Estimating before you add or subtract will help you check whether your answer is reasonable. Helpful Hint

Carly Patterson’s Preliminary Scores At the 2004 U.S. Gymnastics Championships, Carly Patterson and Courtney Kupets tied for the All-Around title. Carly Patterson’s Preliminary Scores Event Points Floor exercise 9.7 Balance beam Vault 9.3 Uneven bars 9.45 To find the total number of points, you add all of the scores.

Additional Example 1A: Sports Application What was Carly Patterson’s total for the events other than the floor exercise? Find the sum of 9.7, 9.3, and 9.45. Estimate by rounding to the nearest whole number. 9.7 + 9.3 + 9.45 The total is about 28 points. 10 + 9 + 9 = 28

Additional Example 1A Continued Align the decimal points. 9.70 Use zeros as placeholders. 9.30 +9.45 Add. Then place the decimal point. 28.45 Since 28.45 is close to the estimate of 28, the answer is reasonable. Carly Patterson’s total for the events other than the floor exercise was 28.45.

Additional Example 1B: Sports Application How many more points did Carly need on the vault to have a perfect score of 10? Find the difference between 10 and 9.3. Align the decimal points. 10.0 Use zeros as placeholders. -9.3 0.7 Subtract. Then place the decimal point. Carly needed another 0.7 of a point to have a perfect score.

Check It Out: Example 1A What was Carly Patterson’s total for the events other than the vault exercise? Find the sum of 9.7, 9.7, and 9.45. Estimate by rounding to the nearest whole number. 9.7 + 9.7 + 9.45 The total is about 29 points. 10 + 10 + 9 = 29

Check It Out: Example 1A Continued Add Align the decimal points. 9.700 Use zeros as placeholders. 9.700 +9.450 Add. Then place the decimal point. 28.850 Since 28.850 is close to the estimate of 29, the answer is reasonable. Carly Patterson’s total for the events other than the vault exercise was 28.85.

Check It Out: Example 1B How many more points did Carly need on the uneven bars to have a perfect score of 10? Find the difference between 10 and 9.45. Align the decimal points. 10.00 Use zeros as placeholders. -9.45 0.55 Subtract. Then place the decimal point. Carly needed another 0.55 of a point to have a perfect score.

Additional Example 2: Using Mental Math to Add and Subtract Decimals Find each sum or difference. A. 1.8 + 0.2 B. 4 – 0.7 Think: 0.8 + 0.2 = 1. 1.8 + 0.2 = 2.0 Think: What number added to 0.7 is 1? 0.7 + 0.3 = 1 So 1 – 0.7 = 0.3 4 – 0.7 = 3.3

Check It Out: Example 2 Find each sum or difference. A. 1.6 + 0.4 B. 6 – 0.3 1.6 + 0.4 = 2.0 Think: 0.6 + 0.4 = 1. Think: What number added to 0.3 is 1? 0.3 + 0.7 = 1 So 1 – 0.3 = 0.7 6 – 0.3 = 5.7

Additional Example 3A: Evaluating Decimal Expressions Evaluate 6.73 – x for each value of x. x = 3.8 6.73 – x Substitute 3.8 for x. 6.73 – 3.8 6.73 Align the decimal points. Use a zero as a placeholder. – 3.80 Subtract. Place the decimal point. 2.93

You can place any number of zeros at the end of a decimal number without changing its value. Helpful Hint

Additional Example 3B: Evaluating Decimal Expressions Evaluate 6.73 – x for each value of x. x = 2.9765 6.73 – x Substitute 2.9765 for x. 6.73 – 2.9765 6.7300 Align the decimal points. Use zeros as placeholders. –2.9765 Subtract. Place the decimal point. 3.7535

Check It Out: Example 3A Evaluate 7.58 – x for each value of x. x = 3.8 7.58 – x Substitute 3.8 for x. 7.58 – 3.8 7.58 Align the decimal points. Use a zero as a placeholder. –3.80 Subtract. Place the decimal point. 3.78