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Solving Proportions

Use cross multiplication to solve proportion problems

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Solving Proportions

What is a Proportion?

A proportion is an equation that states two ratios are equal: ab=cd\frac{a}{b} = \frac{c}{d}

Cross Multiplication

To solve proportions, use cross multiplication:

ab=cd⇒ad=bc\frac{a}{b} = \frac{c}{d} \quad \Rightarrow \quad ad = bc

Example: 34=x12\frac{3}{4} = \frac{x}{12} 3×12=4×x3 \times 12 = 4 \times x 36=4x36 = 4x x=9x = 9

Checking Your Answer

Substitute back to verify: 34=912✓\frac{3}{4} = \frac{9}{12} \quad \checkmark

Real-World Applications

  • Scale drawings
  • Recipe conversions
  • Unit conversions
  • Similar figures

📚 Practice Problems

1Problem 1easy

❓ Question:

Solve for xx: 25=x15\frac{2}{5} = \frac{x}{15}

💡 Show Solution

Solution:

Cross multiply: 2×15=5×x2 \times 15 = 5 \times x 30=5x30 = 5x x=6x = 6

Check: 25=615\frac{2}{5} = \frac{6}{15} ✓ (both simplify to 25\frac{2}{5})

Answer: x=6x = 6

2Problem 2easy

❓ Question:

Solve for xx: 25=x15\frac{2}{5} = \frac{x}{15}

💡 Show Solution

Solution:

Cross multiply: 2×15=5×x2 \times 15 = 5 \times x 30=5x30 = 5x x=6x = 6

Check: 25=615\frac{2}{5} = \frac{6}{15} ✓ (both simplify to 25\frac{2}{5})

Answer: x=6x = 6

3Problem 3medium

❓ Question:

If 3 pounds of apples cost \4.50$, how much do 7 pounds cost?

💡 Show Solution

Solution:

Set up proportion: 3 pounds$4.50=7 poundsx\frac{3 \text{ pounds}}{\$4.50} = \frac{7 \text{ pounds}}{x}

Cross multiply: 3x=4.50×73x = 4.50 \times 7 3x=31.503x = 31.50 x=10.50x = 10.50

Answer: \10.50$

4Problem 4medium

❓ Question:

If 3 pounds of apples cost \4.50$, how much do 7 pounds cost?

💡 Show Solution

Solution:

Set up proportion: 3 pounds$4.50=7 poundsx\frac{3 \text{ pounds}}{\$4.50} = \frac{7 \text{ pounds}}{x}

Cross multiply: 3x=4.50×73x = 4.50 \times 7 3x=31.503x = 31.50 x=10.50x = 10.50

Answer: \10.50$

5Problem 5hard

❓ Question:

On a map, 2 inches represents 50 miles. Two cities are 7 inches apart on the map. What is the actual distance between them?

💡 Show Solution

Solution:

Set up proportion: 2 inches50 miles=7 inchesx miles\frac{2 \text{ inches}}{50 \text{ miles}} = \frac{7 \text{ inches}}{x \text{ miles}}

Cross multiply: 2x=50×72x = 50 \times 7 2x=3502x = 350 x=175x = 175

Answer: 175 miles

6Problem 6hard

❓ Question:

On a map, 2 inches represents 50 miles. Two cities are 7 inches apart on the map. What is the actual distance between them?

💡 Show Solution

Solution:

Set up proportion: 2 inches50 miles=7 inchesx miles\frac{2 \text{ inches}}{50 \text{ miles}} = \frac{7 \text{ inches}}{x \text{ miles}}

Cross multiply: 2x=50×72x = 50 \times 7 2x=3502x = 350 x=175x = 175

Answer: 175 miles

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📌 Related Topics in Proportions and Percents

Percent ApplicationsPercent of ChangeSimple Interest

❓ Frequently Asked Questions

What is Solving Proportions?▾
Use cross multiplication to solve proportion problems
How can I study Solving Proportions effectively?▾
Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Practice with the 6 problems provided, checking solutions as you go. Regular review and active practice are key to retention.
Is this Solving Proportions study guide free?▾
Yes — all study notes, flashcards, and practice problems for Solving Proportions on Study Mondo are free to access. No account is needed.
What course covers Solving Proportions?▾
Solving Proportions is part of the Grade 7 Math course on Study Mondo, specifically in the Proportions and Percents section. You can explore the full course for more related topics and practice resources.
Are there practice problems for Solving Proportions?▾
Yes, this page includes 6 practice problems with detailed solutions. Each problem includes a step-by-step explanation to help you understand the approach.