Holt McDougal Algebra 1 Rates, Ratios, and Proportions Questions on Module 1 HW? P. 28 #1-29 odds 1.…

Holt McDougal Algebra 1

Rates, Ratios, and ProportionsQuestions on Module 1 HW? P. 28 #1-29 odds1. 4 increased by n3. The quotient of g and 25. 1.99g7. 59. 611. 1413. -2115. 36

17. -2119. 313+s=400; 87 GB21. -3623. 1425. 727. 0

29. g=2400; $4000


Rates, Ratios, and Proportions

p. 29 #1212. a) p=3000x+10000b) c)4 trips


Rates, Ratios, and ProportionsRates, Ratios, and Proportions

Holt Algebra 1

2-3 Precision & Accuracy

2-1 Rates, Ratios, & Proportions




Write and use ratios, rates, and unit rates.Write and solve proportions.

Objectives

Analyze and compare measurements forprecision and accuracy. Choose an appropriate level of accuracy when reportingmeasurements.



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



Reading Math

Read the proportion as

“1 is to 15 as x is to 675”.


Rates, Ratios, and ProportionsExample 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.



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.


Rates, Ratios, and ProportionsExample 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.



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

WORDS NUMBERS ALGEBRA

In a proportion, cross products are equal.

2 • 6 = 3 • 4

If and b ≠ 0

and d ≠ 0then ad = bc.


Rates, Ratios, and ProportionsExample 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 +648 = 2y

24 = y

A. B.

Add 6 to both sides.Divide both sides by 2.



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.


Rates, Ratios, and ProportionsVocabulary

A precision is the level of detail in ameasurement and is determined by thesmallest 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.



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 kilometer830.2 m Nearest tenth of a meter



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 inchNearest tenth of an inch

100 cm1 m

Nearest centimeterNearest meter



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.


Rates, Ratios, and ProportionsCheck 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.


Rates, Ratios, and ProportionsCheck It Out! Example 5 Continued

Because 0.07 < 0.2 < 0.3, Scale C is the most accurate.

Scale A: |16.00 – 16.3| = 0.3Scale B: |16.00 – 15.8| = 0.2 Scale C: |16.00 – 16.07| = 0.07



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



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.



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.



14.77 oz–15.23 oz

Example 7: Continued

B. 15 oz ± 1.5%

C. 3 m ± 0.2%

15(0.15) = 0.225 Find 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) = 0.006 Find 0.2% of 3.


Rates, Ratios, and ProportionsExample 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.



Tonight’s HW:p. 52 #1-8, 11-18 all

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Holt McDougal Algebra 1 Rates, Ratios, and Proportions Questions on Module 1 HW? P. 28 #1-29 odds 1.…