Math Problem Statement

Solve each proportion.

Solution

I see your worksheet on proportions. Let me analyze a few problems from it to verify your work. If you'd like me to check or explain any specific ones, feel free to ask. I will now go through some examples step-by-step:


Example 1:

Problem 1: 28n=79\frac{28}{n} = \frac{7}{9}

  • Cross-multiply: 28×9=7×n28 \times 9 = 7 \times n
  • 252=7n252 = 7n
  • Divide by 7: n=2527=36n = \frac{252}{7} = 36

Answer: n=36n = 36
Your solution looks correct!


Example 2:

Problem 3: 23=x2\frac{2}{3} = \frac{x}{2}

  • Cross-multiply: 2×2=3×x2 \times 2 = 3 \times x
  • 4=3x4 = 3x
  • Divide by 3: x=43x = \frac{4}{3} or approximately 1.33

Answer: x=43x = \frac{4}{3} or 1.33
It seems your answer is correct here as well.


Example 3:

Problem 7: 58=15n\frac{5}{8} = \frac{15}{n}

  • Cross-multiply: 5×n=8×155 \times n = 8 \times 15
  • 5n=1205n = 120
  • Divide by 5: n=1205=24n = \frac{120}{5} = 24

Answer: n=24n = 24
Your answer here is correct.


Example 4:

Problem 14: 915=45n\frac{9}{15} = \frac{45}{n}

  • Cross-multiply: 9×n=15×459 \times n = 15 \times 45
  • 9n=6759n = 675
  • Divide by 9: n=6759=75n = \frac{675}{9} = 75

Answer: n=75n = 75
Your written note states, “the values are the same,” but the correct solution for nn is actually 75.


Example 5:

Problem 18: 427=n2\frac{42}{7} = \frac{n}{2}

  • Cross-multiply: 42×2=7×n42 \times 2 = 7 \times n
  • 84=7n84 = 7n
  • Divide by 7: n=847=12n = \frac{84}{7} = 12

Answer: n=12n = 12
Your answer appears correct.


Would you like me to go over any other problem more specifically or help with any step? Below are some follow-up questions related to this topic.


5 Related Questions:

  1. How do you determine when two ratios form a proportion?
  2. What are some strategies to simplify ratios before solving proportions?
  3. Can all proportions be solved using cross-multiplication? Why or why not?
  4. How do proportions apply to problems involving percentages?
  5. What is the difference between a proportion and a ratio?

Tip: Always check whether you can simplify the given ratios before solving the proportion. This can reduce the amount of calculation required.

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Math Problem Analysis

Mathematical Concepts

Proportions
Ratios
Cross Multiplication

Formulas

Cross multiplication for proportions: a/b = c/d implies a * d = b * c

Theorems

Proportion Theorem
Cross Multiplication Property

Suitable Grade Level

Grade 7-9