The angles of a triangle are in the ratio 2 : 3 : 4. Find the largest angle.
- Total parts = 2 + 3 + 4 = 9, and the angles add up to 180°.
- One part = 180° ÷ 9 = 20°.
- Largest angle = 4 parts = 4 × 20° = 80°.
Answer: 80°
Ratio and proportion
Maths · Number. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
The idea
A ratio compares quantities by showing how many equal parts each one has. In the ratio 3 : 5 there are 8 parts in total. A ratio can be simplified like a fraction, but the quantities must be in the same units first.
Most ratio problems are solved by finding the value of one part. Decide what the given number stands for: the total, one share, or the difference between two shares. Divide by that number of parts, then multiply.
In direct proportion two quantities rise together, such as cost and number of items. In inverse proportion one rises as the other falls, such as workers and the time for a job. Map scales are ratios too.
Rules to remember
- one part = given amount ÷ number of parts it stands for
- Sharing in the ratio a : b: the shares are a/(a + b) and b/(a + b) of the total.
- Simplify by dividing every part by the same number, with all quantities in the same units.
- Direct proportion: find the value for one, then multiply (the unitary method).
- Inverse proportion: the product stays the same, so workers × days is constant.
- Scale 1 : n: actual distance = map distance × n. 1 km = 100 000 cm.
- To join a : b and b : c, make the b values equal first.
Common mistake
Dividing by the total number of parts when the question gives a difference or one share. If one person gets $45 more and the ratio is 2 : 7, then $45 is 5 parts, not 9.
Worked example
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