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Ratios, Rates, and Proportions

Ratios, Rates, and Proportions. Ratios. Ratios are used to make comparisons. Ratios can be written in three different ways: Using the word “to” As a fraction Using a colon ( : ). Example of Ratio.

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Ratios, Rates, and Proportions

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  1. Ratios, Rates, and Proportions

  2. Ratios • Ratios are used to make comparisons. • Ratios can be written in three different ways: • Using the word “to” • As a fraction • Using a colon ( : )

  3. Example of Ratio • In Mrs. Davidson’s homeroom, there are 12 boys and 11 girls. Write the ratio of boys to girls. • 12 boys to 11girls • 12 boys/11girls • 12 boys:11girls

  4. Rates • What is a rate? • A rate is a form of ratio in which the two terms are in different units.

  5. Example of Rate • If a car goes 100 miles in 2 hours, then the rate would be:

  6. What is unit rate? • Unitrate is a rate in which the rate is expressed as a quantity of 1. • Simply put, unitrate is a rate which has denominator of 1.

  7. How do you find unit rate? • Rate can be converted to unitratesimply by dividing the first term by second term.

  8. Consider the following example… • Rate: • Unit Rate:

  9. Proportions • Proportions are made up of two equivalent ratios. • Remember, to check to see if two ratios are equivalent, you can: • Cross multiply to see if you get the same thing. • Reduce both ratios to lowest terms and compare. • Convert both ratios to decimals and compare.

  10. Solving Proportions • When solving proportions, you will be given 3 of the 4 pieces of information. • You represent the missing piece of information with a variable (a letter). This is what you are solving for.

  11. Solving Proportions • After your proportion is set up, you cross multiply and set up a one-step equation. • To solve for the variable, you must solve the one-step equation.

  12. Solving Proportions with Real-World Applications • Anytime you are setting up and solving proportions, be sure to LABEL YOUR UNITS!! • Otherwise, your answer means NOTHING!

  13. Setting up a Proportion • Whatever your unit is in the numerator on the left side of your proportion will be your unit for the numerator on the right side of your proportion. • Whatever your unit is in the denominator on the left side of your proportion will be your unit for the denominator on the right side of your proportion. • BE CONSISTENT WITH YOUR UNITS!!!

  14. Example Task • If Michael puts 9 gallons of gas in his car and it costs him $28.49, how much will it cost him to fill up his car if his gas tank will hold 22 gallons? Round to the nearest cent.

  15. Step 1- Set up a proportion. Remember, BE CONSISTENT with how you set it up regarding your unit labels.

  16. Step 2- Cross multiply to create a one-step equation.

  17. Step 3- Solve the one-step equation for x.

  18. So what does your answer mean? • It will cost Michael $69.64 to fill up his 22-gallon gas tank.

  19. Exit Ticket • Ten people are seen before lunch at a doctor’s office. Of those 10 people, 8 had the flu. If 35 patients are seen throughout the course of the day, how many would you expect to have the flu if the morning’s rate was consistent for the rest of the day? Set up and solve a proportion.

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