HFCC Math Lab
Adding, Subtracting, Multiplying and Dividing Decimals
Arithmetic - 6
Part I: Adding and Subtracting Decimals
Procedure: When adding or subtracting decimal numbers,
1.
Arrange the numbers in a column so that the decimal points are all aligned.
2.
Insert zeros so that each number has the same number of decimal places.
3.
Add or subtract the numbers just as you would if they were whole numbers.
4.
Place the decimal point in the answer so it is in the same column as in the other numbers.
Ex 1: Add: 324.6, 79.4, 3.786, and 0.567.
Arrange the numbers in a column with the decimal points aligned.
324.6

79.4
3.786
0.567
Insert zeros so that each number has the same number of decimal places. Then add.
324.600
79.400
3.786

0.567
408.353
Notice that the decimal point in the answer is in the same column as the
decimal points in the other numbers.
Revised 04/10 1

Ex 2: Add: 89 + 0.76 + 1.503. Since 89 is a whole number, the decimal point is understood to be on the right. That is 89 = 89.
89.000
Align the decimal points.
0.760

1.503
Add. 91.263
insert zeros
Note: The decimal point in the answer is in the same column
as the decimal points in the other numbers.
Ex 3: Subtract 3.8 from 21.006.
Align the decimal points, insert zeros, and subtract. Borrow when needed. Be sure that the decimal point in the answer is in the same column as the decimal points in the other numbers.

21.006
3.800
17.206
Ex 4: Subtract 961.16 from 7,625.3.
Align the decimal points, insert zeros, and subtract. Borrow when needed. Be sure that the decimal point in the answer is in the same column as the decimal points in the other numbers.

7625.30
961.16
6664.14
Exercises: Add or subtract.
1.
3. 26.4 7.26 5
5.
7.
3.721 1.25
9. Subtract 2.709 from 5.32
Revised 04/10 2
2.
4.
0.12 1.789 12.6
6.
8.
21.26 7
10. Subtract 69.86 from 96.1

Part II: Multiplying Decimals
Procedure: When multiplying decimal numbers,
1. Multiply the numbers as if they were whole numbers. That is, ignore the decimal points.
2. Place the decimal point in the answer so that the number of places to the right of the decimal point is equal to the total of the number of places to the right of the decimal in the numbers being multiplied.
Ex 5: Multiply 0.4 x 0.3.
0.4
 one place to the right of the decimal

0.3
 one place to the right of the decimal
0.12
 total of two places to the right of the decimal
Ex 6: Multiply 7.63

40.8

7.63
 two places to the right of the decimal point
40.8
 one place to the right of the decimal point
6104
0 000
305200
311.304
 total of three places to the right of the decimal point
Exercises: Multiply.
11. 25.2 3.7
13. 8.64 7.6
15. (2.7)(0.927)
17. 0.0025 0.0026
12. 5.22 4.8
14. (0.321)(0.95)
16. 0.05 3.2003
18. 2.3 5.369
Revised 04/10 3

Part III: Dividing Decimals
Procedure: When dividing decimal numbers,
1. Move the decimal point in the divisor all the way to the right to make a whole number.
2. Move the decimal point in the dividend the same number of places to the right. Add zeros, if necessary. We now have an equivalent division problem whose answer is the answer to the original division problem.
3. Place the decimal point in the quotient directly above the newly placed decimal in the dividend. quotient
Remember: divisor dividend
Ex 7: Divide: 1.8 0.2
0.2 1.8

. 2 . 1. 8 . Move the decimal point in the divisor one place.
 
Move the decimal point in the dividend one place.
This gives us an equivalent division problem: 2 18
Now divide:
9
2 18
18
0
Therefore: 1.8 0.2

9
Ex 8: Divide: 1.832 0.43
Round the answer to the nearest hundredth.
0.43 1.832

.43. 1. 83 .2
 
Move the decimal point in the divisor two places.
Move the decimal point in the dividend two places.
This gives us an equivalent division problem: 43 183.2
Revised 04/10 4

Now divide:
4.260
43 183.200
Notice that the decimal point in the quotient is

172 directly above the decimal point in the dividend.

112
86
260

258
20

00
20
Rounded off to the hundredth, the quotient is 4.26.
Therefore: 1.832 0.43

4.26
Ex 9: Divide: 74 0.78
Round the answer to the nearest tenth.
0.78 74

0. 78 . 74.00. Move the decimal point in the divisor two places to the right.
 
Move the decimal point in the dividend two places to the right.
Remember that 74

74. We must insert two zeros to sh ow that the decimal point in the dividend moved two places to the right.
This gives us the equivalent division problem: 78 7400.
94.87
Now divide: 78 7400.00
Notice that the decimal point in the quotient is

702 directly above the decimal point in the dividend.
380

312
680

624
560

546
14
Rounded off to the nearest tenth, the quotient is 94.9.
Revised 04/10 5

Ex 10: Divide: 18.2 0.013

0.013 18.2
0.013 18.2

0. 013 . 18. 200 .
 
Move the decimal point in the divisor three places to the right.
Move the decimal point in the dividend three places to the right.
We must insert two zeros to show that th e decimal point in the dividend moved three places to the right.
This gives us the equivalent division problem: 13 18200.
1400.
Now divide: 13 18200.

13
52

52
00

00
00

00
0
Notice that the decimal point in the quotient is directly above the decimal point in the dividend.
Therefore: 18.2 0.013 1, 400
Exercises: Divide.
19. 10.8625 1.25
21. 21.6 0.012
23. 3.1154 0.37
25. 6.642 92.25
20. 0.48 0.017856
22. 17.23 2.5 Round to the nearest tenth.
24. 0.31234 3.22
26. 0.044826 0.062
Revised 04/10 6

Answers to the odd numbered problems and solutions to the even numbered problems.
Adding and subtracting:
1. 16.655
2. 0.120
1.789

12.600
14.509
3. 38.66
4. 0.370

0.126
21.400
21.896
5. 2.471
7. 14.16
9. 2.611
6.
21.26

7.00
14.26
8. 9.820

0.776
9.044
10. 96.10

69.86
26.24
Multiplying:
11. 93.24
13. 65.664
12. 5.22

4.8
4176
20880
25.056
14. 0.321

0.95
1605
28890
.30495
Revised 04/10 7

15. 2.5029
17. 0.0000065
Dividing:
19. 8.69
21. 1,800
Revised 04/10 8
16. 3.2003

0.05
.160015
18. 5.369

2.3
16107
107380
12.3487
20. 0.48 0.017856

0. 4 8 . 0. 0 1 .7856
   
0.0372

48 1.7856
14 4
345
336
96
96
0
Therefore: 0.017856 0.48

0.0372
22. 2.5 17.23

2. 5 . 17. 2 .3
 
6.89

25 172.30
150
2 23
2 0 0
230
225
5
Rounded to the nearest tenth, the quotient is 6.89
Therefore: 17.23 2.5

6.9

23. 8.42
25. 0.072
Revised 04/10 9
24. 3.22 0.31234

3. 2 2 . 0. 3 1 .234
   
0.097

322 31.234
2898
2254
2254
0
Therefore: 0.31234 3.22

0.097
26. 0.062 0.044826

0. 062 . 0. 044 .826
 
0.723

62 44.826
4 3 4
142
124
186
186
0
Therefore: 0.044826 0.062

0.723