Ratios, 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:b'.

Front

What is a unit rate?

Back

A unit rate is a ratio that compares a quantity to one unit of another quantity, often used to determine the cost per item or the speed per hour.

Front

How do you calculate a unit rate?

Back

To calculate a unit rate, divide the total quantity by the number of units. For example, if you have 15 gallons of gas for $31.20, the unit rate is $31.20 ÷ 15 = $2.08 per gallon.

Front

What is the ratio of shaded squares to total squares if there are 10 shaded and 6 not shaded?

Back

The ratio of shaded squares to total squares is 10:16, which simplifies to 5:8.

Front

If Scott exercised for 18 minutes running, 20 minutes biking, and 15 minutes lifting weights, what is the total time he exercised?

Back

The total time Scott exercised is 18 + 20 + 15 = 53 minutes.

Front

What is the ratio of time spent biking to total exercise time if he biked for 20 minutes?

Back

The ratio of time spent biking to total exercise time is 20:53.

Front

How do you simplify a ratio?

Back

To simplify a ratio, divide both terms by their greatest common divisor (GCD). For example, to simplify 10:6, divide both by 2 to get 5:3.

Front

What is the relationship between ratios and fractions?

Back

Ratios can be expressed as fractions, where the first term is the numerator and the second term is the denominator.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal, such as a:b = c:d.

Front

How can you check if two ratios form a proportion?

Back

To check if two ratios form a proportion, cross-multiply and see if the products are equal. For example, for 1:2 and 2:4, check if 1*4 = 2*2.