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Estimating Change When Shopping: A Practical Example

In this exercise, you buy a T-shirt priced at $9.21 and pay the clerk with a $20 bill. The task is to estimate your change and assess whether the estimate is high or low. By rounding the T-shirt price to the nearest dollar, you can determine your change is approximately $11, which is an overestimate due to rounding down too much. This example highlights the importance of estimation in daily shopping.

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Estimating Change When Shopping: A Practical Example

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  1. EXAMPLE 2 Predicting Results Shopping You buy a T-shirt that costs $9.21. You give the clerk $20.00. Estimate your change. Is this estimate high or low?

  2. EXAMPLE 2 Predicting Results Shopping You buy a T-shirt that costs $9.21. You give the clerk $20.00. Estimate your change. Is this estimate high or low? $20.00 – $9.21

  3. EXAMPLE 2 Predicting Results Shopping You buy a T-shirt that costs $9.21. You give the clerk $20.00. Estimate your change. Is this estimate high or low? $20.00 $20 – – Round 9.21 down to 9. $9.21 $9

  4. EXAMPLE 2 Predicting Results Shopping You buy a T-shirt that costs $9.21. You give the clerk $20.00. Estimate your change. Is this estimate high or low? $20.00 $20 – – Round 9.21 down to 9. $9.21 $9 ANSWER Your change is about $11. This estimate is high because you subtracted too little by rounding $9.21 to $9.

  5. EXAMPLE 3 Solve a Multi-Step Problem Groceries You have $10 to buy bread, milk, and cereal. If you have enough money, you would like to buy popcorn. The prices of these items are shown. Do you have enough money to buy popcorn?

  6. EXAMPLE 3 Solve a Multi-Step Problem Groceries You have $10 to buy bread, milk, and cereal. If you have enough money, you would like to buy popcorn. The prices of these items are shown. Do you have enough money to buy popcorn? SOLUTION Estimate the sum of all the prices, including the price of the popcorn.

  7. EXAMPLE 3 Solve a Multi-Step Problem STEP 1 ADD the front-end digits: the dollars.

  8. EXAMPLE 3 Solve a Multi-Step Problem STEP 1 STEP 2 ESTIMATE the sum of remaining digits: the cents. ADD the front-end digits: the dollars.

  9. EXAMPLE 3 Solve a Multi-Step Problem STEP 1 STEP 2 ESTIMATE the sum of remaining digits: the cents. STEP 3 ADD your results. ADD the front-end digits: the dollars.

  10. EXAMPLE 3 Solve a Multi-Step Problem STEP 1 STEP 2 ESTIMATE the sum of remaining digits: the cents. STEP 3 ADD your results. ADD the front-end digits: the dollars. $ 1 .79 $ 2 .18 $ 3 .34 + $ 3 .65

  11. EXAMPLE 3 Solve a Multi-Step Problem STEP 1 STEP 2 ESTIMATE the sum of remaining digits: the cents. STEP 3 ADD your results. ADD the front-end digits: the dollars. $ 1 .79 $ 2 .18 $ 3 .34 + $ 3 .65 $ 9 .00

  12. EXAMPLE 3 Solve a Multi-Step Problem STEP 1 STEP 2 ESTIMATE the sum of remaining digits: the cents. STEP 3 ADD your results. ADD the front-end digits: the dollars. $ 1 .79 $1. 79 $ 2 .18 $2. 18 $ 3 .34 $3. 34 + $3. 65 $ 3 .65 + $ 9 .00

  13. EXAMPLE 3 Solve a Multi-Step Problem STEP 1 STEP 2 ESTIMATE the sum of remaining digits: the cents. STEP 3 ADD your results. ADD the front-end digits: the dollars. $ 1 .79 $1. 79 $ 2 .18 $2. 18 $ 1 $ 3 .34 $3. 34 + $3. 65 $ 3 .65 + $ 1 $ 9 .00

  14. EXAMPLE 3 Solve a Multi-Step Problem STEP 1 STEP 2 ESTIMATE the sum of remaining digits: the cents. STEP 3 ADD your results. ADD the front-end digits: the dollars. $ 1 .79 $1. 79 $ 2 .18 $2. 18 $ 1 $ 3 .34 $3. 34 + $3. 65 $ 3 .65 + $ 1 $ 9 .00

  15. EXAMPLE 3 Solve a Multi-Step Problem STEP 1 STEP 2 ESTIMATE the sum of remaining digits: the cents. STEP 3 ADD your results. ADD the front-end digits: the dollars. $ 1 .79 $1. 79 $ 2 .18 $2. 18 $ 1 $ 3 .34 $3. 34 $ 9 + $3. 65 $ 3 .65 + + $ 1 $ 2 $ 9 .00

  16. EXAMPLE 3 Solve a Multi-Step Problem STEP 1 STEP 2 ESTIMATE the sum of remaining digits: the cents. STEP 3 ADD your results. ADD the front-end digits: the dollars. $ 1 .79 $1. 79 $ 2 .18 $2. 18 $ 1 $ 3 .34 $3. 34 $ 9 + $3. 65 $ 3 .65 + + $ 1 $ 2 $ 9 .00 $11

  17. EXAMPLE 3 Solve a Multi-Step Problem ANSWER Because 11 > 10 you do not have enough money to buy popcorn.

  18. for Examples 2 and 3 GUIDED PRACTICE Use front-end estimation to estimate the sum. 3. 6.42 + 7.64 + 3.94 + 2.21

  19. for Examples 2 and 3 GUIDED PRACTICE Use front-end estimation to estimate the sum. 3. 6.42 + 7.64 + 3.94 + 2.21 ANSWER 20

  20. for Examples 2 and 3 GUIDED PRACTICE Use front-end estimation to estimate the sum. 4. 8.59 + 1.37 + 2 + 6.12

  21. for Examples 2 and 3 GUIDED PRACTICE Use front-end estimation to estimate the sum. 4. 8.59 + 1.37 + 2 + 6.12 ANSWER 18

  22. for Examples 2 and 3 GUIDED PRACTICE Use front-end estimation to estimate the sum. How can you estimate the difference in Example 2 so that your answer is a low estimate? $20.00 – $9.21

  23. for Examples 2 and 3 GUIDED PRACTICE Use front-end estimation to estimate the sum. How can you estimate the difference in Example 2 so that your answer is a low estimate? $20.00 $20.00 – – $10.00 $9.21 Round 9.21 up to 10.

  24. for Examples 2 and 3 GUIDED PRACTICE Use front-end estimation to estimate the sum. How can you estimate the difference in Example 2 so that your answer is a low estimate? 20.00 20.00 – – 10.00 9.21 Round 9.21 up to 10. ANSWER Your change is about 10. This estimate is low because you subtracted too much by rounding 9.21 to 10.

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