1. +
1 5
3 5 =
4 5

2. a c
b c
a + b c + =

3. a c
b c
a – b c – =

4. Adding and Subtracting with Like Denominators
Add or subtract numerators.
Write the sum or difference over the like denominator.
If necessary, rename the answer in lowest terms.
Improper fractions in a sum or difference can be renamed as mixed numbers.

5. Example 1
4 9
7 9 +
Add +
4 9
7 9 = =
11 9
2 9 = 1

6. Example 1 11 12 3 12 – Subtract . – 11 12 3 12 = 11 – 3 12 = 8 12 2 3
2 3 =

7. Exercise
4 7
2 7
6 7 =
Add. +

8. Exercise
5 9
2 9
1 3 = –
Subtract.

9. Adding and Subtracting with Unlike Denominators
Find the LCM of the denominators.
Rename as equivalent fractions using the LCM as the new denominator.
Add or subtract the fractions.
If necessary, rename the answer in lowest terms.

10. Example 2 5 8 2 3 + Add . 8 = 23 3 = 3 LCM = 23 • 3 = 24 + 5 8 2 3 +
8 8 =
15 24
16 24 + =
31 24
7 24 = 1

11. Example 3 7 10 4 15 – Subtract . 10 = 2 • 5 15 = 3 • 5
LCM = 2 • 3 • 5 = 30 –
7 10
4 15 –
7 10
4 15 =
3 3
2 2 =
21 30
8 30 – =

12. Exercise
2 3
4 5
7 15 = 4
Add. 2 + 1

13. – 5 6
5 – 6
5 6 – = =

14. Rules for Performing Operations on Rational Numbers
The sum of two positive numbers is positive, and the sum of two negative numbers is negative.

15. Rules for Performing Operations on Rational Numbers
2. To find the sum of two rational numbers with different signs, take the difference of their absolute values. The answer takes the sign of the rational number with a larger absolute value.

16. Rules for Performing Operations on Rational Numbers
3. Subtract rational numbers by adding the opposite of the subtrahend.

17. Example 4 5 8 1 5 – + Add . 8 = 23 5 = 5 LCM = 23 • 5 = 40 + 5 8 1 5 –
5 5
8 8 – =
25 40
8 40 + – = – = –

18. Example 5 2 3 1 9 – – Subtract . 3 = 3 9 = 32 LCM = 32 = 9 – 2 3 1 9 –
3 3 =
6 9
1 9 + – =
– 6 + (– 1) 9
7 9 = –

19. Example 6
11 12
3 4 – +
Add
12 = 3 x 4 +
11 12
3 4 – +
3 4 =
3 3
11 12 – =
11 12
9 12 + – = –
1 6 = –

20. Example 7
5 6
4 9 +
Add
5 6 1
15 18 1 =
4 9 4
8 18 4 = +
23 18 5
5 18
5 + 1 =
5 18 6 =

21. Example 8
1 4
3 8 –
Subtract
1 4 5 =
2 8 5 =
8 8 4
2 8 +
10 8 4 =
3 8 2
3 8 2 – =
7 8 2

22. Example 9
Add

23. Example 9
Subtract – 0.25 –
– – 0.375
– 0.625

24. Example 9
Subtract 13 – 8.4.
13.0 – 8.4
4.6

25. Example
Add or subtract.
5 6
3 8 = –

26. Example
Add or subtract.
7 18
7 12
3536 = 11 8 + 3

27. Example
Add or subtract.
5 6
3 8
1124 = 3 – 7 4

28. Example
Add or subtract.
5 12
7 8
1324 = 4 – 12 7

29. Example
Add or subtract.
5 8
5 6
7 9
4972 = 1 – + 2 1