6th Grade Math: Help with Ratios and Rates

Ratio and Rate Help

What's a Ratio?

A ratio expresses the relationship between 2 related amounts. For instance, in a recipe, the amount of each ingredient that you add is related to the amounts of the other ingredients used. If you're making bread that has 2 cups of flour and 1 cup of water, you could write this as the ratio 2:1 (2 to 1). This information is helpful if you wanted to double the recipe because you'd know that if you doubled the flour to 4 cups, you'd also need to double the water to 2 cups.

Ratios are used in lots of other situations as well. For example, imagine that you're given a picture containing 2 triangles and 7 circles, and asked to write the ratio of triangles to circles. You'd simply count the number of each type of shape and write the ratio, which is 2:7. If you'd been asked to write the ratio of circles to triangles instead, it would be 7:2.

It's important to note that ratios can also be written as fractions. For instance, 2:7 would be 2/7 and 7:2 would be 7/2. You'll see why this is critical in the next section.

Understanding Unit Rates

You can think of a unit rate as yet another way of expressing a ratio. To calculate a unit rate, write the ratio as a fraction, and then divide the top number by the bottom number. This will tell you how many of the units on top there are for each bottom unit.

Let's use an example to make this a bit more concrete. Going back to the triangles and circles, recall that we said the ratio of triangles to circles was 2:7 or 2/7. To find the unit rate, solve 2 ÷ 7 to get a decimal that rounds to 0.3. This means there are about 0.3 triangles for every 1 circle.

You can also reverse this by stating the unit rate in terms of the ratio of circles to squares (7:2 or 7/2). Since 7 ÷ 2 = 3.5, you can also say there are 3.5 circles for every 1 triangle.

Unit rates are commonly used for situations that involve rates of speed. For instance, let's say you can ride your bike 20 miles every 2 hours, which can be represented by the ratio 20:2. To find the unit rate of speed in miles per hour (mph), write the ratio as a fraction and divide: 20/2 = 20 ÷ 2 = 10. This means that you're riding your bike at a speed of 10 mph if you cover 20 miles every 2 hours.