey of 120 km at 40 km/h, the time is 120 ÷ 40 = 3 hours. Make sure the units are consistent first.
Study This Topic
Topic Details
- Stage
- Year 9
- Strand
- Number
- Framework ref
- 9Nf
- Difficulty
- High
Build strong foundations in Ratio, Proportion & Compound Measures
A free trial class with Teacher Rig helps your Year 9 child master Ratio, Proportion & Compound Measures now — so IGCSE Maths feels familiar, not frightening, later.
Heading toward IGCSE? See how Ratio, Proportion & Compound Measures develops in IGCSE Number (Cambridge 0580) →