1. Holt McDougal Algebra 1 Rates, Ratios, and Proportions Questions on Module 1 HW? P. 28 #1-29 odds 1. 4 increased by n 3. The quotient of g and 2 5. 1.99g 7. 5 9. 6 11. 14 13. -21 15. 36 17. -21 19. 313+s=400; 87 GB 21. -36 23. 14 25. 7 27. 0

2. Holt McDougal Algebra 1 Rates, Ratios, and Proportions p. 29 #12 12. a) p=3000x+10000 b)c)4 trips

3. Holt McDougal Algebra 1 Rates, Ratios, and Proportions Holt Algebra 1 2-3 Precision & Accuracy 2-3 Precision & Accuracy 2-1 Rates, Ratios, & Proportions 2-1 Rates, Ratios, & Proportions Holt McDougal Algebra 1

4. Rates, Ratios, and Proportions Write and use ratios, rates, and unit rates. Write and solve proportions. Objectives Analyze and compare measurements for precision and accuracy. Choose an appropriate level of accuracy when reporting measurements.

5. Holt McDougal Algebra 1 Rates, Ratios, and Proportions A ratio is a comparison of two quantities by division. The ratio of a to b can be written a:b or, where b ≠ 0. Ratios that name the same comparison are said to be equivalent. A statement that two ratios are equivalent, such as, is called a proportion. Vocabulary

6. Holt McDougal Algebra 1 Rates, Ratios, and Proportions Reading Math Read the proportion as “1 is to 15 as x is to 675”.

7. Holt McDougal Algebra 1 Rates, Ratios, and Proportions Example 1: Using Ratios The ratio of the number of bones in a human ’ s ears to the number of bones in the skull is 3:11. There are 22 bones in the skull. How many bones are in the ears? Write a ratio comparing bones in ears to bones in skull. Write a proportion. Let x be the number of bones in ears. Since x is divided by 22, multiply both sides of the equation by 22. There are 6 bones in the ears.

8. Holt McDougal Algebra 1 Rates, Ratios, and Proportions A rate is a ratio of two quantities with different units, such as Rates are usually written as unit rates. A unit rate is a rate with a second quantity of 1 unit, such as or 17 mi/gal.

9. Holt McDougal Algebra 1 Rates, Ratios, and Proportions Example 2: Finding Unit Rates Raulf Laue of Germany flipped a pancake 416 times in 120 seconds to set the world record. Find the unit rate. Round your answer to the nearest hundredth. The unit rate is about 3.47 flips/s. Write a proportion to find an equivalent ratio with a second quantity of 1. Divide on the left side to find x.

10. Holt McDougal Algebra 1 Rates, Ratios, and Proportions In the proportion, the products a d and b c are called cross products. You can solve a proportion for a missing value by using the Cross Products property. Cross Products Property WORDSNUMBERS ALGEBRA In a proportion, cross products are equal. 2 6 = 3 4 If and b ≠ 0 and d ≠ 0 then ad = bc.

11. Holt McDougal Algebra 1 Rates, Ratios, and Proportions Example 3: Solving Proportions Solve each proportion. 3(m) = 5(9) 3m = 45 m = 15 Use cross products. Divide both sides by 3. Use cross products. 6(7) = 2(y – 3) 42 = 2y – 6 +6 48 = 2y 24 = y A.B. Add 6 to both sides. Divide both sides by 2.

12. Holt McDougal Algebra 1 Rates, Ratios, and Proportions A scale is a ratio between two sets of measurements, such as 1 in:5 mi. A scale drawing or scale model uses a scale to represent an object as smaller or larger than the actual object. A map is an example of a scale drawing.

13. Holt McDougal Algebra 1 Rates, Ratios, and Proportions Vocabulary A precision is the level of detail in a measurement and is determined by the smallest unit or fraction of a unit that you can reasonably measure. The accuracy of a measurement is the closeness of a measured value to the actual or true value. Tolerance describes the amount by which a measurement is permitted to vary from a specified value.

14. Holt McDougal Algebra 1 Rates, Ratios, and Proportions A. 0.8 km; 830.2 m A tenth of a meter is smaller than a tenth of a kilometer, so 830.2 m is more precise. Example 4: Comparing Precision of Measurements B. 2.45 in.; 2.5 in. Choose the more precise measurement in each pair. 0.8 km Nearest tenth of a kilometer 830.2 m Nearest tenth of a meter

15. Holt McDougal Algebra 1 Rates, Ratios, and Proportions A hundredth of an inch is smaller than a tenth of an inch, so 2.45 in. is more precise. A centimeter is smaller than a meter, so 100 cm is more precise. Example 4: Continued C. 100 cm; 1 m 2.45 in. 2.5 in. Nearest hundredth of an inch Nearest tenth of an inch 100 cm 1 m Nearest centimeter Nearest meter

16. Holt McDougal Algebra 1 Rates, Ratios, and Proportions A standard mass of 16 ounces is used to test three postal scales. The results are shown below. Check It Out! Example 5 A. Which scale is the most precise? Scales A and B measure to the nearest tenth of an ounce.

17. Holt McDougal Algebra 1 Rates, Ratios, and Proportions Check It Out! Example 5 Continued B. Which scale is the most accurate? Scale C measures to the nearest hundredth of an ounce. Because a hundredth of an ounce is smaller than a thousandth of an ounce, Scale C is the most precise. For each scale, find the absolute value of the difference of the standard mass and the scale reading.

18. Holt McDougal Algebra 1 Rates, Ratios, and Proportions Check It Out! Example 5 Continued Because 0.07 < 0.2 < 0.3, Scale C is the most accurate. Scale A: |16.00 – 16.3| = 0.3 Scale B: |16.00 – 15.8| = 0.2 Scale C: |16.00 – 16.07| = 0.07

19. Holt McDougal Algebra 1 Rates, Ratios, and Proportions Bright Days Blinds makes window shades. The width of a 30-inch shade should be within 0.18 in. of 30 in. A batch of shades has the widths shown in the table. Example 6 : Using a Specified Tolerance

20. Holt McDougal Algebra 1 Rates, Ratios, and Proportions Do all of the shades measure within the specified tolerance? If not, which shade(s) are not within the specified tolerance? No, Shade B measures 29.75 in., so it is not within the specified tolerance. Example 6 : Continued 30 – 0.18 = 29.82 30 in. ± 0.18 in. means that the shade must be 30 + 0.18 = 30.18 between 29.82 and 30.18 in.

21. Holt McDougal Algebra 1 Rates, Ratios, and Proportions A. 12 lb ± 3% 11.64 lb–12.36 lb Example 7: Using Tolerance Expressed as a Percent Write the possible range of each measurement. Round to the nearest hundredth if necessary. 12(0.03) = 0.36 Find 3% of 12. 12 lb  0.36 lb Write the measurement and tolerance. Write the measurement as a range.

22. Holt McDougal Algebra 1 Rates, Ratios, and Proportions 14.77 oz–15.23 oz Example 7: Continued B. 15 oz ± 1.5% C. 3 m ± 0.2% 15(0.15) = 0.225Find 1.5% of 15. 15 oz  0.23 oz Write the measurement and tolerance. Round to the nearest hundredth. Write the measurement as a range. 3(0.002) = 0.006Find 0.2% of 3.

23. Holt McDougal Algebra 1 Rates, Ratios, and Proportions Example 7: Continued 2.99 m–3.01 m 3 m  0.01 m Write the measurement and tolerance. Round to the nearest hundredth. Write the measurement as a range.

24. Holt McDougal Algebra 1 Rates, Ratios, and Proportions Tonight’s HW: p. 52 #1-8, 11-18 all