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3-4 Ratios and Proportions

3-4 Ratios and Proportions. Ratio – comparison of two numbers by division. There are three ways to write a ratio . Using the word “to” 2 to 3 . Using a colon 2:3. Using a fraction bar. They are all read as “two to three” . A r ate is a ratio with units

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3-4 Ratios and Proportions

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  1. 3-4Ratios and Proportions

  2. Ratio– comparison of two numbers by division • There are three ways to write a ratio • Using the word “to” • 2 to 3 Using a colon 2:3 Using a fraction bar • They are all read as • “two to three”

  3. A rateis a ratio with units Ex. 2 pounds or $2.49 $5 8 oz

  4. Ratios and rates work just like fractions…so finding an equivalent ratio or rate is the same as finding an equivalent fraction. Example: Is equivalent to

  5. Identify some equivalent ratios & rates:

  6. A unit rate is a special type of rate. It’s denominator is one, so it tells “how much for one?” If a rate is 2 pounds, $5 • The unit rate would be how many pounds for $1? If a rate is $2.49, 8 oz • The unit rate would be how much for 1 ounce?

  7. Proportions A proportion is a set of two equal ratios. A proportion can be written two ways: or a:b = c:d • No matter which way it is written, it should be read as: • a is to b as c is to d

  8. ORDER IS IMPORTANT!! INCLUDING LABELS WILL HELP YOU WRITE PROPORTIONS CORRECTLY! For example: A basketball team scores 17 points in the first 8 minutes of play. At this rate how many points will the team score in a 32 minute game? I can find out the answer by writing and solving a proportion. 17 points is to 8 minutes as x points is to 32 minutes OR 17 points : 8 minutes = x points : 32 minutes

  9. To solve this problem, we will use the “inside-outside” method. This means, you multiply to inside numbers, multiply the outside numbers, then set them equal to each other. In our example, we had 17 points : 8 minutes = x points : 32 minutes inside outside When I multiply the inside numbers I get 8x. When I multiply the outside numbers I get 544. Next, I set them equal to each other, so 8x = 544. That’s just a simple, one-step equation. Solve it by dividing both sides by 8, and you get x=68.

  10. Another way to solve proportion problems is using the cross products method. When using cross products, you set up your proportion as two fractions. Then you find the cross products by multiplying diagonally and setting the products equal to each other. ad = cb

  11. Going back to our example. A basketball team scores 17 points in the first 8 minutes of play. At this rate how many points will the team score in a 32 minute game? Going back to our example. A basketball team scores 17 points in the first 8 minutes of play. At this rate how many points will the team score in a 32 minute game? ORDER IS IMPORTANT!! INCLUDING LABELS WILL HELP YOU WRITE PROPORTIONS CORRECTLY! Find the cross products: 17 ● 32 = 8 ● x 544 = 8x Does this equation look familiar?? Again, you get a simple one-step equation to solve. Solve it by dividing both sides by 8, and you get: x = 32

  12. Which method is better? Inside/Outside or Cross-products? Inside/Outside Cross-products pros cons pros cons

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