Rate and Unit Rate

rate and unit rate applications

Rates and unit rates are used to solve many real-world problems. Look at the following problem. "Tonya works 60 hours every 3 weeks. At that rate, how many hours will she work in 12 weeks?" The problem tells you that Tonya works at the rate of 60 hours every 3 weeks. To find the number of hours she will work in 12 weeks, write a ratio equal to 60/3 that has a second term of 12. 60/3 = 240/12 Tonya will work 240 hours in 12 weeks. You could also solve this problem by first finding the unit rate and multiplying it by 12. 60/3 = 20/1 20 x 12 = 240

unit price

When prices are expressed as a quantity of 1, such as $25 per ticket or $0.89 per can, they are called unit prices. If you have a multiple-unit price, such as $5.50 for 5 pounds of potatoes, and want to find the single-unit price, divide the multiple-unit price by the number of units. $5.50 ÷ 5 = $1.10 The unit price of potatoes that cost $5.50 for 5 pounds is $1.10 per pound.

unit rate

When rates are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour Ex: If you have a multiple-unit rate such as 120 students for every 3 buses, and want to find the single-unit rate, write a ratio equal to the multiple-unit rate with 1 as the second term. 120/3 = 40/1 The unit rate of 120 students for every 3 buses is 40 students per bus. You could also find the unit rate by dividing the first term of the ratio by the second term.

equal or equivalent ratios

When you find equal ratios, it is important to remember that if you multiply or divide one term of a ratio by a number, then you need to multiply or divide the other term by that same number. Example with Unit Price: A sign in a store says 3 Pens for $2.70. How much would 10 pens cost? To solve the problem, find the unit price of the pens, then multiply by 10. $2.70 ÷ 3 = $0.90 $0.90 times 10 = $9.00 Finding the cost of one unit first makes it easier to find the cost of multiple units.

ratio

a comparison of two numbers or measurements

rate

a special ratio in which the two terms are in different units Ex: If a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. The first term of the ratio is measured in cents; the second term in ounces. You can write this rate as 69¢/12 ounces or 69¢:12 ounces. Both expressions mean that you pay 69¢ "for every" 12 ounces of corn.

terms of a ratio

the numbers or measurements being compared