Direct proportion
Objective. Use multiplicative reasoning in direct proportion problems.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Two quantities are in direct proportion when one is always a constant multiple of the other, so if one quantity doubles, the other also doubles. This constant relationship means dividing one quantity by the other always gives the same value, called the constant of proportionality. For example, if 3 kg of apples costs £6, then the cost per kilogram is £2, a value that stays fixed no matter how many kilograms are bought. Using multiplicative reasoning, if 5 kg costs an unknown amount, multiply the unit cost by 5 to get £10 directly.
Worked example
If 8 identical pens cost £6.40, use direct proportion to find the cost of 5 pens.
- 1Find the cost of one pen by dividing: 6.40÷8=0.80.
- 2Multiply the unit cost by the number of pens required: 0.80×5=4.00.
- 3Check by dividing the answer by 5: 4.00÷5=0.80, matching the unit cost.
- 4State the cost clearly in pounds.
Answer: £4.00
Concept mastery
Based on your past attempts at this lesson — the question types to practise again come first.
Complete a practice set to see your concept breakdown here.
Practice
Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.
Start practisingCommon mistake. Pupils sometimes assume a relationship is proportional just because both quantities increase, without checking the ratio stays constant. Always verify that dividing corresponding values gives the same constant each time.
Your progress
Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.
0 of 5 steps complete
Your place saves automatically as you read.