Solving Proportions

Problem Statement

• Solve the proportion: 8/36 = 10/n
• Objective: Find the value of n that makes the fractions equivalent.

Methods to Solve the Proportion

Method 1: Equivalent Fractions

• Concept: The ratios or fractions must remain equivalent.
• Steps:
  1. Determine multiplier for numerator:
     • 8 * (10/8) = 10
     • This multiplier (10/8) is simplified to 5/4.
  2. Apply multiplier to the denominator:
     • 36 * (5/4)
     • Simplify:
       • 36/4 = 9
       • 9 * 5 = 45
  3. Therefore, n = 45.

Method 2: Ratios and Multipliers

• Concept: Scaling the numerator and denominator consistently.
• Steps:
  1. Find the ratio of the denominator to the numerator:
     • 36 / 8 = 4.5 (or simplified as 9/2)
  2. Apply this ratio to the second fraction:
     • 10 * (9/2) = 45
  3. Therefore, n = 45.

Method 3: Cross-Multiplication

• Concept: Cross-multiplying to find the unknown.
• Steps:
  1. Set up equation: 8/36 = 10/n
  2. Cross-multiply:
     • 8 * n = 36 * 10
     • 8n = 360
  3. Solve for n by dividing both sides by 8:
     • n = 360 / 8
     • 8 goes into 36 (4 times) = 32 + carry over 4 (40), 40/8 = 5
     • n = 45
  4. Therefore, n = 45.

Method 4: Algebraic Approach

• Concept: Using algebra to isolate the variable.
• Steps:
  1. Set up equation: 8/36 = 10/n
  2. Multiply both sides by n:
     • (8/36) * n = 10
  3. Multiply both sides by 36 to isolate n:
     • n = 10 * (36/8)
     • Simplify: 360 / 8
     • n = 45

4. Therefore, n = 45

Conclusion

• Regardless of the method used (Equivalent Fractions, Ratios and Multipliers, Cross-Multiplication, or Algebra), the value of n is consistently found to be 45.