8 5 Estimating with Percents Learn to estimate

8 -5 Estimating with Percents Learn to estimate with percents. Pre-Algebra

8 -5 Estimating with Percents Some problems require only an estimate. Estimates involving percents and fractions can be found by using friendly numbers, numbers that go well together because they are easy to work with. not friendly 13 ≈ 12 friendly 24 24 Pre-Algebra

8 -5 Estimating with Percents Example 1 A: Estimating with Percents Estimate. A. 21% of 66 Instead of computing the exact answer of 21% 66, estimate. 21% = 21 ≈ 20 100 ≈ 1 5 66 ≈ 65 1 65 = 13 5 Use friendly numbers, 20 and 100. Simplify. Use friendly numbers, 65 and 5. Use mental math: 65 ÷ 5. So 21% of 66 is about 13. Pre-Algebra

8 -5 Estimating with Percents Example 1 B: Estimating with Percents Estimate. B. 36% of 120 Instead of computing the exact answer of 36% 120, estimate. 36% ≈ 35% ≈ 30% + 5% ≈ 3 Pre-Algebra 10% + 5% Round. Break down the percent into smaller parts.

8 -5 Estimating with Percents Example 1 B Continued = 36 + 6 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 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 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 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% = 25 = 1 Find an equivalent ratio for 25%. 100 4 Pre-Algebra

8 -5 Estimating with Percents Example 2 Continued 3 Solve 1 what number? of 4 2000 = 1 e 4 8000 = e Think: 2000 is The diameter of Earth is approximately 8000 miles. Pre-Algebra

8 -5 Estimating with Percents Example 2 Continued 3 Solve Think: 2000 is 4 1 what number? of 4 2000 = e 8000 = e The diameter of Earth is approximately 8000 miles. Pre-Algebra

8 -5 Estimating with Percents 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 Estimate. Try This: Example 1 A A. 29% of 86 Instead of computing the exact answer of 29% 86, estimate. 29% = 29 ≈ 30 100 ≈ 3 10 86 ≈ 90 3 90 = 27 10 So 29% of 86 is Pre-Algebra Use friendly numbers, 30 and 100. Simplify. Use friendly numbers, 90 and 10. Use mental math: 90 ÷ 10. about 27.

8 -5 Estimating with Percents Try This: Example 1 B Estimate. B. 44% of 130 Instead of computing the exact answer of 44% 130, estimate. 44% ≈ 45% ≈ 40% + 5% ≈ 4 Pre-Algebra 10% + 5% Round. Break down the percent into smaller parts.

8 -5 Estimating with Percents Try This: Example 1 B Continued = 52 + 6. 5 = 58. 5 10% of 130 is 13, so 5% of 130 is 6. 5. So 44% of 130 is about 58. 5. Pre-Algebra