Ratio and proportion

• Simplify a ratio by dividing every part by a common factor; write it as 1 : n when asked.
• In a ratio a : b, the fractions of the whole are a/(a + b) and b/(a + b).
• Divide a quantity in a ratio: total ÷ number of parts = one part.
• Use the unitary method (find one first) and direct proportion to find unknown quantities.
• Solve word problems involving maps and scale diagrams.

Same units, then simplify

A ratio a : b compares two quantities. Simplify it like a fraction, by dividing both parts by their HCF, after writing both in the same units. To write a ratio in the form 1 : n, divide both parts by the first part (n may be a decimal).

Link to fractions: if boys : girls = 3 : 5, there are 3 + 5 = 8 parts, so 3/8 of the group are boys and 5/8 are girls.

Find one part first

Add the parts, divide the total by the number of parts to get the value of one part, then multiply by each share. Check that the shares add to the total.

Find the value of one

To use proportionality, find the value of one unit, then multiply up. To compare value, find the price of the same amount of each (for example the cost per 100 g).

s varies directly as t

Two quantities are in direct proportion if they increase at the same rate: doubling one doubles the other, and their ratio stays constant. If s varies directly as t, then s = kt for a constant k. (The algebraic form with ∝ is in 2.5 Proportion, Higher tier.)

Scale 1 : n means multiply by n