Ratios, Unit Rates, Proportions

Front

What is a ratio?

Back

A ratio is a comparison of two quantities that shows the relative size of one quantity to another, often expressed as 'a to b' or a:b.

Front

How do you write a ratio as a fraction?

Back

To write a ratio as a fraction, place the first quantity over the second quantity. For example, the ratio 5 to 3 can be written as 5/3.

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities when they are combined together, expressed as a quantity per one unit of another quantity.

Front

How do you find the unit rate from a total distance and total gallons of gas?

Back

To find the unit rate, divide the total distance by the total gallons of gas. For example, if 92 miles are driven using 4 gallons, the unit rate is 92/4 = 23 miles per gallon.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal. For example, if a/b = c/d, then a, b, c, and d are in proportion.

Front

How can you solve a proportion?

Back

To solve a proportion, cross-multiply the terms and then solve for the unknown variable. For example, if 5/3 = x/15, then 5*15 = 3*x.

Front

What does it mean to simplify a ratio?

Back

Simplifying a ratio means reducing it to its simplest form by dividing both quantities by their greatest common factor.

Front

If the ratio of dogs to cats is 5 to 3 and there are 25 dogs, how many cats are there?

Back

Using the proportion 5/3 = 25/c, we find c = 15. So, there are 15 cats.

Front

How do you maintain proportions in a recipe?

Back

To maintain proportions in a recipe, you can multiply or divide all ingredients by the same factor to keep the ratio of ingredients the same.

Front

If you earn $15 every 3 weeks, how much will you earn in 5 weeks?

Back

To find out, first find the weekly rate: $15/3 weeks = $5 per week. Then, multiply by 5 weeks: $5 * 5 = $25.