3-3 Adding and Subtracting Decimals

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

3-3 Adding and Subtracting Decimals

Warm UpEstimate by rounding to the indicated place value.

1. 70.27 + 15.36; ones2. 84.37 – 21.82; tenths

Estimate each product or quotient.3. 27.25 8.74. 44.52 ÷ 3.27

8562.6

27015

3-3 Adding and Subtracting Decimals

Problem of the Day

Find a three-digit number that rounds to 440 and includes a digit that is the quotient of 24 and 3. Is there more than one possible answer? Explain your thinking.438; no; the numbers that round to 440 are 435-444, 24 divided by 3 is 8, and 438 is the only number with 8 as a digit.

3-3 Adding and Subtracting Decimals

MA.6.A.5.3 Estimate the results of computations with…decimals…and judge the reasonableness of the results.

Also Review of MA.5.A.2.2

Sunshine State Standards

3-3 Adding and Subtracting Decimals

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

Helpful Hint

3-3 Adding and Subtracting Decimals

Carly Patterson’s Preliminary Scores

Event Points

Floor exercise 9.7

Balance beam 9.7

Vault 9.3

Uneven bars 9.45

At the 2004 U.S. Gymnastics Championships, Carly Patterson and Courtney Kupets tied for the All-Around title.

To find the total number of points, you add all of the scores.

3-3 Adding and Subtracting Decimals

Additional Example 1A: Sports Application

What was Carly Patterson’s total for the events other than the floor exercise?

Estimate by rounding to the nearest whole number.

9.7 + 9.3 + 9.45

The total is about 28 points.10 + 9 + 9 = 28

First estimate the sum of 9.7, 9.3, and 9.45.

3-3 Adding and Subtracting Decimals

Additional Example 1A Continued

Then add.

9.70

9.30

+9.4528.45

Align the decimal points.

Use zeros as placeholders.

Add. Then place the decimal point.

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.

3-3 Adding and Subtracting Decimals

Additional Example 1B: Sports Application

How many more points did Carly need on the vault to have a perfect score of 10?

10.0

–9.30.7

Align the decimal points.

Use zeros as placeholders.

Subtract. Then place the decimal point.

Carly needed another 0.7 of a point to have a perfect score.

Find the difference between 10 and 9.3.

3-3 Adding and Subtracting Decimals

Check It Out: Example 1A

What was Carly Patterson’s total for the events other than the vault exercise?

Estimate by rounding to the nearest whole number.9.7 + 9.7 + 9.45

The total is about 29 points.10 + 10 + 9 = 29

First estimate the sum of 9.7, 9.7, and 9.45.

3-3 Adding and Subtracting Decimals

Check It Out: Example 1A Continued

Then add.

9.700

9.700

+9.45028.850

Align the decimal points.

Use zeros as placeholders.

Add. Then place the decimal point.

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.

3-3 Adding and Subtracting Decimals

Check It Out: Example 1B

How many more points did Carly need on the uneven bars to have a perfect score of 10?

10.00

–9.450.55

Align the decimal points.

Use zeros as placeholders.

Subtract. Then place the decimal point.

Carly needed another 0.55 of a point to have a perfect score.

Find the difference between 10 and 9.45.

3-3 Adding and Subtracting Decimals

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

4 – 0.7 = 3.3 Think: 0.7 + 0.3 = 1, so 1 – 0.7 = 0.3.

3-3 Adding and Subtracting Decimals

Check It Out: Example 2

Find each sum or difference.

A. 1.6 + 0.4

B. 6 – 0.3

Think: 0.6 + 0.4 = 1.1.6 + 0.4 = 2.0

6 – 0.3 = 5.7 Think: 0.3 + 0.7 = 1, so 1 – 0.3 = 0.7.

3-3 Adding and Subtracting Decimals

Additional Example 3A: Evaluating Decimal Expressions

Evaluate 6.73 – x for each value of x.

x = 3.8

Substitute 3.8 for x.

6.73 – x

6.73 – 3.8 6.73 Align the decimal points.

– 3.80 Use a zero as a placeholder.

2.93 Subtract. Place the decimal point.

3-3 Adding and Subtracting Decimals

You can place any number of zeros at theend of a decimal number without changing its value.

Helpful Hint

3-3 Adding and Subtracting Decimals

Additional Example 3B: Evaluating Decimal Expressions

Evaluate 6.73 – x for each value of x.

x = 2.9765

Substitute 2.9765 for x.

6.73 – x

6.73 – 2.9765 6.7300 Align the decimal points.

–2.9765 Use zeros as placeholders.

3.7535 Subtract. Place the decimal point.

3-3 Adding and Subtracting Decimals

Check It Out: Example 3A

Evaluate 7.58 – x for each value of x.

x = 3.8

Substitute 3.8 for x.

7.58 – x

7.58 – 3.8 7.58 Align the decimal points.

–3.80 Use a zero as a placeholder. 3.78 Subtract. Place the decimal point.

3-3 Adding and Subtracting Decimals

Check It Out: Example 3B

Evaluate 8.17 – x for each value of x.

x = 2.9765

Substitute 2.9765 for x.

8.17 – x

8.17 – 2.9765 8.1700 Align the decimal points.

– 2.9765 Use zeros as placeholders.

5.1935 Subtract. Place the decimal point.