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Estimating Sums and Differences of Decimals

Learn how to estimate sums and differences of decimals using front-end estimation and clustering. Practice using real-life examples.

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Estimating Sums and Differences of Decimals

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  1. Transparency 4 Click the mouse button or press the Space Bar to display the answers.

  2. Splash Screen

  3. Example 4-4c Objective Estimate sums and differences of decimals

  4. Example 4-4c Vocabulary Front-end estimation Add or subtract the front digits

  5. Example 4-4c Vocabulary Clustering A form of estimating when all the addends are close to the same number

  6. Lesson 4 Contents Example 1Use Estimation to Solve Problems Example 2Use Estimation to Solve Problems Example 3Use Front-End Estimation Example 4Use Clustering

  7. Colony Population (thousands) Colony Population (thousands) Connecticut 183.9 New York 162.9 Delaware 35.5 North Carolina 197.2 Georgia 23.4 240.1 Pennsylvania Rhode Island Maryland 202.6 58.2 Massachusetts 235.3 124.2 South Carolina New Hampshire 62.4 447.0 Virginia New Jersey 117.4 Example 4-1a POPULATIONThe table below shows the population of the American colonies in 1770. Estimate the total population of North Carolina and South Carolina. North Carolina 197.2 Write colony then population South Carolina 124.2 1/4

  8. Example 4-1b North Carolina 197.2 South Carolina 124.2 Round each number to the nearest tens for easier adding North Carolina 197.2 Remember: When add 1 to 9 it = 10 so place a 0 in the 9’s place value and carry the 1 200 20 Annex a zero to hold the one’s place value South Carolina 124.2 Again, annex a zero to hold the one’s place value 1 12 120 1/4

  9. Example 4-1b Add the numbers North Carolina 200 + South Carolina 120 320 1/4

  10. Example 4-1b Colony Population (thousands) Colony Population (thousands) Connecticut 183.9 New York 162.9 Delaware 35.5 North Carolina 197.2 Georgia 23.4 240.1 Pennsylvania Rhode Island Maryland 202.6 58.2 Massachusetts 235.3 124.2 South Carolina New Hampshire 62.4 447.0 Virginia New Jersey 117.4 320 Answer: about 320 thousand 1/4

  11. Colony Population (thousands) Colony Population (thousands) Connecticut 183.9 New York 162.9 Delaware 35.5 North Carolina 197.2 Georgia 23.4 240.1 Pennsylvania Rhode Island Maryland 202.6 58.2 Massachusetts 235.3 124.2 South Carolina New Hampshire 62.4 447.0 Virginia New Jersey 117.4 Example 4-1c POPULATIONThe table below shows the population of the American colonies in 1770. Estimate how many more people were in Massachusetts than in Connecticut. Answer: about 60 thousand more people 1/4

  12. Colony Population (thousands) Colony Population (thousands) Connecticut 183.9 New York 162.9 Delaware 35.5 North Carolina 197.2 Georgia 23.4 240.1 Pennsylvania Rhode Island Maryland 202.6 58.2 Massachusetts 235.3 124.2 South Carolina New Hampshire 62.4 447.0 Virginia New Jersey 117.4 Example 4-2a POPULATIONThe table below shows the population of the American colonies in 1770. Estimate how many more people lived in Rhode Island than in Georgia in 1770. Rhode Island 58.2 Write colony then population Georgia 23.4 2/4

  13. Example 4-2b Round each number to the nearest ten for easier adding and subtracting. Rhode Island 58.2 Georgia 23.4 If 5 or greater, add 1 to the rounding place value Rhode Island 58.2 Annex a zero to hold the one’s place value If less than 5, leave the place value as is 6 60 Georgia 23.4 Annex a zero to hold the one’s place value 2 20 2/4

  14. Example 4-2b Need to find how many more people lived in Rhode Island than in Georgia Rhode Island 60 - Georgia 20 Decide what process? 40 Subtract Numbers are Population (thousands) Answer: Rhode Island had 40 thousand more people than Georgia 2/4

  15. Colony Population (thousands) Colony Population (thousands) Connecticut 183.9 New York 162.9 Delaware 35.5 North Carolina 197.2 Georgia 23.4 240.1 Pennsylvania Rhode Island Maryland 202.6 58.2 Massachusetts 235.3 124.2 South Carolina New Hampshire 62.4 447.0 Virginia New Jersey 117.4 Example 4-2c POPULATIONThe table below shows the population of the American colonies in 1770. Estimate the total number of people in Pennsylvania and New Jersey in 1770. Answer: 360 thousand people 2/4

  16. Estimate using front-end estimation. 14.8 + 55.9 Example 4-3a Write the problem vertically Add the front digits. 6 9 Then add the next digits. Do not add the decimals Answer: about 69 3/4

  17. Estimate using front-end estimation. Example 4-3b Answer: about 97 3/4

  18. Example 4-4a MULTIPLE-CHOICE TEST ITEM A cage of guinea pigs at the pet store is given a vitamin-water solution each day. Last week the guinea pigs consumed 21.8 ounces, 19.1 ounces, 20.3 ounces, 18.9 ounces, and 22.0 ounces of the solution each day. Use this information to estimate the total amount of vitamin solution consumed in one day. A 70 oz B 90 oz C 100 oz D 120 oz 21.8 Since there are several numbers, use clustering 19.1 20.3 18.9 Write the numbers vertically 22.0 4/4

  19. Example 4-4b Clustering means to round all numbers to the same number → 21.8 20 → 20 19.1 Since all the numbers are close to 20, round all the numbers to 20 → 20 20.3 → 18.9 20 → 22.0 20 Since all numbers are 20, multiply by how many numbers there are 20  20  5 There are 5 numbers 100 4/4

  20. Example 4-4a Choose the appropriate multiple choice answer 100 is a good estimation A 70 oz B 90 oz C 100 oz D 120 oz Answer: C 4/4

  21. Example 4-4c * MULTIPLE-CHOICE TEST ITEM During the month of February, Jonathon spends $14.78 on gasoline the first week, $15.35 on gasoline during the second week, $15.94 on gasoline during the third week, and $14.07 on gasoline during the fourth week. Use this information to estimate the total amount Jonathon spent on gasoline during February. A $35 B$50 C $60 D $100 Answer: C 4/4

  22. End of Lesson 4 Assignment

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