Ratios, Rates, Unit Rates, Proportions, Percents
A ratio is a comparison of two things. We might compare boys to girls, cars to trucks or hours asleep to hours awake.
Whatever we choose to compare can then be written as a ratio. There are three different forms. A ratio can be written as a to b, a : b or
Ratios can be part-to-part, part-to-whole, or whole-to-part. For more on ratios, visit https://www.mathsisfun.com/numbers/ratio.html
Quick game to help students recognize ratios: http://www.mathplayground.com/ASB_RatioMartian.html
A rate is a comparison of two measurements or amounts that have different units. For example, 60 miles in 2 hours is a rate. A unit rate is a rate in which the second rate is 1 unit. For example, 30 miles in 1 hour, or 30 miles per hour, is a unit rate.
Unit Rate Games & Practice
A proportion is an equation stating that two ratios are equivalent.
4 dogs:1 cat = 12 dogs: 3 cats is a proportion.
We usually write proportions in fraction form because it is easier to work with them that way.
We can use Cross Multiplication to solve a missing part of a proportion:
Multiply across the known corners, then divide by the third number. And we get this: (42 × 10) / 20 = 420 / 20 = 21
Proportions Dirt Bike Racing Game: http://www.mathplayground.com/ASB_DirtBikeProportions.html
Proportions practice in IXL: https://www.ixl.com/math/grade-7/solve-proportions-word-problems
We can use the proportion to solve problems when we are missing one of the following: part, whole or percentage.
The video on the left works 3 problems, each solving for a different part of the proportion.
Here's another great video with more step-by-step problems: https://www.youtube.com/watch?v=ao89Kz-6Ed8