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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.

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Complexity=5, Mode=fraction

Solve for n

1.  
10
4
= n
12
n:
2.  
24
18
= 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.  
70
30
= n
18
n:
2.   9 : 54 = n : 18
n:

Complexity=20

Solve for n

1.   77 : 119 = n : 51
n:
2.  
20
24
= n
18
n:

Answers

Complexity=5, Mode=fraction

Solve for n

#ProblemCorrect AnswerYour Answer
1
10
4
= n
12
 n:
Solution
First simplify the fraction on the left: 10/4 = 5/2
5
2
= 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
5
2
= n
12

n
12		 =
5
2

n
12		 = 5 × 6
2 × 6		 =
30
12
#ProblemCorrect AnswerYour Answer
2
24
18
= n
15
 n:
Solution
First simplify the fraction on the left: 24/18 = 4/3
4
3
= 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
4
3
= n
15

n
15		 =
4
3

n
15		 = 4 × 5
3 × 5		 =
20
15

Complexity=8, Mode=ratio

Solve for n

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

14
35
= n
20
Then simplify the fraction on the left: 14/35 = 2/5
2
5
= 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
#ProblemCorrect AnswerYour Answer
224 : 48 = n : 32
n:
Solution
Begin by rewriting the ratios as fractions: '24 : 48 = n : 32' becomes

24
48
= n
32
Then simplify the fraction on the left: 24/48 = 4/8
4
8
= 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

#ProblemCorrect AnswerYour Answer
1
70
30
= n
18
 n:
Solution
First simplify the fraction on the left: 70/30 = 7/3
7
3
= 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
7
3
= n
18

n
18		 =
7
3

n
18		 = 7 × 6
3 × 6		 =
42
18
#ProblemCorrect AnswerYour Answer
29 : 54 = n : 18
n:
Solution
Begin by rewriting the ratios as fractions: '9 : 54 = n : 18' becomes

9
54
= n
18
Then simplify the fraction on the left: 9/54 = 1/6
1
6
= 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

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

77
119
= n
51
Then simplify the fraction on the left: 77/119 = 11/17
11
17
= 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
#ProblemCorrect AnswerYour Answer
2
20
24
= n
18
 n:
Solution
First simplify the fraction on the left: 20/24 = 5/6
5
6
= 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
5
6
= n
18

n
18		 =
5
6

n
18		 = 5 × 3
6 × 3		 =
15
18
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