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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.
 23
+
 13
2.
 23
+
 23

Complexity=4, Mode=simple

Add each pair of fractions and simplify the result.

1.
 22
+
 12
2.
 22
+
 44

Complexity=6, Mode=simple

Add each pair of fractions and simplify the result.

1.
 12
+
 23
2.
 24
+
 14

Complexity=3, Mode=improper

Add each pair of fractions and simplify the result.

1.
 13
+
 33
2.
 22
+
 33

Complexity=5, Mode=improper

Add each pair of fractions and simplify the result.

1.
 15
+
 14
2.
 42
+
 52

Complexity=7, Mode=improper

Add each pair of fractions and simplify the result.

1.
 17
+
 65
2.
 23
+
 24

Complexity=3, Mode=mixed

Add each pair of fractions and simplify the result.

1.
 1 13
+
 1 23
2.
 3 12
+
 2 13

Complexity=6, Mode=mixed

Add each pair of fractions and simplify the result.

1.
 13
+
 2 45
2.
 2 46
+
 25

Complexity=10, Mode=mixed

Add each pair of fractions and simplify the result.

1.
 1 19
+
 2 49
2.
 1 610
+
 2 410

Complexity=12, Mode=mixed-imp

Add each pair of fractions and simplify the result.

1.
 3 1112
+
 2 54
2.
 2 58
+
 2 710

Complexity=20, Mode=mixed-imp

Add each pair of fractions and simplify the result.

1.
 3 18
+
 1 510
2.
 2 1518
+
 3 312

Complexity=50, Mode=mixed-imp

Add each pair of fractions and simplify the result.

1.
 2 1032
+
 3 544
2.
 1122
+
 3 3532

Complexity=3, Mode=simple

Add each pair of fractions and simplify the result.

1
 23
+
 13
Solution
 33
Now simplify to get this:
1
2
 23
+
 23
Solution
 43
Now simplify to get this:
 1 13

Complexity=4, Mode=simple

Add each pair of fractions and simplify the result.

1
 22
+
 12
Solution
Simplify fractions
1 +
 12
 1 12
2
 22
+
 44
Solution
Simplify fractions
 1 + 1
2

Complexity=6, Mode=simple

Add each pair of fractions and simplify the result.

1
 12
+
 23
Solution
The lowest common denominator (LCD) is 6
Adjust the denominators to get this:
 36
+
 46
 76
Now simplify to get this:
 1 16
2
 24
+
 14
Solution
 34

Complexity=3, Mode=improper

Add each pair of fractions and simplify the result.

1
 13
+
 33
Solution
Simplify fractions
 13
+ 1
 1 13
2
 22
+
 33
Solution
Simplify fractions
 1 + 1
2

Complexity=5, Mode=improper

Add each pair of fractions and simplify the result.

1
 15
+
 14
Solution
The lowest common denominator (LCD) is 20
Adjust the denominators to get this:
 420
+
 520
 920
2
 42
+
 52
Solution
 92
Now simplify to get this:
 4 12

Complexity=7, Mode=improper

Add each pair of fractions and simplify the result.

1
 17
+
 65
Solution
Simplify fractions
 17
+
 1 15
The lowest common denominator (LCD) is 35
Adjust the denominators to get this:
 535
+
 1 735
 1 1235
2
 23
+
 24
Solution
Simplify fractions
 23
+
 12
The lowest common denominator (LCD) is 6
Adjust the denominators to get this:
 46
+
 36
 76
Now simplify to get this:
 1 16

Complexity=3, Mode=mixed

Add each pair of fractions and simplify the result.

1
 1 13
+
 1 23
Solution
 2 33
Now simplify to get this:
3
2
 3 12
+
 2 13
Solution
The lowest common denominator (LCD) is 6
Adjust the denominators to get this:
 3 36
+
 2 26
 5 56

Complexity=6, Mode=mixed

Add each pair of fractions and simplify the result.

1
 13
+
 2 45
Solution
The lowest common denominator (LCD) is 15
Adjust the denominators to get this:
 515
+
 2 1215
 2 1715
Now simplify to get this:
 3 215
2
 2 46
+
 25
Solution
Simplify fractions
 2 23
+
 25
The lowest common denominator (LCD) is 15
Adjust the denominators to get this:
 2 1015
+
 615
 2 1615
Now simplify to get this:
 3 115

Complexity=10, Mode=mixed

Add each pair of fractions and simplify the result.

1
 1 19
+
 2 49
Solution
 3 59
2
 1 610
+
 2 410
Solution
 3 1010
Now simplify to get this:
4

Complexity=12, Mode=mixed-imp

Add each pair of fractions and simplify the result.

1
 3 1112
+
 2 54
Solution
Simplify fractions
 3 1112
+
 3 14
The lowest common denominator (LCD) is 12
Adjust the denominators to get this:
 3 1112
+
 3 312
 6 1412
Now simplify to get this:
 7 16
2
 2 58
+
 2 710
Solution
The lowest common denominator (LCD) is 40
Adjust the denominators to get this:
 2 2540
+
 2 2840
 4 5340
Now simplify to get this:
 5 1340

Complexity=20, Mode=mixed-imp

Add each pair of fractions and simplify the result.

1
 3 18
+
 1 510
Solution
Simplify fractions
 3 18
+
 1 12
The lowest common denominator (LCD) is 8
Adjust the denominators to get this:
 3 18
+
 1 48
 4 58
2
 2 1518
+
 3 312
Solution
Simplify fractions
 2 56
+
 3 14
The lowest common denominator (LCD) is 12
Adjust the denominators to get this:
 2 1012
+
 3 312
 5 1312
Now simplify to get this:
 6 112

Complexity=50, Mode=mixed-imp

Add each pair of fractions and simplify the result.

1
 2 1032
+
 3 544
Solution
Simplify fractions
 2 516
+
 3 544
The lowest common denominator (LCD) is 176
Adjust the denominators to get this:
 2 55176
+
 3 20176
 5 75176
2
 1122
+
 3 3532
Solution
Simplify fractions
 12
+
 4 332
The lowest common denominator (LCD) is 32
Adjust the denominators to get this:
 1632
+
 4 332   