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Finding and Using Unit Rates for Mathematical and Real-World Problems

This lesson focuses on calculating unit rates, representing constant rates of change, and solving problems involving ratios, rates, and percents. It also includes examples and practice questions.

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Finding and Using Unit Rates for Mathematical and Real-World Problems

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  1. Unit Rates 2.1 How do you find and use unit rates?

  2. Texas Essential Knowledge and Skills The student is expected to: Proportionality—7.4.B Calculate unit rates from rates in mathematical and real-world problems. Proportionality—7.4.A Represent constant rates of change in mathematical and real-world problems given pictorial, tabular, verbal, numeric, graphical, and algebraic representations, including d = rt. Proportionality—7.4.D Solve problems involving ratios, rate, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems.

  3. Texas Essential Knowledge and Skills 7.1.A Apply mathematics to problems arising in everyday life, society, and the workplace. Mathematical Processes The student is expected to:

  4. ADDITIONAL EXAMPLE 1 Georgio is building a patio. He estimates that he can install 8 square feet of paver bricks every quarter hour. How many square feet does Georgio install per hour? 32

  5. ADDITIONAL EXAMPLE 2 Two water heater tanks are leaking. Tank A has leaked of a gallon in minute, and Tank B has leaked of a gallon in minute. Which tank is leaking faster? Tank B

  6. 2.1 LESSON QUIZ 7.4.B 1. Jorge’s printer can print 24 pages in 15 minutes. How many pages can it print in hour? in 1 hour? 72 pages; 96 pages 2. Richard estimates that he can apply fertilizer to 4,485 square feet of grass in hour. How many square feet of grass can Richard fertilize per hour? 5,980 square feet

  7. Elle wanted to order candy online. Company A is offering pounds of chocolate for $32.50, while Company B is offering pounds of the same chocolate for $35.00. Which company is offering the lowest price per pound? 3. Company B

  8. The population density of a state is the average number of people per square mile. Write the population densities of each state. Round your answers to the nearest person per square mile. Then rank the states from least population density to greatest population density.

  9. [Source: 2010.census.gov/2010census] New Mexico, Utah, Oklahoma, Arizona, Texas

  10. How do you find and use unit rates? To find a unit rate, divide the numerator of the rate by the denominator. To compare rates with the same units, find and compare the unit rates.

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