1. 5-1 Estimate with Fractions and Mixed Numbers Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. 1. 5.2x = 127.92 2. = 64.2 3. 2.6 = Bellwork Divide. x t 4.1 x 15.1

3. 1. 5.2x = 127.92 2. = 64.2 3. 2.6 = Bellwork Divide. x = 24.6 x = 39.26 x = 263.22 x t 4.1 x 15.1

4. Problem of the Day Fill in the square using the numbers 5–13 so that all sums (rows, columns, and main diagonals) are the same. 8136 7911 12510

5. Learning Objective: to estimate sums and differences of fractions and mixed numbers.

6. Sometimes, when solving problems, you may not need an exact answer. To estimate sums and differences of fractions and mixed numbers, round each fraction to 0,, or 1. you can use a number line to help. 1212 1212 0 1 2525 2525 is closer to than to 0. 1212

7. You can also round fractions by comparing numerators with denominators. Benchmarks for Rounding Fractions Round to 0 if the numerator is much smaller than the denominator. Examples: Round to 1212 if the numerator is about half the denominator. Examples: Round to 1 if the numerator is nearly equal to the denominator. Examples: 1919 3 20 2 11, 2525 5 12 7 13, 23 25 97 100 8989,

8. Additional Example 1: Measurement Application A blue whale can grow to 33 m long, while 3535 the great white shark may be as long as 4 m. 1212 Estimate how much longer the blue whale is than the great white shark. 33 3535 – 4 1212 3535 1212 4 1212 4 1212 Round each mixed number. Subtract. The blue whale is about 29 m longer. = 29– 33 1212 4 1212 Round to, round to, and round to 1. Helpful Hint 3535 1212 1313 1212 3434

9. Check It Out: Example 1 11 1212 – 2 7878 1212 1212 2 7878 3 Round each mixed number. Subtract. = 8 – 11 1212 3 1212 A Cocker Spaniel may grow to weigh about 11 kilograms while the Chihuahua will not weigh more than 2 kilograms. Estimate how much more the Cocker Spaniel weighs than the Chihuahua. 7878 1212 The Cocker Spaniel weighs about 8 kg more. 1212

10. Estimate each sum or difference. Additional Example 2: Estimating Sums and Differences A. 7979 – 2525 1 2525 1212 1 – = 7979 Round each fraction. Add. 5959 B. 4 + 3 1818 4 5959 4 1212 3 1818 3 Round each mixed fraction. Subtract. 4 1212 + 3 = 7 1212 1212 1212

11. Estimate the sum. Additional Example 2: Estimating Sums and Differences Add. 1818 C. –2 + 7 12 –2 1818 Round each number. 7 12 1212 1212 + = –1 1212 –2 In the fraction -2, the numerator is close in value to the denominator. So round -2 to -2. Helpful Hint 1818 1818

12. Estimate each sum or difference. Check It Out: Example 2 A. 7878 – 1616 1 1616 0 1 – 0 = 1 7878 Round each fraction. Add. 3535 B. 5 + 2 2929 5 3535 5 1212 2 2929 2 Round each mixed fraction. Subtract. 5 1212 + 2 = 7 1212

13. Estimate the sum. Check It Out: Example 2 Add. 2929 C. –4 + 8 15 –4 2929 Round each number. 8 15 1212 1212 + = –3 1212 –4

14. You can estimate products and quotients of mixed numbers by rounding to the nearest whole number. If the fraction in a mixed number is greater than or equal to, you can round the mixed number up to the next whole number. If the fraction is less than, you can round down to a whole number by dropping the fraction. 1212 1212

15. Products and Quotients: Round to nearest whole number. Fractions > round up Fraction < drop the fraction 1212 1212

16. Additional Example 3A: Estimating Products and Quotients Estimate each product or quotient. 3 7 = 21. Multiply. 2929 3 6 5656 3 2929 3 6 5656 7 Round each mixed number to the nearest whole number.

17. Additional Example 3B: Estimating Products and Quotients Estimate each product or quotient. 14 ÷ 2 = 7. Divide. 4545 13 ÷ 2 1414 13 4545 14 2 1414 2 Round each mixed number to the nearest whole number.

18. Check It Out: Example 3A Estimate each product or quotient. 8 3 = 24. Multiply. 2323 7 2 3434 7 2323 8 2 3434 3 Round each mixed number to the nearest whole number.

19. Check It Out: Example 3B Estimate each product or quotient. 12 ÷ 3 = 4. Divide. 7878 11 ÷ 3 1313 11 7878 12 3 1313 3 Round each mixed number to the nearest whole number.

20. Lesson Quiz Estimate each sum or difference. 1. The new show arena being built in Franklin County is 150 feet long and 110 feet wide. Estimate the difference between the length and width. 3434 1212 2. 5959 + 4545 3. 7878 – 3737 4. 9 3434 – 6 1515 5. 5 2 4 40 ft 1 1212 1212 12 Estimate each product or quotient. 7878 1616 6. 17 ÷ 3 6 5656 1313