Proportional Reasoning-1

Ratios compare quantities of the same kind. Share an amount in a ratio, test for proportion, and use the unitary method to find the better buy.

Key ideas

• A ratio compares two quantities in the same unit; simplify it by dividing both parts by their HCF.
• Convert to the same unit first: 50 cm : 2 m = 50 : 200 = 1 : 4.
• To share in the ratio a : b, divide the total into a + b equal parts.
• Four numbers are in proportion when the first two have the same ratio as the last two.
• Unitary method: find the value of one unit, then multiply.
• The better buy is the one with the lower price per unit.

Remember

Watch out

• Comparing quantities in different units.
• Dividing the total by a and b instead of by a + b.
• Choosing the cheaper pack instead of the cheaper price per unit.

Worked example