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## Proportions 1 - 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.

Solve for n

1.
 104
= n
12
n:
2.
 2418
= n
15
n:

### Complexity=8, Mode=ratio

Solve for n

 1.   14 : 35 = n : 20 n: 2.   24 : 48 = n : 32 n:

### Complexity=10

Solve for n

1.
 7030
= n
18
n:
2.   9 : 54 = n : 18
n:

### Complexity=20

Solve for n

1.   77 : 119 = n : 51
n:
2.
 2024
= n
18
n:

### Complexity=5, Mode=fraction

Solve for n

1
 104
= n
12
n:
Solution
First simplify the fraction on the left: 10/4 = 5/2
 52
= n
12
Cross Multiplication: First fraction numerator × second fraction denominator = first fraction denominator × second fraction numerator.
5 × 12 = 2n.
Dividing both sides by 2,
n = 5 × 12 ÷ 2 = 30

Alternate Explanation:
First simplify the fraction on the left: 10/4 = 5/2
 52
= n
12

n
12
=
 52

n
12
= 5 × 6
2 × 6
=
 3012
2
 2418
= n
15
n:
Solution
First simplify the fraction on the left: 24/18 = 4/3
 43
= n
15
Cross Multiplication: First fraction numerator × second fraction denominator = first fraction denominator × second fraction numerator.
4 × 15 = 3n.
Dividing both sides by 3,
n = 4 × 15 ÷ 3 = 20

Alternate Explanation:
First simplify the fraction on the left: 24/18 = 4/3
 43
= n
15

n
15
=
 43

n
15
= 4 × 5
3 × 5
=
 2015

### Complexity=8, Mode=ratio

Solve for n

114 : 35 = n : 20
n:
Solution
Begin by rewriting the ratios as fractions: '14 : 35 = n : 20' becomes

 1435
= n
20
Then simplify the fraction on the left: 14/35 = 2/5
 25
= n
20
Cross Multiplication: First fraction numerator × second fraction denominator = first fraction denominator × second fraction numerator.
2 × 20 = 5n.
Dividing both sides by 5,
n = 2 × 20 ÷ 5 = 8
224 : 48 = n : 32
n:
Solution
Begin by rewriting the ratios as fractions: '24 : 48 = n : 32' becomes

 2448
= n
32
Then simplify the fraction on the left: 24/48 = 4/8
 48
= n
32
Cross Multiplication: First fraction numerator × second fraction denominator = first fraction denominator × second fraction numerator.
4 × 32 = 8n.
Dividing both sides by 8,
n = 4 × 32 ÷ 8 = 16

### Complexity=10

Solve for n

1
 7030
= n
18
n:
Solution
First simplify the fraction on the left: 70/30 = 7/3
 73
= n
18
Cross Multiplication: First fraction numerator × second fraction denominator = first fraction denominator × second fraction numerator.
7 × 18 = 3n.
Dividing both sides by 3,
n = 7 × 18 ÷ 3 = 42

Alternate Explanation:
First simplify the fraction on the left: 70/30 = 7/3
 73
= n
18

n
18
=
 73

n
18
= 7 × 6
3 × 6
=
 4218
29 : 54 = n : 18
n:
Solution
Begin by rewriting the ratios as fractions: '9 : 54 = n : 18' becomes

 954
= n
18
Then simplify the fraction on the left: 9/54 = 1/6
 16
= n
18
Cross Multiplication: First fraction numerator × second fraction denominator = first fraction denominator × second fraction numerator.
1 × 18 = 6n.
Dividing both sides by 6,
n = 1 × 18 ÷ 6 = 3

### Complexity=20

Solve for n

177 : 119 = n : 51
n:
Solution
Begin by rewriting the ratios as fractions: '77 : 119 = n : 51' becomes

 77119
= n
51
Then simplify the fraction on the left: 77/119 = 11/17
 1117
= n
51
Cross Multiplication: First fraction numerator × second fraction denominator = first fraction denominator × second fraction numerator.
11 × 51 = 17n.
Dividing both sides by 17,
n = 11 × 51 ÷ 17 = 33
2
 2024
= n
18
n:
Solution
First simplify the fraction on the left: 20/24 = 5/6
 56
= n
18
Cross Multiplication: First fraction numerator × second fraction denominator = first fraction denominator × second fraction numerator.
5 × 18 = 6n.
Dividing both sides by 6,
n = 5 × 18 ÷ 6 = 15

Alternate Explanation:
First simplify the fraction on the left: 20/24 = 5/6
 56
= n
18

n
18
=
 56

n
18
= 5 × 3
6 × 3
=
 1518