Ratio
A comparison of two numbers or quantities. They are measured in the same or similar units.
Example:
If the ratio of adults to children is 2 to 5, then there are two adults for every 5 children. So, if
there are 50 children in attendance, then there are 20 adults.
Ratios can be written in three ways: 2 to 5 2:5 2/5
The ratio is the comparison between two quantities in terms of their magnitudes. The ratio of two quantities a and b in some units is the fraction a/b and we write it as a: b. In the ratio a:b, we call ‘a’ the first term or antecedent and ‘b’, as the second term or consequent.
There are 3 blue squares to 1 yellow square
Ratios can be shown in different ways:
Use the “:” to separate the values: | 3 : 1 | |
Or we can use the word “to”: | 3 to 1 | |
Or write it like a fraction: | 3/1 |
A ratio can be scaled up:
Here the ratio is also 3 blue squares to 1 yellow square, even though there are more squares.
Recipes
Example: A Recipe for pancakes uses 3 cups of flour and 2 cups of milk.
So the ratio of flour to milk is 3 : 2
To make pancakes for a LOT of people we might need 4 times the quantity, so we multiply the numbers by 4:
3×4 : 2×4 = 12 : 8
In other words, 12 cups of flour and 8 cups of milk.
The ratio is still the same, so the pancakes should be just as yummy.
“Part-to-Part” and “Part-to-Whole” Ratios
The examples so far have been “part-to-part” (comparing one part to another part).
But a ratio can also show a part compared to the whole lot.
Example: There are 5 pups, 2 are boys, and 3 are girls
Part-to-Part:
The ratio of boys to girls is 2:3 or 2/3
The ratio of girls to boys is 3:2 or 3/2
Part-to-Whole:
The ratio of boys to all pups is 2:5 or 2/5
The ratio of girls to all pups is 3:5 or 3/5
Scaling
We can use ratios to scale drawings up or down (by multiplying or dividing).
Example: To draw a horse at 1/10th normal size, multiply all sizes by 1/10th
This horse in real life is 1500 mm high and 2000 mm long, so the ratio of its height to length is
1500 : 2000
What is that ratio when we draw it at 1/10th normal size?
1500 : 2000 | = 1500×1/10 : 2000×1/10 | |
= 150 : 200 |
We can make any reduction/enlargement we want that way.