Lecture Notes: Percent Proportions

Introduction to Percent Proportions

• Definition: The ratio between the part and the whole is equivalent to the ratio between the percent and 100.
• Equation: ( \frac{\text{Part}}{\text{Whole}} = \frac{\text{Percent}}{100} )

Solving Problems with Percent Proportions

Finding the Percent

• Example 1: "20 is what percent of 45?"
  • Equation setup: ( \frac{20}{45} = \frac{x}{100} )
  • Cross-multiply and solve: 45x = 2000
  • Solve for x: ( x = \frac{2000}{45} \approx 44.4 )
  • Result: 20 is 44.4% of 45.
• Example 2: "What percent of 12 is 27?"
  • Equation setup: ( \frac{27}{12} = \frac{x}{100} )
  • Cross-multiply and solve: 12x = 2700
  • Solve for x: ( x = \frac{2700}{12} = 225 )
  • Result: 27 is 225% of 12.

Finding the Part

• Example 1: "What is 32% of 86?"
  • Equation setup: ( \frac{x}{86} = \frac{32}{100} )
  • Cross-multiply and solve: 100x = 2752
  • Solve for x: ( x = \frac{2752}{100} = 27.52 )
  • Result: 27.52 is 32% of 86.
• Example 2: "What number is 21% of 250?"
  • Equation setup: ( \frac{x}{250} = \frac{21}{100} )
  • Cross-multiply and solve: 100x = 5250
  • Solve for x: ( x = \frac{5250}{100} = 52.5 )
  • Result: 52.5 is 21% of 250.

Finding the Base (Whole)

• Example 1: "30 is 45% of what number?"
  • Equation setup: ( \frac{30}{x} = \frac{45}{100} )
  • Cross-multiply and solve: 3000 = 45x
  • Solve for x: ( x = \frac{3000}{45} \approx 66.7 )
  • Result: 30 is 45% of 66.7.
• Example 2: "22 is 34% of what number?"
  • Equation setup: ( \frac{22}{x} = \frac{34}{100} )
  • Cross-multiply and solve: 2200 = 34x
  • Solve for x: ( x = \frac{2200}{34} \approx 64.7 )
  • Result: 22 is 34% of 64.7.

Algebra Course Overview

• Platform: Udemy

• Course Content:

  • Basic arithmetic (addition, subtraction, multiplication, division), includes video quizzes.
  • Fractions: addition, subtraction, multiplication, division, conversion to decimals.
  • Linear equations: solving and examples, order of operations, graphing linear equations.
  • Inequalities and absolute value expressions.
  • Polynomials and factoring.
  • Systems of equations: elimination, substitution, word problems.
  • Quadratic equations: using quadratic formula, graphing, conversion.
  • Rational and radical expressions: solving and simplifying.
  • Complex numbers, exponential functions, logarithms.
  • Functions: vertical and horizontal line tests, even/odd functions.
  • Conic sections: circles, hyperbolas, ellipses, parabolas.
  • Sequences and series: arithmetic and geometric.

• Note: Each section includes a quiz to review learning.