percents/proportions

Understanding Percents

  • Definition of Percent: A percent is a way to express a proportion or ratio out of 100, making it easier to compare different values.

    • For instance, in evaluating graduation rates from schools of different sizes, percent allows for fair comparison.

Calculating Percentages

  • Percent Proportion Formula:

    • The formula to calculate a percent is:[ \frac{percent}{100} = \frac{part}{whole} ]

    • Here, percent refers to the percent value provided, part refers to the subset being examined, and whole refers to the total amount.

Identifying Values

  • Identifying Components:

    • The percent is noted with a percent symbol or the word "percent".

    • The whole often follows the phrase "of", while the part can be trickier to locate as it may appear anywhere.

Example Problems

  • Example 1: "What is 35% of 200?"

    • Identify the values:

      • Percent = 35%

      • Whole = 200

      • Part = Unknown (let's call it x)

    • Set up the equation:[ \frac{35}{100} = \frac{x}{200} ]

    • Cross-multiply and solve for x:

      • 35 * 200 = 100 * x

      • x = 70

  • Example 2: "What percent is 35 of 200?"

    • Identify the values:

      • Part = 35

      • Whole = 200

      • Percent = Unknown (let's call it x)

    • Set up the equation:[ \frac{x}{100} = \frac{35}{200} ]

    • Cross-multiply and solve:

      • x = (35 * 100) / 200 = 17.5%

Applying the Concept in Word Problems

  • Reading Comprehension:

    • Focus on the question to identify what percent is being asked, the whole, and the part.

Example - Gallup Poll:

  • Problem: "In a Gallup full of 976 adults, 68 said they drink alcohol every day. Find the percentage."

    • Identify the values:

      • Whole = 976

      • Part = 68

      • Percent = Unknown (let's call it x)

    • Set up the equation:[ \frac{x}{100} = \frac{68}{976} ]

    • Solve:

      • x = (68 * 100) / 976 = approximately 6.97%

Multi-Step Percentage Problems

  • When multiple statistics are involved, identify each segment distinctly and ensure clarity on what each part or whole refers to.

Example - Northwest Vista College:

  • Scenario: "What percentage of students transfer to UTSA and major in biology?"

    • Transition through each piece of data to calculate both transfer students and those majoring in biology using sequential steps.

Important Formulas

  1. Tax Calculation:

    • Price including tax = Original Price x (1 + Tax Rate)

  2. Discount Calculation:

    • Final Price after discount = Original Price - (Original Price x Discount Rate)

  3. Percent Change:

    • Percent Change = ( \frac{(New Value - Original Value)}{Original Value} \times 100)

Final Note on Application

  • For any percent-related problem, breaking the problem into identifiable parts (percent, part, whole) allows for easier calculation and deeper comprehension.