Ratio & Proportion flashcards

Key points

• Divide every part by the same number, as you would simplify a fraction.
• Dividing by the highest common factor gets there in one step.
• A ratio is in its simplest form when no whole number bigger than 1 divides every part.

Example

Key points

• Write every part in the same unit first, usually the smaller one.
• Then the units can go, and the ratio simplifies as normal.
• £1 = 100p, 1 m = 100 cm, 1 kg = 1000 g.

Example

Key points

• Divide both parts by the first number.
• n can be a decimal: that is fine in this form.
• The form 1 : n makes ratios easy to compare, such as two map scales.

Example

Key points

• Add the numbers in the ratio to find the total number of parts.
• Divide the amount by the number of parts to find what one part is worth.
• Multiply one part by each number in the ratio.
• Check that the shares add back up to the amount.

£60 in the ratio 2 : 3 : 5

Key points

• Match the share you know to its number of parts.
• Divide to find what one part is worth.
• Multiply up to find the other shares, or the total.

Shared 3 : 5, the larger share is £40

Key points

• The difference is the gap in parts: in 3 : 8, it is 8 − 3 = 5 parts.
• Divide the difference by the gap to find one part.
• Then multiply up to find each share.

Ali : Ben = 3 : 8, Ben gets £30 more

Key points

• A ratio compares one part with another; a fraction compares a part with the whole.
• Add the parts to find the whole: 2 : 5 has 7 parts, so the first is $\frac{2}{7}$ of the whole.
• From a fraction: if $\frac{3}{8}$ are boys, $\frac{5}{8}$ are girls, so boys : girls = 3 : 5.
• In 2 : 5, the first part is $\frac{2}{5}$ of the second part.

Red : blue = 2 : 5, 42 beads

Key points

• 1 : 50,000 means every real length is 50,000 times the length on the map.
• Map to real life: multiply by the scale. Real life to map: divide.
• Work in centimetres, then convert at the end: 100 cm = 1 m and 100,000 cm = 1 km.

Example

Key points

• The scale says what one unit on the drawing stands for in real life.
• Drawing to real life: multiply by what 1 cm stands for.
• Real life to drawing: divide by it.
• Angles are not scaled: an angle is the same on the drawing as in real life.

A plan drawn 1 cm to 2 m

Key points

• Work out the price of one unit of each, such as the price per gram.
• The lowest price per unit is the best value.
• Change pounds to pence first, so the numbers are easier to compare.

400 g for £2.40 or 250 g for £1.60

Key points

• The rate says what £1 buys, such as £1 = €1.15.
• Pounds to the other currency: multiply by the rate.
• The other currency back to pounds: divide by the rate.
• Sense-check: if £1 buys more than 1 euro, you get more euros than pounds.

Example