1 / 8

Today we will explore the Essential Question, “What is the process for solving problems involving rated measures ?”

Today we will explore the Essential Question, “What is the process for solving problems involving rated measures ?”.

fathi
Download Presentation

Today we will explore the Essential Question, “What is the process for solving problems involving rated measures ?”

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Today we will explore the Essential Question, “What is the process for solving problems involving rated measures?” A rated measure is a ratio of two unlike quantities such as feet per second, words per minute, or dollars per day. If a car travels at 15 feet per second, it travels a distance of 15 feet in 1 second. If a person types 60 words per minute, then 60 words are typed in 1 minute. If an employee earns $125 per day, he earns $125 in 1 day. Problems involving rated measure can be solved using proportions. A proportion is a statement that two rates (or ratios) are equal. When setting up the proportion, make sure that the units of the ratios match each other. When solving a problem involving rated measure, sometimes it is necessary to convert to a different unit. Here are the rules for conversion: • To convert from a larger unit to a smaller unit, multiply. (Multiply to change feet to inches.) • To convert from a smaller unit to larger unit, divide. (Divide to convert inches to feet.)

  2. Example 1: A receipt from the grocery store shows that 14 ounces of grapes cost $3.64. What was the cost per ounce of the grapes? 1 ounce costs ? The numbers that are used for the conversions are called conversion factors. These can be found on the FCAT formula sheet under “Conversions”. Set up a proportion with matching units as follows: Once the proportion is set up, drop the units and solve the proportion as shown: Therefore, the cost for 1 ounce of the grapes is $0.26.

  3. Next it is necessary to convert 156 pints into quarts. Since the conversion is from a smaller to a larger measure, divide by the conversion factor. Looking at the formula sheet, 1 quart = 2 pints, we see that the conversion factor is 2. Since = 78 , 78 quarts of soda should be ordered. Example 2: A picnic is being planned for 52 people and 3 pints of soda per person will be needed. How many quarts of soda should be ordered? The problem states that 3 pints are needed for 1 person. Set up a proportion to determine the number of pints that are needed for 52 people as follows: Now drop the units and solve the proportion as follows: Therefore, 156 pints of soda are needed.

  4. Guided Practice Problems: 1. Some friends will be hiking on the Appalachian Trail. They will hike 281 miles through Maine, 161 miles through New Hampshire, and 146 miles through Vermont. They expect to travel at a rate of 12 miles per day. How many days of hiking will it take them to reach the Massachusetts border? Total miles of hiking is 281 + 161 + 146 = 588. Proportion: Solution: It will take 49 days of hiking.

  5. Next it is necessary to convert 90 minutes into hours. Since the conversion is from a smaller to a larger measure, divide by the conversion factor. Looking at the formula sheet, 1 hour = 60 minutes, we see that the conversion factor is 60. Since = 1.5 , 1.5 hours is needed to burn 1,080 calories. 2. A rock climber burns 12 calories per minute of climbing. How many hours will it take him to burn 1,080 calories? Proportion: Solution: Therefore, it take 90 minutes to burn 1080 calories.

  6. 3. The sun travels along the Milky Way’s spiral arm at a rate of 250 kilometers per second. How far, in kilometers, will the sun travel in 3.5 minutes? In order to have matching units in the proportion, we must convert 3.5 minutes into seconds by multiplying by the conversion factor of 60. (3.5) x 60 = 210 seconds Proportion: Solution: The sun will travel 52,500 kilometers in 3.5 minutes.

  7. 4. Deidra works at a computer store and earns a bonus for each computer she sells. Her bonus check was $756 for 21 days of work. If she sold the same number of computers each day, how much bonus money did Diedra earn per day? Proportion: Solution: Deidra earned $36 per day in bonus money.

  8. Independent Practice Problems: Independently complete two sample questions on solving problems using rated measures. 1. A soup recipe calls for two 6 ounce cans of chicken broth. The recipe serves 4 people. A cook wants to adapt the recipe to serve 28 people. If he buys chicken broth in 1-pint containers, how many containers does he need to buy? (He can't buy a part of a container.) 1cup = 8 ounces 1 pint = 2 cups Therefore, 1 pint = 16 ounces. He must buy 6 containers. 2. Orlando is located 91 miles from Tampa. If a person can travel at an average rate of 65 miles per hour, how many minutes will it take to travel from Orlando to Tampa? (1.4)(60) = 84 minutes

More Related