Chapter 07
Ratios and proportions
A ratio compares two amounts without saying how much of either there is. Ten boys and fifteen girls is the same comparison as two boys for every three girls, and the second form is the useful one.
Once two ratios are known to be equal, a missing amount in one of them can be found from the other. That is what a proportion is for.
Ratios and proportions
A ratio compares two amounts. A proportion says that two ratios are equal.
- A class with 10 boys and 15 girls has a ratio of 10:15.
- That ratio simplifies to 2:3, the same way a fraction simplifies.
- 1/2 = 2/4 is a proportion, because both sides are the same amount.
Word problem
If 3 notebooks cost $6, how much do 6 notebooks cost?
$12
Speed and distance
A few of these are usually memorised. The rest follow from what they describe: profit is what is left after the cost comes off, which is the formula itself stated in words.
Speed and distance
- Speed
s = d ÷ t
- s is speed
- d is distance
- t is time
How far you went, shared out over how long it took.
Example
A car goes 150 miles in 3 hours.
150 ÷ 3 = 50
The speed is 50 mph.
- Distance
d = s × t
- d is distance
- s is speed
- t is time
The same formula turned around, when you know the speed and the time.
Example
A car goes 60 mph for 4 hours.
60 × 4 = 240
It travels 240 miles.