Level 4 · Ages 13–15
Read it again any time, including while you work through the exercises.
Two friends wash cars all Saturday. One worked 2 hours, the other 3 hours. Splitting the 35 € earned into two equal parts would be unfair: you share in the ratio 2:3. The ratio says how many parts each person gets.
The method is always the same. Count the total number of parts: 2 + 3 = 5. Compute the value of one part: 35 ÷ 5 = 7 €. Then distribute: 2 × 7 = 14 € for one, 3 × 7 = 21 € for the other. Check: 14 + 21 = 35, everything is distributed.
Be careful not to confuse a ratio with a fraction of the total. In a ratio 2:3, the smaller share is not 2/3 of the total: it is 2 parts out of 5, so 2/5 of the total. The denominator is the total number of parts.
Scales work on the same idea of proportionality. A scale of 1/200 means 1 cm on the plan represents 200 cm in real life. To go from plan to reality, multiply by 200; to go from reality to plan, divide by 200. Remember to convert units at the end: 600 cm is 6 m.
In this lesson you will share amounts in two-part and three-part ratios, and read scale drawings like an architect.
Share 35 € between Lea and Tom in the ratio 2:3 (2 parts for Lea, 3 for Tom).
2 + 3 = 5
I count the total number of parts: 2 parts for Lea and 3 for Tom, so 5 parts in total.
35 ÷ 5 = 7
I compute the value of one part: 35 € split into 5 equal parts, each part is worth 7 €.
2 × 7 = 14 ; 3 × 7 = 21
I distribute: Lea gets 2 parts (14 €) and Tom 3 parts (21 €).
14 + 21 = 35
I check that all the money is distributed: 14 + 21 = 35. Perfect.
Result: Lea gets 14 € and Tom gets 21 €.
On a plan at scale 1/200, a room is 3 cm long. What is its real length?
3 × 200 = 600
Scale 1/200: each centimetre on the plan represents 200 real centimetres. So I multiply by 200.
600 cm = 6 m
I convert to a suitable unit: 600 cm is 6 m.
Result: The room is 6 m long in real life.