Definition: A ratio is a comparison of two quantities by division, written a:b, a to b, or a/b, showing how much of one there is for each amount of the other.
What does a ratio tell you?
A ratio compares two amounts that share a context. Mathbot, our robot coach, keeps 12 wrenches and 8 screwdrivers in his toolbox, so the ratio of wrenches to screwdrivers is 12:8.
How do you write and simplify one?
You can write 12:8, 12 to 8, or 12/8. Order matters: 12:8 is wrenches first, while 8:12 flips the story. Divide both parts by the same nonzero number to simplify. Here both parts divide by 4, giving 3:2. That means 3 wrenches for every 2 screwdrivers.
A ratio can be part-to-part, as above, or part-to-whole. The part-to-whole ratio of wrenches to all tools is 12:20, which simplifies to 3:5.
What mistake should you avoid?
Do not subtract. Saying the ratio 12:8 is the same as 4:0 because 12 minus 8 is 4 is wrong. Ratios scale by multiplying or dividing both parts by one number, never by adding or subtracting the same amount.