Solving Proportions

Problem Statement

We need to solve the proportion: 8/36 = 10/n.

Methods to Solve the Proportion

Method 1: Equivalent Fractions

• These ratios need to be equivalent.
• Determine what to multiply 8 by to get 10.
  • Multiply by 10/8 (which is equivalent to 5/4).
• Apply this same factor to the denominator (36):
  • n = 36 * 5/4 = 36 * 5 / 4
  • Simplify: n = 45

Method 2: Scale Factor

• Find how much larger the denominator (36) is compared to the numerator (8) by dividing:
  • 36 / 8 = 9/2
• Apply the same factor to 10 to find n:
  • n = 10 * 9/2 = 45

Method 3: Cross-Multiplication

• Set up the proportion: 8/36 = 10/n
• Cross-multiply to form an equation: 8n = 360
• Solve for n by dividing both sides by 8:
  • n = 360 / 8 = 45

Method 4: Algebraic Approach

• Start with the proportion: 8/36 = 10/n
• Multiply both sides by n: 8n/36 = 10
• Simplify to isolate n: 8n = 360
• Divide both sides by 8 to solve for n:
  • n = 360 / 8 = 45

Summary

• We solved the proportion using different methods and consistently found n = 45.*