Transcript 8-5
8-5 Estimating with Percents Pledge & Moment of Silence Pre-Algebra 8-5 Estimating with Percents Pre-Algebra HOMEWORK Page 423 #31-38 & Spiral Review Pre-Algebra (#39-45) 8-5 Estimating with Percents Our Learning Goal Students will be able to determine and construct fractions, decimals, and percents by understanding their relationships, solving for the unknown, solving increase and decrease, solving sales tax/total cost contextual problems and compute simple interest. Pre-Algebra Our Learning Goal Assignments • Learn to relate decimals, fractions, & percents (8-1) • Learn to find percents (8-2) • Learn to find a number when the percent is known (8-3) • Learn to find percent increase and decrease (8-4) • Learn to estimate with percents (8-5) • Learn to find commission, sales tax, and withholding tax (8-6) • Learn to compute simple interest (8-7) 8-5 Estimating with Percents Learning Goal Scale Students are able to determine & construct fractions, decimals, & percents: 4 • • • • • Clear understanding their relationships Able to solve for the unknown Understands how to solve for increase & decrease Calculating solving sales tax/total cost contextual problems Computing simple interest Pre-Algebra 3 • • • Understands their relationships Some solving for the unknown Difficulty solving for increase & decrease 2 • • Understands their relationships Difficulty solving for the unknown 1 • Some • understanding their relationships 0 Even with help, no understanding or skill demonstrated 8-5 Estimating with Percents Student Learning Goal Chart Pre-Algebra 8-5 8-5 Estimating Estimatingwith withPercents Percents Warm Up Problem of the Day Lesson Presentation Pre-Algebra Pre-Algebra 8-5 Estimating with Percents Warm Up Find each percent increase or decrease to the nearest percent. 1. from 1 to 0.62 2. from 162 to 177 38% decrease 9% increase 3. from 16 to 22 38% increase 4. from 3 to 5 17% decrease 4 Pre-Algebra 8 8-5 Estimating with Percents Problem of the Day If you enlarge a picture by 25%, by what percent do you need to reduce it to return it to its original size? (Hint: Try using a simple number for the original area of the picture.) 20% Pre-Algebra 8-5 Estimating with Percents Today’s Learning Goal Assignment Learn to estimate with percents. Pre-Algebra 8-5 Estimating with Percents Vocabulary estimate compatible numbers Pre-Algebra 8-5 Estimating with Percents Some problems require only an estimate. Estimates involving percents and fractions can be found by using compatible numbers, numbers that go well together because they have common factors. not compatible 13 12 compatible 24 24 Pre-Algebra 8-5 Estimating with Percents Additional Example 1A: Estimating with Percents Estimate. A. 21% of 66 Instead of computing the exact answer of 21% 66, estimate. 21% = 21 20 Use compatible numbers, 20 and 100 100 100. 1 Simplify. 5 1 5 66 65 Use compatible numbers, 65 and 5. 65 = 13 Use mental math: 65 ÷ 5. So 21% of 66 is about 13. Pre-Algebra 8-5 Estimating with Percents Try This: Example 1A Estimate. A. 29% of 86 Instead of computing the exact answer of 29% 86, estimate. 29% = 29 30 Use compatible numbers, 30 and 100 100 100. 3 10 Simplify. 86 90 3 10 90 = 27 Use compatible numbers, 90 and 10. Use mental math: 90 ÷ 10. So 29% of 86 is about 27. Pre-Algebra 8-5 Estimating with Percents Additional Example 1B: Estimating with Percents Estimate. B. 36% of 120 Instead of computing the exact answer of 36% 120, estimate. 36% 35% Round. 30% + 5% 3 35% Pre-Algebra Break down the percent into smaller parts. 10% + 5% 120 = (3 10% + 5%) 120 Set up an equation. 8-5 Estimating with Percents Additional Example 1B Continued =3 10% = 36 + 6 120 + 5% 120 Use Distributive Property. 10% of 120 is 12, so 5% of 120 is 6. = 42 So 36% of 120 is about 42. Pre-Algebra 8-5 Estimating with Percents Try This: Example 1B Estimate. B. 44% of 130 Instead of computing the exact answer of 44% 130, estimate. 44% 45% Round. 40% + 5% 4 45% Pre-Algebra Break down the percent into smaller parts. 10% + 5% 130 = (4 10% + 5%) 130 Set up an equation. 8-5 Estimating with Percents Try This: Example 1B Continued =4 10% = 52 + 6.5 = 58.5 130 + 5% 130 10% of 130 is 13, so 5% of 130 is 6.5. So 44% of 130 is about 58.5. Pre-Algebra Setup an equation. 8-5 Estimating with Percents Additional Example 2: Problem Solving Application The diameter of the Moon is about 2160 miles. If the diameter of the Moon is about 27% of the diameter of Earth, what is the approximate diameter of Earth? Pre-Algebra 8-5 Estimating with Percents Additional Example 2 Continued 1 Understand the Problem The answer is the approximate diameter of Earth. List the important information: • The diameter of the Moon is about 2160 miles. • The diameter of the Moon is about 27% of the diameter of the Earth. Let e represent the diameter of the Earth. Diameter of the Moon 27% 2160 Pre-Algebra 27% Diameter of Earth e 8-5 Estimating with Percents Additional Example 2 Continued 2 Make a Plan Think: The numbers 2160 and 27% are difficult to work with. Use compatible numbers: 2160 is close to 2000; 27% is close to 25% 1 25 25% = = Find an equivalent ratio for 25%. 100 4 Pre-Algebra 8-5 Estimating with Percents Additional Example 2 Continued 3 Solve Think: 2000 is 1 of what number? 4 4 2000 = e 8000 = e The diameter of Earth is approximately 8000 miles. Pre-Algebra 8-5 Estimating with Percents Additional Example 2 Continued 4 Look Back 25% of 8000 mi is 8000 , or 2000 mi. This is the 4 approximate diameter of the moon. Pre-Algebra 8-5 Estimating with Percents Try This: Example 2 The length of a football field is 83% of the length of a soccer field. If a football field is 100 yards, what is the approximate length of a soccer field? Pre-Algebra 8-5 Estimating with Percents Try This: Example 2 Continued 1 Understand the Problem The answer is the approximate length of a soccer field. List the important information: • The length of a football is about 100 yards. • The length of a football field is 83% of a soccer field. Let l represent the length of a soccer field. Length of football field 83% 100 Pre-Algebra 83% Length of soccer field l 8-5 Estimating with Percents Try This: Example 2 Continued 2 Make a Plan Think: The number 83% is difficult to work with. Use compatible numbers: 83% is close to 80% 4 80 80% = = Find an equivalent ratio for 80%. 100 5 Pre-Algebra 8-5 Estimating with Percents Try This: Example 2 Continued 3 Solve Think: 100 is 4 of what number? 5 5 4 100 = l 125 = l The length of a soccer field is approximately 125 yards. Pre-Algebra 8-5 Estimating with Percents Try This: Example 2 Continued 4 Look Back 80% of 125 yards is 4 125 , or 100 yards. This is 5 the length of a soccer field. Pre-Algebra 8-5 Estimating with Percents Lesson Quiz Estimate. Possible answers: 1. 34% of 12 4 2. 47 out of 236 20% 3. 113% of 80 90 4. 22 out of 51 40% 5. According to the last census, 33,871,648 people live in California, and 3,694,820 of those people live in Los Angeles. Estimate the percent of Californians who live in Los Angeles. 10% Pre-Algebra