## - 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.

See some of our other supported math practice problems.

### Complexity=3, Mode=simple

Multiply each pair of fractions and simplify the result.
1.
 13
×
 23
2.
 23
×
 13

### Complexity=4, Mode=simple

Multiply each pair of fractions and simplify the result.
1.
 13
×
 33
2.
 23
×
 34

### Complexity=6, Mode=simple

Multiply each pair of fractions and simplify the result.
1.
 46
×
 14
2.
 14
×
 14

### Complexity=3, Mode=improper

Multiply each pair of fractions and simplify the result.
1.
 32
×
 33
2.
 32
×
 13

### Complexity=5, Mode=improper

Multiply each pair of fractions and simplify the result.
1.
 45
×
 33
2.
 14
×
 34

### Complexity=7, Mode=improper

Multiply each pair of fractions and simplify the result.
1.
 26
×
 55
2.
 14
×
 37

### Complexity=3, Mode=mixed

Multiply each pair of fractions and simplify the result.
1.
 13
×
 1 23
2.
 12
×
 3 23

### Complexity=6, Mode=mixed

Multiply each pair of fractions and simplify the result.
1.
 3 45
×
 1 13
2.
 26
×
 3 12

### Complexity=10, Mode=mixed

Multiply each pair of fractions and simplify the result.
1.
 2 36
×
 1 810
2.
 58
×
 1 46

### Complexity=12, Mode=mixed-imp

Multiply each pair of fractions and simplify the result.
1.
 3 108
×
 3 106
2.
 3 109
×
 1 68

### Complexity=20, Mode=mixed-imp

Multiply each pair of fractions and simplify the result.
1.
 1 79
×
 2 1112
2.
 215
×
 149

### Complexity=50, Mode=mixed-imp

Multiply each pair of fractions and simplify the result.
1.
 1 3933
×
 1 4012
2.
 1 2732
×
 3 136

### Complexity=3, Mode=simple

Multiply each pair of fractions and simplify the result.
1
 13
×
 23
Solution
Multiply numerators and denominators.
 29
2
 23
×
 13
Solution
Multiply numerators and denominators.
 29

### Complexity=4, Mode=simple

Multiply each pair of fractions and simplify the result.
1
 13
×
 33
Solution
Simplify fractions to reduce denominators.
 13
× 1
 13
2
 23
×
 34
Solution
Eliminate common factors.
 1 × 21 × 3
×
 1 × 32 × 2
 11
×
 12
Multiply numerators and denominators.
 12

### Complexity=6, Mode=simple

Multiply each pair of fractions and simplify the result.
1
 46
×
 14
Solution
Simplify fractions to reduce denominators.
 23
×
 14
Eliminate common factors.
 1 × 23
×
 12 × 2
 13
×
 12
Multiply numerators and denominators.
 16
2
 14
×
 14
Solution
Multiply numerators and denominators.
 116

### Complexity=3, Mode=improper

Multiply each pair of fractions and simplify the result.
1
 32
×
 33
Solution
Simplify fractions to reduce denominators.
 32
× 1
Now simplify.
 1 12
2
 32
×
 13
Solution
Eliminate common factors.
 1 × 32
×
 11 × 3
 12
×
 11
Multiply numerators and denominators.
 12

### Complexity=5, Mode=improper

Multiply each pair of fractions and simplify the result.
1
 45
×
 33
Solution
Simplify fractions to reduce denominators.
 45
× 1
 45
2
 14
×
 34
Solution
Multiply numerators and denominators.
 316

### Complexity=7, Mode=improper

Multiply each pair of fractions and simplify the result.
1
 26
×
 55
Solution
Simplify fractions to reduce denominators.
 13
× 1
 13
2
 14
×
 37
Solution
Multiply numerators and denominators.
 328

### Complexity=3, Mode=mixed

Multiply each pair of fractions and simplify the result.
1
 13
×
 1 23
Solution
Convert to improper fractions.
 13
×
 53
Multiply numerators and denominators.
 59
2
 12
×
 3 23
Solution
Convert to improper fractions.
 12
×
 113
Multiply numerators and denominators.
 116
Now simplify.
 1 56

### Complexity=6, Mode=mixed

Multiply each pair of fractions and simplify the result.
1
 3 45
×
 1 13
Solution
Convert to improper fractions.
 195
×
 43
Multiply numerators and denominators.
 7615
Now simplify.
 5 115
2
 26
×
 3 12
Solution
Simplify fractions to reduce denominators.
 13
×
 3 12
Convert to improper fractions.
 13
×
 72
Multiply numerators and denominators.
 76
Now simplify.
 1 16

### Complexity=10, Mode=mixed

Multiply each pair of fractions and simplify the result.
1
 2 36
×
 1 810
Solution
Simplify fractions to reduce denominators.
 2 12
×
 1 45
Convert to improper fractions.
 52
×
 95
Eliminate common factors.
 1 × 52
×
 91 × 5
 12
×
 91
Multiply numerators and denominators.
 92
Now simplify.
 4 12
2
 58
×
 1 46
Solution
Simplify fractions to reduce denominators.
 58
×
 1 23
Convert to improper fractions.
 58
×
 53
Multiply numerators and denominators.
 2524
Now simplify.
 1 124

### Complexity=12, Mode=mixed-imp

Multiply each pair of fractions and simplify the result.
1
 3 108
×
 3 106
Solution
Simplify fractions to reduce denominators.
 4 14
×
 4 23
Convert to improper fractions.
 174
×
 143
Eliminate common factors.
 172 × 2
×
 7 × 23
 172
×
 73
Multiply numerators and denominators.
 1196
Now simplify.
 19 56
2
 3 109
×
 1 68
Solution
Simplify fractions to reduce denominators.
 3 109
×
 1 34
Convert to improper fractions.
 379
×
 74
Multiply numerators and denominators.
 25936
Now simplify.
 7 736

### Complexity=20, Mode=mixed-imp

Multiply each pair of fractions and simplify the result.
1
 1 79
×
 2 1112
Solution
Convert to improper fractions.
 169
×
 3512
Eliminate common factors.
 4 × 49
×
 353 × 4
 49
×
 353
Multiply numerators and denominators.
 14027
Now simplify.
 5 527
2
 215
×
 149
Solution
Multiply numerators and denominators.
 28135

### Complexity=50, Mode=mixed-imp

Multiply each pair of fractions and simplify the result.
1
 1 3933
×
 1 4012
Solution
Simplify fractions to reduce denominators.
 2 211
×
 4 13
Convert to improper fractions.
 2411
×
 133
Eliminate common factors.
 8 × 311
×
 131 × 3
 811
×
 131
Multiply numerators and denominators.
 10411
Now simplify.
 9 511
2
 1 2732
×
 3 136
Solution
Convert to improper fractions.
 5932
×
 316
Multiply numerators and denominators.
 1829192
Now simplify.
 9 101192