View Lesson | View Sample Problems | Do Worksheet

Instructional videos are displayed with permission from Khan Academy.

For this topic, you need to know the basics of fractions and fraction simplification.
To review the basics of fractions (pictures), see here.
To review basic fraction simplification, see here.

Use the following steps to add fractions:

1. Check the denominators
NOTE: Do NOT add the denominators.

Example:

1
6
+ 3
6

Step 1: Check the denominators.
When adding fractions, the denominators must be the same.

 16 and 36 have the same denominator, 6.

Add the numerators and keep the denominator the same.

 16 + 36 = 1 + 36 = 46

 46 simplifies to 23

### Complexity=4, Mode=same-den

Add each pair of fractions and simplify the result.
1.
 13
+
 13
2.
 23
+
 13

### Complexity=5, Mode=same-den

Add each pair of fractions and simplify the result.
1.
 15
+
 45
2.
 13
+
 13

### Complexity=7, Mode=same-den

Add each pair of fractions and simplify the result.
1.
 13
+
 23
2.
 24
+
 24

### Complexity=9, Mode=same-den

Add each pair of fractions and simplify the result.
1.
 69
+
 19
2.
 69
+
 29

### Complexity=12, Mode=same-den

Add each pair of fractions and simplify the result.
1.
 210
+
 610
2.
 59
+
 49

### Complexity=4, Mode=simple

Add each pair of fractions and simplify the result.
1.
 34
+
 13
2.
 22
+
 12

### Complexity=6, Mode=simple

Add each pair of fractions and simplify the result.
1.
 46
+
 35
2.
 24
+
 14

### Complexity=4, Mode=same-den

Add each pair of fractions and simplify the result.
1
 13
+
 13
Solution
 23
2
 23
+
 13
Solution
 33
Now simplify to get this:
1

### Complexity=5, Mode=same-den

Add each pair of fractions and simplify the result.
1
 15
+
 45
Solution
 55
Now simplify to get this:
1
2
 13
+
 13
Solution
 23

### Complexity=7, Mode=same-den

Add each pair of fractions and simplify the result.
1
 13
+
 23
Solution
 33
Now simplify to get this:
1
2
 24
+
 24
Solution
 44
Now simplify to get this:
1

### Complexity=9, Mode=same-den

Add each pair of fractions and simplify the result.
1
 69
+
 19
Solution
 79
2
 69
+
 29
Solution
 89

### Complexity=12, Mode=same-den

Add each pair of fractions and simplify the result.
1
 210
+
 610
Solution
 810
Now simplify to get this:
 45
2
 59
+
 49
Solution
 99
Now simplify to get this:
1

### Complexity=4, Mode=simple

Add each pair of fractions and simplify the result.
1
 34
+
 13
Solution
The lowest common denominator (LCD) is 12
Adjust the denominators to get this:
 912
+
 412
 1312
Now simplify to get this:
 1 112
2
 22
+
 12
Solution
Simplify fractions
1 +
 12
 1 12

### Complexity=6, Mode=simple

Add each pair of fractions and simplify the result.
1
 46
+
 35
Solution
Simplify fractions
 23
+
 35
The lowest common denominator (LCD) is 15
Adjust the denominators to get this:
 1015
+
 915