Unit Rate and Proportions

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities where one of the quantities is expressed as a quantity of one. For example, if a car travels 300 miles on 10 gallons of gas, the unit rate is 30 miles per gallon.

Front

How do you calculate the unit price of an item?

Back

To calculate the unit price, divide the total price by the number of items. For example, if 8 items cost $14, the unit price is $14 ÷ 8 = $1.75 per item.

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 form a proportion.

Front

How can you determine if two ratios form a proportion?

Back

To determine if two ratios form a proportion, cross-multiply and see if the products are equal. If a/b = c/d, then check if a*d = b*c.

Front

If a recipe calls for 3 cups of flour for 4 servings, how much flour is needed for 10 servings?

Back

To find the amount of flour for 10 servings, set up a proportion: 3/4 = x/10. Cross-multiply to find x = 7.5 cups of flour.

Front

What is the formula for finding the unit rate of speed?

Back

The unit rate of speed is calculated by dividing the distance traveled by the time taken. For example, if a car travels 150 miles in 3 hours, the speed is 150 miles ÷ 3 hours = 50 miles per hour.

Front

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

Back

To find the total cost, multiply the unit price by the number of items. For example, if the unit price is $2 and you buy 5 items, the total cost is $2 × 5 = $10.

Front

What is the relationship between ratios and proportions?

Back

Ratios compare two quantities, while proportions state that two ratios are equal. For example, if the ratio of boys to girls is 2:3, a proportion could be 2/3 = 4/6.

Front

If 5 pounds of apples cost $10, what is the cost per pound?

Back

To find the cost per pound, divide the total cost by the weight: $10 ÷ 5 pounds = $2 per pound.

Front

What is the significance of unit rates in real-life situations?

Back

Unit rates help compare prices, speeds, and other quantities in real-life situations, making it easier to make informed decisions.