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Ratios and Direct Proportion
Converting units
Converting currencies
 Scale (maps and drawings)
Example 1:
A recipe uses 200g of flour to make 4 cakes.
How much flour would I need for 5 cakes?
1. Write down column headings Cakes
TiDi stands for
Times and Divide
Flour (g)
2. Write down what you know
3. Write down new information
4 200
4. Write ? for the unknown quantity 5
5. Draw the diagonals as shown
?
6. One diagonal connects two numbers . . .
Multiply these numbers together 5 x 200 = 1000
7. The other diagonal connects the question mark and a single number . . .
Divide your answer by this single number 1000 ÷ 4 = 250
Answer: 5 cakes need 250g of flour
Example 2:
Write 285 minutes in hours. (Give your answer as a decimal)
1. Write down column headings
2. Write down what you know
Hours Minutes
(the conversion factor)
3. Write down new information
1 60
4. Write ? for the unknown quantity ? 285
4. Draw the diagonals
5. Multiply the two numbers joined with a line 1 x 285 = 285
6. Divide your answer by the single number 285 ÷ 60 = 4.75
Answer: 4.75 hours (that’s 4¾ hours, or 4 hr 45 min)
6 0
4 .
7 5
2 8 5 .
45
0
30
0
1

(b)
Example 3:
Once upon a time, £1 = 1.6 euros (€)
(a) How many euros in £7?
(b) How many pounds in 32 euros?
(a) Headings
What you know (the exchange rate)
£ €
1 1.6
New information and ? for unknown 7 ?
? = 7 × 1.6 = 11.20 euros
1
Headings
What you know (the exchange rate)
New information and ? for unknown ?
? = 1 × 32 = £20
1.6
£ €
1 1.6
32
Example 4:
A map has a scale of 4 cm : 1 km
(a) Two towns are 7 cm apart on the map.
How far is the actual distance between the towns?
(b) A lane is 1.4 km long. How many centimetres would this be on the map?
(a) Headings
What you know(the scale)
Map (cm) Actual (km)
4 1
New information and ? for unknown 7 ?
(b)
? = 7 × 1 = 1.75 km
4
Headings Map (cm) Actual (km)
What you know(the scale) 4 1
New information and ? for unknown ? 1.4
? = 4 × 1.4 = 5.6 cm
1
Make sure you work in the correct units.
2

Example 5:
The ratio of men to women in a factory is 5 : 8
If there are 600 women in the factory, how many men are there?
Headings
What you know (the ratio)
Men Women
5 8
New information and ? for unknown ? 600
? = 5 × 600 = 375 men
8
1 -- identify that the problem involves inverse (not direct) proportion:
as one quantity increases, a second quantity decreases (in the same ratio).
2 -- draw parallel lines rather than a diagonal cross.
3 -- you still multiply along the line joining two numbers.
4 -- you still divide by the single number (connected by the line to the question mark).
Example 6:
20 cows take 6 days to eat a supply of hay.
How many days would 30 cows take to eat the same amount of hay?
Headings
What you know (the ratio)
Cows Days
20 6
New information and ? for unknown 30 ?
Example 7:
? = 20 × 6 = 4 days
30
4 men can complete a job in 15 days. If the job must be finished
in 12 days, how many men must be employed?
Headings
What you know (the ratio)
Men Days
4 15
New information and ? for unknown ? 12
? = 4 × 15 = 5 days
12
3

(Answer on a separate sheet. Show your working)
Direct Proportion
1. Write 375 cm in metres
2. Write 4.8 litres in millilitres
3. Write 3½ hours in minutes
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You need to memorise common conversion factors
4. Write 15 miles in kilometres (5 miles = 8 km)
5. Write 50 km in miles (5 miles = 8 km)
6. If there are $1.9 to the pound, change $95 to pounds.
7. If there are $1.9 to the pound, change £4 to dollars.
8. A recipe needs 50g of butter to make 12 cakes.
How much butter would I need for 9 cakes?
9. I mix red and yellow paint in the ratio 3 : 2.
If I use 450 ml of red, how much yellow should I use?
10. A plan has a scale of 1:20. A table measures 150cm in length.
How long should I draw it on the plan?
11. There are 12 inches in a foot. How many inches in 7 feet?
12. There are 12 inches in a foot. How many feet in 132 inches?
Inverse Proportion
13. 10 bakers can ice 45 buns in 24 minutes. How long would it take 6 bakers to ice 45 buns, working at the same rate?
14. A car journey takes 20 minutes, travelling at an average speed of 48 mph.
How long would the same journey take by bike, travelling at 15 mph?
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