Direct Proportion
Ages 11–15Difficulty adapts to you
Direct Proportion
Two quantities are directly proportional when they grow or shrink by the same factor. Find one unit or use a scale factor to solve.
Your goals
- ✓You can scale quantities using unitary methods and tables.
- ✓You can use direct proportion, unitary method correctly.
- ✓You can divide matching values to confirm the ratio stays constant.
Words to know
- direct proportion:
- A relationship in which both quantities scale by the same factor.
- unitary method:
- Find the value for one unit, then scale to the amount needed.
Examples
- 13 notebooks cost ₦1,500, so one costs ₦500 and 8 cost ₦4,000.
- 2A recipe for 4 uses 300 g of rice; for 10 people use 750 g.
More than one way to solve it
Try each method, then choose the one you can explain and check most clearly.
Method 1
Unitary method
- 1.Divide to find one unit.
- 2.Multiply by the target quantity.
- 3.Label the answer with units.
Example: 3 items cost ₦1,500, so one costs ₦500 and 8 cost ₦4,000.
Method 2
Scale-factor method
- 1.Compare the known and target quantities.
- 2.Find the scale factor.
- 3.Apply the same factor to the matching value.
Example: A recipe for 4 scaled to 12 uses a factor of 3, so every ingredient is tripled.
Check these
- • Do not add the same amount when the relationship requires multiplication.
- • Keep every number, symbol, label, and unit in its correct place.
- • Choose the method that makes each step easiest to explain and check.
Helpful habits
- • Read the whole question before choosing what to do.
- • Show one clear step at a time and check each step.
- • If you are stuck, draw a model, try smaller numbers, or revisit the example.
Now try your own
Create your own direct proportion example, solve it, and explain how you checked it.
Spark
Creativity & Innovation“Create your own maths challenge and solve it!”