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Holt McDougal Algebra 1 Rates, Ratios, and Proportions Holt Algebra Precision & Accuracy 2-3 Precision & Accuracy 2-1 Rates, Ratios, & Proportions 2-1 Rates, Ratios, & Proportions Holt McDougal Algebra 1
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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
Holt McDougal Algebra 1
Rates, Ratios, and Proportions
p. 29 #1212. a) p=3000x+10000b) c)4 trips
Holt McDougal Algebra 1
Rates, Ratios, and ProportionsRates, Ratios, and Proportions
Holt Algebra 1
2-3 Precision & Accuracy
2-1 Rates, Ratios, & Proportions
Holt McDougal Algebra 1
Holt McDougal Algebra 1
Rates, Ratios, and 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.
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
Holt McDougal Algebra 1
Rates, Ratios, and Proportions
Reading Math
Read the proportion as
“1 is to 15 as x is to 675”.
Holt McDougal Algebra 1
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.
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.
Holt McDougal Algebra 1
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.
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
WORDS NUMBERS ALGEBRA
In a proportion, cross products are equal.
2 • 6 = 3 • 4
If and b ≠ 0
and d ≠ 0then ad = bc.
Holt McDougal Algebra 1
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.
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.
Holt McDougal Algebra 1
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.
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 kilometer830.2 m Nearest tenth of a meter
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 inchNearest tenth of an inch
100 cm1 m
Nearest centimeterNearest meter
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.
Holt McDougal Algebra 1
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.
Holt McDougal Algebra 1
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
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
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.
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.
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) = 0.225 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.
Holt McDougal Algebra 1
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.
Holt McDougal Algebra 1
Rates, Ratios, and Proportions
Tonight’s HW:p. 52 #1-8, 11-18 all