Math Skill: Basic Fraction Addition
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Basic Fraction Addition


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
  2. Add the numerators
  3. Simplify the answer
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.

1
6		   and   3
6		   have the same denominator, 6.

Step 2: Add the numerators.
Add the numerators and keep the denominator the same.

1
6		 + 3
6		   =   1 + 3
6		   =   4
6

Step 3: Simplify the answer.

4
6		   simplifies to   2
3
The answer is

Complexity=4, Mode=same-den

Add each pair of fractions and simplify the result.
1.  
1
3
+
1
3
2.  
2
3
+
1
3

Complexity=5, Mode=same-den

Add each pair of fractions and simplify the result.
1.  
1
5
+
4
5
2.  
1
3
+
1
3

Complexity=7, Mode=same-den

Add each pair of fractions and simplify the result.
1.  
1
3
+
2
3
2.  
2
4
+
2
4

Complexity=9, Mode=same-den

Add each pair of fractions and simplify the result.
1.  
6
9
+
1
9
2.  
6
9
+
2
9

Complexity=12, Mode=same-den

Add each pair of fractions and simplify the result.
1.  
2
10
+
6
10
2.  
5
9
+
4
9

Complexity=4, Mode=simple

Add each pair of fractions and simplify the result.
1.  
3
4
+
1
3
2.  
2
2
+
1
2

Complexity=6, Mode=simple

Add each pair of fractions and simplify the result.
1.  
4
6
+
3
5
2.  
2
4
+
1
4

Answers

Complexity=4, Mode=same-den

Add each pair of fractions and simplify the result.
#ProblemCorrect AnswerYour Answer
1
1
3
+
1
3
Solution
Add numerators to get this:
2
3
#ProblemCorrect AnswerYour Answer
2
2
3
+
1
3
Solution
Add numerators to get this:
3
3
Now simplify to get this:
1

Complexity=5, Mode=same-den

Add each pair of fractions and simplify the result.
#ProblemCorrect AnswerYour Answer
1
1
5
+
4
5
Solution
Add numerators to get this:
5
5
Now simplify to get this:
1
#ProblemCorrect AnswerYour Answer
2
1
3
+
1
3
Solution
Add numerators to get this:
2
3

Complexity=7, Mode=same-den

Add each pair of fractions and simplify the result.
#ProblemCorrect AnswerYour Answer
1
1
3
+
2
3
Solution
Add numerators to get this:
3
3
Now simplify to get this:
1
#ProblemCorrect AnswerYour Answer
2
2
4
+
2
4
Solution
Add numerators to get this:
4
4
Now simplify to get this:
1

Complexity=9, Mode=same-den

Add each pair of fractions and simplify the result.
#ProblemCorrect AnswerYour Answer
1
6
9
+
1
9
Solution
Add numerators to get this:
7
9
#ProblemCorrect AnswerYour Answer
2
6
9
+
2
9
Solution
Add numerators to get this:
8
9

Complexity=12, Mode=same-den

Add each pair of fractions and simplify the result.
#ProblemCorrect AnswerYour Answer
1
2
10
+
6
10
Solution
Add numerators to get this:
8
10
Now simplify to get this:
4
5
#ProblemCorrect AnswerYour Answer
2
5
9
+
4
9
Solution
Add numerators to get this:
9
9
Now simplify to get this:
1

Complexity=4, Mode=simple

Add each pair of fractions and simplify the result.
#ProblemCorrect AnswerYour Answer
1
3
4
+
1
3
Solution
The lowest common denominator (LCD) is 12
Adjust the denominators to get this:
9
12
+
4
12
Add numerators to get this:
13
12
Now simplify to get this:
1 1
12
#ProblemCorrect AnswerYour Answer
2
2
2
+
1
2
Solution
Simplify fractions
1 +
1
2
Add the whole numbers
1 1
2

Complexity=6, Mode=simple

Add each pair of fractions and simplify the result.
#ProblemCorrect AnswerYour Answer
1
4
6
+
3
5
Solution
Simplify fractions
2
3
+
3
5
The lowest common denominator (LCD) is 15
Adjust the denominators to get this:
10
15
+
9
15
Add numerators to get this:
19
15
Now simplify to get this:
1 4
15
#ProblemCorrect AnswerYour Answer
2
2
4
+
1
4
Solution
Add numerators to get this:
3
4
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