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Fraction Addition - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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Complexity=3, Mode=simple

Add each pair of fractions and simplify the result.

1.  
2
3
+
1
3

2.  
2
3
+
2
3

Complexity=4, Mode=simple

Add each pair of fractions and simplify the result.

1.  
2
2
+
1
2

2.  
2
2
+
4
4

Complexity=6, Mode=simple

Add each pair of fractions and simplify the result.

1.  
1
2
+
2
3

2.  
2
4
+
1
4

Complexity=3, Mode=improper

Add each pair of fractions and simplify the result.

1.  
1
3
+
3
3

2.  
2
2
+
3
3

Complexity=5, Mode=improper

Add each pair of fractions and simplify the result.

1.  
1
5
+
1
4

2.  
4
2
+
5
2

Complexity=7, Mode=improper

Add each pair of fractions and simplify the result.

1.  
1
7
+
6
5

2.  
2
3
+
2
4

Complexity=3, Mode=mixed

Add each pair of fractions and simplify the result.

1.  
1 1
3
+
1 2
3

2.  
3 1
2
+
2 1
3

Complexity=6, Mode=mixed

Add each pair of fractions and simplify the result.

1.  
1
3
+
2 4
5

2.  
2 4
6
+
2
5

Complexity=10, Mode=mixed

Add each pair of fractions and simplify the result.

1.  
1 1
9
+
2 4
9

2.  
1 6
10
+
2 4
10

Complexity=12, Mode=mixed-imp

Add each pair of fractions and simplify the result.

1.  
3 11
12
+
2 5
4

2.  
2 5
8
+
2 7
10

Complexity=20, Mode=mixed-imp

Add each pair of fractions and simplify the result.

1.  
3 1
8
+
1 5
10

2.  
2 15
18
+
3 3
12

Complexity=50, Mode=mixed-imp

Add each pair of fractions and simplify the result.

1.  
2 10
32
+
3 5
44

2.  
11
22
+
3 35
32


Answers


Complexity=3, Mode=simple

Add each pair of fractions and simplify the result.

#ProblemCorrect AnswerYour Answer
1
2
3
+
1
3

Solution
Add numerators to get this:
3
3
Now simplify to get this:
1
#ProblemCorrect AnswerYour Answer
2
2
3
+
2
3

Solution
Add numerators to get this:
4
3
Now simplify to get this:
1 1
3

Complexity=4, Mode=simple

Add each pair of fractions and simplify the result.

#ProblemCorrect AnswerYour Answer
1
2
2
+
1
2

Solution
Simplify fractions
1 +
1
2
Add the whole numbers
1 1
2
#ProblemCorrect AnswerYour Answer
2
2
2
+
4
4

Solution
Simplify fractions
1 + 1
Add the whole numbers
2

Complexity=6, Mode=simple

Add each pair of fractions and simplify the result.

#ProblemCorrect AnswerYour Answer
1
1
2
+
2
3

Solution
The lowest common denominator (LCD) is 6
Adjust the denominators to get this:
3
6
+
4
6
Add numerators to get this:
7
6
Now simplify to get this:
1 1
6
#ProblemCorrect AnswerYour Answer
2
2
4
+
1
4

Solution
Add numerators to get this:
3
4

Complexity=3, Mode=improper

Add each pair of fractions and simplify the result.

#ProblemCorrect AnswerYour Answer
1
1
3
+
3
3

Solution
Simplify fractions
1
3
+ 1
Add the whole numbers
1 1
3
#ProblemCorrect AnswerYour Answer
2
2
2
+
3
3

Solution
Simplify fractions
1 + 1
Add the whole numbers
2

Complexity=5, Mode=improper

Add each pair of fractions and simplify the result.

#ProblemCorrect AnswerYour Answer
1
1
5
+
1
4

Solution
The lowest common denominator (LCD) is 20
Adjust the denominators to get this:
4
20
+
5
20
Add numerators to get this:
9
20
#ProblemCorrect AnswerYour Answer
2
4
2
+
5
2

Solution
Add numerators to get this:
9
2
Now simplify to get this:
4 1
2

Complexity=7, Mode=improper

Add each pair of fractions and simplify the result.

#ProblemCorrect AnswerYour Answer
1
1
7
+
6
5

Solution
Simplify fractions
1
7
+
1 1
5
The lowest common denominator (LCD) is 35
Adjust the denominators to get this:
5
35
+
1 7
35
Add numerators to get this:
1 12
35
#ProblemCorrect AnswerYour Answer
2
2
3
+
2
4

Solution
Simplify fractions
2
3
+
1
2
The lowest common denominator (LCD) is 6
Adjust the denominators to get this:
4
6
+
3
6
Add numerators to get this:
7
6
Now simplify to get this:
1 1
6

Complexity=3, Mode=mixed

Add each pair of fractions and simplify the result.

#ProblemCorrect AnswerYour Answer
1
1 1
3
+
1 2
3

Solution
Add numerators to get this:
2 3
3
Now simplify to get this:
3
#ProblemCorrect AnswerYour Answer
2
3 1
2
+
2 1
3

Solution
The lowest common denominator (LCD) is 6
Adjust the denominators to get this:
3 3
6
+
2 2
6
Add numerators to get this:
5 5
6

Complexity=6, Mode=mixed

Add each pair of fractions and simplify the result.

#ProblemCorrect AnswerYour Answer
1
1
3
+
2 4
5

Solution
The lowest common denominator (LCD) is 15
Adjust the denominators to get this:
5
15
+
2 12
15
Add numerators to get this:
2 17
15
Now simplify to get this:
3 2
15
#ProblemCorrect AnswerYour Answer
2
2 4
6
+
2
5

Solution
Simplify fractions
2 2
3
+
2
5
The lowest common denominator (LCD) is 15
Adjust the denominators to get this:
2 10
15
+
6
15
Add numerators to get this:
2 16
15
Now simplify to get this:
3 1
15

Complexity=10, Mode=mixed

Add each pair of fractions and simplify the result.

#ProblemCorrect AnswerYour Answer
1
1 1
9
+
2 4
9

Solution
Add numerators to get this:
3 5
9
#ProblemCorrect AnswerYour Answer
2
1 6
10
+
2 4
10

Solution
Add numerators to get this:
3 10
10
Now simplify to get this:
4

Complexity=12, Mode=mixed-imp

Add each pair of fractions and simplify the result.

#ProblemCorrect AnswerYour Answer
1
3 11
12
+
2 5
4

Solution
Simplify fractions
3 11
12
+
3 1
4
The lowest common denominator (LCD) is 12
Adjust the denominators to get this:
3 11
12
+
3 3
12
Add numerators to get this:
6 14
12
Now simplify to get this:
7 1
6
#ProblemCorrect AnswerYour Answer
2
2 5
8
+
2 7
10

Solution
The lowest common denominator (LCD) is 40
Adjust the denominators to get this:
2 25
40
+
2 28
40
Add numerators to get this:
4 53
40
Now simplify to get this:
5 13
40

Complexity=20, Mode=mixed-imp

Add each pair of fractions and simplify the result.

#ProblemCorrect AnswerYour Answer
1
3 1
8
+
1 5
10

Solution
Simplify fractions
3 1
8
+
1 1
2
The lowest common denominator (LCD) is 8
Adjust the denominators to get this:
3 1
8
+
1 4
8
Add numerators to get this:
4 5
8
#ProblemCorrect AnswerYour Answer
2
2 15
18
+
3 3
12

Solution
Simplify fractions
2 5
6
+
3 1
4
The lowest common denominator (LCD) is 12
Adjust the denominators to get this:
2 10
12
+
3 3
12
Add numerators to get this:
5 13
12
Now simplify to get this:
6 1
12

Complexity=50, Mode=mixed-imp

Add each pair of fractions and simplify the result.

#ProblemCorrect AnswerYour Answer
1
2 10
32
+
3 5
44

Solution
Simplify fractions
2 5
16
+
3 5
44
The lowest common denominator (LCD) is 176
Adjust the denominators to get this:
2 55
176
+
3 20
176
Add numerators to get this:
5 75
176
#ProblemCorrect AnswerYour Answer
2
11
22
+
3 35
32

Solution
Simplify fractions
1
2
+
4 3
32
The lowest common denominator (LCD) is 32
Adjust the denominators to get this:
16
32
+
4 3
32
Add numerators to get this:
4 19
32
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