Direct Proportion

Ages 1115

Difficulty 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

Best for: Any target quantity
  1. 1.Divide to find one unit.
  2. 2.Multiply by the target quantity.
  3. 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

Best for: Targets that are simple multiples
  1. 1.Compare the known and target quantities.
  2. 2.Find the scale factor.
  3. 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

Spark

Creativity & Innovation

Create your own maths challenge and solve it!