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Help.ai Learn · Skill guide

Proportions

Identify a proportional relationship and scale it consistently. Use a unit rate or equivalent ratios while keeping the meaning and units of both quantities clear.

Fraction pieces and simple shapes illustrate relationships between numbers.

What you’ll learn

  • Explain when two ratios describe the same relationship.
  • Find a unit rate and use it to scale a quantity.
  • Recognize an assumption behind a proportional model.

Keep the relationship constant

Two quantities are directly proportional when multiplying one by a factor multiplies the other by the same factor. Their ratio stays constant; a table can make that pattern visible.

Find one unit or scale both quantities

A unit rate expresses the amount for one unit. Alternatively, multiply both parts of a ratio by the same factor. Choose whichever makes the quantities easiest to interpret.

A mistake to avoid

Adding the same amount to both quantities usually changes their ratio. A fixed fee, discount threshold, or changing rate can also mean a real situation is not proportional.

Worked example

Price five identical notebooks

If 3 identical notebooks cost 6 currency units at a constant price, one costs 6 ÷ 3 = 2. Five therefore cost 5 × 2 = 10. This assumes there is no fixed fee or quantity discount.

Learning paths that include this skill

Choose the route that fits your goal. The same skill can be useful in more than one subject or stage of learning.