Ratios that change, recipes with a limit, mixtures, average speed, density, inverse and squared proportion, and pressure.
What you will learn
- Turn a ratio into shares and find one share first
- Use a ratio that changes as an equation
- Work with compound measures over two stages
- Find and use the constant in a proportion
Find one share
Most ratio problems turn on the value of one part.
- cement : sand : gravel = 1 : 2 : 4, so 7 parts in all
- 800 kg of concrete: one part is 800 ÷ 7 = 114.28... kg
- cement is 1 part: 114.3 kg, so 25 kg bags: 114.3 ÷ 25 = 4.57, round up to 5 bags
When a ratio changes (money given away, people joining), write each amount with a letter, then make an equation from the new ratio: (3x − 10) : (2x + 10) = 1 : 1 gives 3x − 10 = 2x + 10.
The rest of this lesson and its 11 practice questions are locked.
In this lesson
- Find one share
- Two-stage rates
- Proportion
11 practice questions, marked as you go; about 30 minutes in all.
Key terms
One part, Changes
In this unit: Exam problems
The long problems that end a paper, worth 4 to 6 marks: number, algebra, ratio, geometry and statistics, Foundation and Higher, with and without a calculator, marked step by step.
- Number problems
- Algebra problems
- Ratio and rates problems
- Geometry problems
- Statistics and probability problems