Rates, Unit Rates, Proportions

Front

What is a rate?

Back

A rate is a ratio that compares two different quantities, usually with different units, such as miles per hour or cost per item.

Front

What is a unit rate?

Back

A unit rate is a rate in which the second quantity is one unit. For example, if a car travels 60 miles in 1 hour, the unit rate is 60 miles per hour.

Front

How do you calculate a percentage?

Back

To calculate a percentage, divide the part by the whole and then multiply by 100. For example, if a student scores 45 out of 60, the percentage is (45/60) * 100 = 75%.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal. For example, if 1/2 = 2/4, then these two ratios are in proportion.

Front

How do you find the total cost when given a unit price?

Back

Multiply the unit price by the quantity purchased. For example, if the unit price is $5 and you buy 3 items, the total cost is 5 * 3 = $15.

Front

If a car travels 440 miles in 8 hours, how do you find the unit rate?

Back

Divide the total distance by the total time. In this case, 440 miles ÷ 8 hours = 55 miles per hour.

Front

What is the formula for finding the percentage of a quantity?

Back

The formula is (part/whole) * 100. For example, to find what percentage 30 is of 150, calculate (30/150) * 100 = 20%.

Front

How do you set up a proportion to solve for an unknown?

Back

Set up the equation as a/b = c/d, where a and b are known values, and c is the unknown. Cross-multiply to solve for the unknown.

Front

What is the relationship between rates and proportions?

Back

Rates can be expressed as proportions. For example, if 3 apples cost $6, the rate is 2 apples per dollar, which can be expressed as a proportion.

Front

How do you convert a fraction to a percentage?

Back

To convert a fraction to a percentage, divide the numerator by the denominator and multiply by 100. For example, 1/4 = (1 ÷ 4) * 100 = 25%.