1. 4
Chapter
Chapter 2
Decimals

2. Adding and Subtracting Decimals
Section
4.2
Adding and Subtracting Decimals

3. Objective A
Add Decimals.

4. Adding and Subtracting Decimals
Adding or Subtracting Decimals
Step 1: Write the decimals so that the decimal points line up vertically.
Step 2: Add or subtract as with whole numbers.
Step 3: Place the decimal point in the sum or difference so that it lines up vertically with the decimal points in the problem.
Objective A

5. Helpful Hint
Recall that 0s may be inserted to the right of the decimal point after the last digit without changing the value of the decimal. This may be used to help line up place values when adding or subtracting decimals.
becomes
two 0s inserted
71.74

6. Adding Decimals Step Example
Step 1: Write the decimals so that the decimal points line up vertically.
Add:
Step 2: Add or subtract as with whole numbers.
Step 3: Place the decimal point in the sum or difference so that it lines up vertically with the decimal points in the problem.
Objective A 6

7. Example Add: 756.23 + 26.504 + 1.087 Insert one zero 783.821
Objective A 7

8. Example
Add: insert a decimal point and add 0’s

9. Example
Add: (–9.92) Recall that to add two numbers with different signs, we find the difference of the larger absolute value and the smaller absolute value. The sign of the answer is the same as the sign of the number with the larger absolute value – The sign will be negative (–9.92) = –2.8

10. Objective B
Subtract Decimals.

11. Example
Subtract: – 5.9
Objective A 11

12. Example Subtract: 28 – 3.3 24.7 Insert decimal point and one zero
Line up decimal points
24.7
Subtract.
Objective A 12

13. Example
Subtract 19 from – insert 2 0s 6.91

14. Example
Subtract: –5.4 – 9.6 Recall that to subtract 9.6, we add the opposite of 9.6 or –9.6. –5.4 – 9.6 = –5.4 + (– 9.6) = –15

15. Example
Subtract: –1.05 – (–7.23) To subtract, add the opposite of –7.23. –1.05 – (–7.23) = – = 6.18

16. Estimate when Adding or Subtracting Decimals.
Objective C
Estimate when Adding or Subtracting Decimals.

17. Estimating when Adding or Subtracting Decimals
To help avoid errors, we can estimate to see if our answer is reasonable by rounding the given numbers and adding or subtracting.
Example: 7.6 – 2.1
Exact
rounds to
Objective A
Since the exact answer is close, it is reasonable. 17

18. Chapter 1 / Whole Numbers and Introduction to Algebra
Example
Add
Exact
Estimate
rounds to
rounds to
This is a reasonable answer.

19. Evaluate Expressions with Decimal Replacement Values.
Objective D
Evaluate Expressions with Decimal Replacement Values.

20. Chapter 1 / Whole Numbers and Introduction to Algebra
Example
Evaluate x + y for x = 5.5 and y = 2.8.
Replace x with 5.5 and y with 2.8 in x + y.
x + y = ( ) + ( )
5.5
2.8
= 8.3

21. Example
Simplify by combining like terms: –4.3y – 20.1y = –4.3y + (–20.1y) = –24.4y

22. Solve Problems That Involve Adding or Subtracting Decimals.
Objective E
Solve Problems That Involve Adding or Subtracting Decimals.

23. Example
Find the total monthly cost of owning and operating a certain automobile given the expenses shown. Monthly car payment: $ Monthly insurance cost: $52.68 Average gasoline bill per month: $ $ $ $127.50
Continued

24. Example (cont)
$ rounds to 600 $52.68 round to 50 + $ rounds to 100 $ estimate Check your work. Since the estimate is close to the exact answer, our answer is reasonable. The total monthly cost is $

25. Example
The bar graph shows the current average heights for adults in various countries. How much greater is the average height in the Netherlands than the average height in Czechoslovakia?
Continued

26. Example (cont)
Netherlands = 72.6 Czechoslovakia = 70.8 Subtract to find how much greater rounds to 73 – 70.8 rounds to Our estimate is close to our exact answer. The average height is 1.8 inches greater.