1 / 26

Proportions

Ratios: Review. Ratios are a comparison between two numbers.Ratio:2-cycle engines: gas to oilMetro area: renters to home ownersMetal shop: contract work to custom workFormat:4 to 54:54/5. Write a Ratio. State the ratio of length to width of a picture frame with the following dimensions..

zared
Download Presentation

Proportions

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. Proportions Chapter 4 Section 5

    2. Ratios: Review Ratios are a comparison between two numbers. Ratio: 2-cycle engines: gas to oil Metro area: renters to home owners Metal shop: contract work to custom work Format: 4 to 5 4:5 4/5

    3. Write a Ratio State the ratio of length to width of a picture frame with the following dimensions.

    4. Proportion A proportion is an equation that says one ratio is equal to another.

    5. Solve Proportions When 3 of the 4 values are known in a proportion, we must solve for the missing number.

    6. Proportions are a good problem solving tool when you know two related quantities… Quantity and Price …and you make a change to one of them. Use Proportions to Solve Problems

    7. Sample Problem 5 quarts of oil cost $6.75. If you want to buy 7 quarts, the price should be _____________.

    8. An increase in one quantity leads to an increase in the related quantity: A decrease in one quantity leads to a decrease in the related quantity: Direct Proportions General Characteristics

    9. Practice Worksheet MathXL

    10. Use equations of variation to solve problems.

    11. Solve using equations of variation In this problem… 5 quarts of oil cost $6.75. If you want to buy 7 quarts, the price should be $9.45. …there is a “hidden” number:

    12. Direct Variation “cost varies directly as quantity” c = 1.35q If I have $15, how many quarts of oil can I buy? If I buy 18 quarts of oil, how much will it cost?

    13. Direct Variation General Form y = kx “y varies directly as x” “y is directly proportional to x” “y varies as x”

    14. Direct Variation Example (generic) y is directly proportional to x. When y is 27, x is 3. Find y when x is 6.

    15. Application Direct Variation The weight on the end of a spring varies directly as the length that the spring stretches. If a weight of 8.0 lb stretches the spring 2.3”, what weight will stretch it 5.7”?

    17. Sample Problem At an average speed of 50 mph you can reach Madison in 95 minutes. If you are able to increase your average speed to 60 mph, how long should it take to reach Madison?

    18. Inverse Variation

    20. Inverse Variation Practice Problem In theory, the length of time needed to complete a construction project is inversely proportional to the amount of workers on the job. If a small construction job takes 58 hours using 7 workers, how long would a similar job take if 9 workers were used?

    21. Other scenarios: y varies directly as the square of x. y varies directly as r and t. y varies inversely as x and directly as the square of w. t varies directly as r and s and inversely as the square root u. Combined Variation

    22. Combined Variation Applications When an electrical current flows through a wire, the resistance to the flow varies directly as the length and inversely as the cross-sectional area. The intensity of illumination on a surface varies inversely as the square of the distance from the source.

    23. Application

    24. Practice Problem The wing area of model airplane is 1550 square inches. The wingspan of the model is 65”. If a new model was build where all dimensions were 20% longer, what will be the area of the resulting wing?

    25. Application The maximum safe load of a rectangular beam varies jointly as the width and the square of the depth, and inversely as the length of the beam. If a beam 8” wide, 11.5” deep, and 16 ft long can safely support 15,000 lb… …find the safe load for a beam 6.5” wide, 13.4” deep and 21 ft long made of the same material.

    26. Practice MathXL

More Related