What are ratios and rates? (6th/7th grade math)

First, we look at the basic concept of a RATIO. A ratio is a comparison of two numbers (or quantities) using division. For example, if I have 4 hearts and 3 stars, then the ratio of hearts to stars is 4:3 (four to three). Then I also show how to simplify ratios (just like you'd simplify fractions!) and what are equivalent ratios.

If each term of a ratio is a quantity with some unit, and the two units are different, then we have a RATE. For example, 160 km to 2 hours is a rate. It can be simplified to 80 km to 1 hr, and then is usually written as 80 km/h (using "per" instead of "to").

We also practice writing equivalent rates and simplifying rates.

See also

How to find a unit rate, including with fractions — video lesson

Math Mammoth Grade 6 curriculum

Math Mammoth Grade 7 curriculum (pre-algebra)

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