Math with Mr. J: Solving Percent Problems Using the Percent Equation

Introduction

• Objective: Learn to solve percent problems using the percent equation.
• Percent Equation: [ \text{percent} \times \text{whole} = \text{part} ]
• Use: Helps find the percent, whole, or part by plugging in known values.

Sections Covered

1. Finding the Whole
2. Finding the Part
3. Finding the Percent

Section 1: Finding the Whole

Example 1

• Problem: 12 is 80% of what number?
• Equation: [ 0.8 \times W = 12 ]
• Solution:
  • Convert 80% to decimal: 0.8
  • Solve for W: [ W = \frac{12}{0.8} ]
  • W = 15

Example 2

• Problem: 55% of what number is 33?
• Equation: [ 0.55 \times W = 33 ]
• Solution:
  • Convert 55% to decimal: 0.55
  • Solve for W: [ W = \frac{33}{0.55} ]
  • W = 60

Section 2: Finding the Part

Example 1

• Problem: What is 65% of 80?
• Equation: [ 0.65 \times 80 = A ]
• Solution:
  • Convert 65% to decimal: 0.65
  • Solve: A = 52

Example 2

• Problem: 42% of 27 is what number?
• Equation: [ 0.42 \times 27 = A ]
• Solution:
  • Convert 42% to decimal: 0.42
  • Solve: A = 11.34

Section 3: Finding the Percent

Example 1

• Problem: 21 is what percent of 30?
• Equation: [ P \times 30 = 21 ]
• Solution:
  • Solve for P: [ P = \frac{21}{30} = 0.7 ]
  • Convert to percent: 70%

Example 2

• Problem: What percent of 16 is 10?
• Equation: [ P \times 16 = 10 ]
• Solution:
  • Solve for P: [ P = \frac{10}{16} = 0.625 ]
  • Convert to percent: 62.5%

Conclusion

• The percent equation is a versatile tool for solving various percent problems.
• Remember to convert percentages to decimals by dividing by 100 when using them in equations.
• Practice identifying the parts of the problem to effectively use the equation.

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Note: Always ensure to align the decimal correctly when performing division or multiplication in the context of percent problems.