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MATHS11WK60051
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Flashcards in this deck (26)

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  • What is 12% written as a decimal?

    0.12

    percent decimal

  • What is 12% of $91?

    $10.92

    percent of

  • After increasing $64 by 15%, what is the new amount?

    • 115% × $64 = 1.15 × 64 = $73.60
    increase percent

  • After decreasing $45 by 10%, what is the new amount?

    • 90% × $45 = 0.9 × 45 = $40.50
    decrease percent

  • What percent represents a 15% increase of a quantity?

    115%

    percent increase

  • What percent of the original remains after a 10% decrease?

    90%

    percent decrease

  • What is 5% commission on $8750 of kitchenware?

    • $437.50
    percent commission

  • Calculate the sale price of jeans priced at $74.60 with 12% off.

    • $65.65
    percent discount

  • Calculate the sale price of caps priced at $12.80 with 12% off.

    • $11.26
    percent discount

  • Calculate the sale price of shirts priced at $37.50 with 12% off.

    • $33.00
    percent discount

  • What is Patrick's new salary after an 8.5% pay rise on $78,290?

    • $84,945.65
    percent salary

  • Increasing $5000 by 7% is the same as multiplying \(5000\) by what factor?

    • \(1.07\)
    percent multiplier

  • What is the size of a $5000 investment after one year at 7% interest?

    • $5350.00
    interest compound

  • What is the size of the $5000 investment after a second year at 7%?

    • $5724.50
    interest compound

  • How much is the $5000 investment after three years at 7% per year?

    • $6123.62
    interest compound

  • What does the formula \(A=5000\times(1.07)\) represent in this context?

    • The amount \(A\) after increasing \(5000\) by 7% (one year at 7% interest).
    formula interest

  • What is the answer for 1a?

    0.12

    answers nelsonnet

  • What is the answer for 1g?

    0.031

    answers nelsonnet

  • What is the answer for 2a?

    $14.40

    answers nelsonnet

  • What is the answer for 2g?

    74c

    answers nelsonnet

  • What is the answer for 3a?

    $90.85

    answers nelsonnet

  • What is the answer for 3g?

    $82.94

    answers nelsonnet

  • What is the total listed as answer 7?

    $84 944.65

    answers nelsonnet

  • What is the answer for 8a?

    1.07

    answers nelsonnet

  • What is the answer for 8b (numeric)?

    0.73

    answers nelsonnet

  • What is the answer for 8h (numeric)?

    1.22

    answers nelsonnet
Study Notes

Percentage shortcuts — concise study notes

Key idea

  • A percentage is a fraction of 100; convert to a decimal by dividing by 100.
  • Always perform percentage calculations by using decimals on a calculator for accuracy and speed.

Converting percentages

  • Rule: \(r\% = \dfrac{r}{100}\) (so 12% = \(0.12\), 150% = \(1.5\)).
  • Percent of an amount: \(r\%\ \text{of }A = \dfrac{r}{100}A\).

Increase and decrease (single-step)

  • Increase by \(r\%\): multiply by \(1+\dfrac{r}{100}\).
  • Formula: new = \(A\times\left(1+\dfrac{r}{100}\right)\).
  • Decrease by \(r\%\) (discount): multiply by \(1-\dfrac{r}{100}\).
  • Formula: new = \(A\times\left(1-\dfrac{r}{100}\right)\).

Compound (repeated) percentage change — growth/decay

  • For repeated equal changes (e.g., interest each year): \(A = P(1+r)^n\), where \(r\) is the decimal rate per period.
  • Example: principal \(P=5000\), annual rate \(7\%\) (\(r=0.07\)), after \(n\) years: \(A=5000(1.07)^n\).

Quick mental shortcuts (common fractions)

  • 10% = divide by 10; 1% = divide by 100.
  • 5% = half of 10%.
  • 2% = 2×1%.
  • 15% = 10% + 5%.
  • 25% = quarter (divide by 4), 50% = half.

Worked examples from the worksheet

  • Example: 12% of \(91\).
  • Convert: \(12\% = 0.12\).

  • Compute: \(0.12\times 91 = 10.92\), so result = \(\$10.92\).

  • Example: Increase \(64\) by 15%.

  • Multiply by \(1.15\): \(1.15\times 64 = 73.60\), so new amount = \(\$73.60\).

  • Example: Decrease \(45\) by 10%.

  • Multiply by \(0.90\): \(0.9\times 45 = 40.50\), so sale price = \(\$40.50\).

Practical problems (methods + answers)

  • Commission: Georgia earns 5% on sales of kitchenware. For sales \(8750\):

  • Compute \(0.05\times 8750 = 437.50\). (Earnings = \(\$437.50\).)

  • Salary increase: \(78\,290\) raised by \(8.5\%\):

  • New salary \(=78\,290\times 1.085 = 84\,944.65\).

  • Savings with annual interest \(7\%\), principal \(5000\):

  • After 1 year: \(5000\times 1.07 = 5350\).
  • After 2 years: \(5000\times 1.07^2 = 5724.50\).
  • After 3 years: \(5000\times 1.07^3 \approx 6125.22\).

Tips for accuracy and checking

  • Always convert percent to decimal before multiplying (avoid computing 12\% as 12 on the calculator).
  • For increases/decreases, check by reversing the operation: decreasing the increased value by the same percent does not return the original (except trivial cases).
  • Round money answers to two decimal places unless instructed otherwise.

Common mistakes to avoid

  • Using \(r\) (not \(r\%\)) in formulas: use decimal \(r\) (e.g., \(8.5\% = 0.085\)) when applying \(1+r\).
  • Treating percent change as additive across sequential percentage changes — use multiplication (compound) instead.

Summary practice (how to solve any percent question)

  1. Convert percentage to decimal: \(r\% \to r/100\).
  2. Decide the multiplier: \(r/100\) for "of", \(1+r/100\) to increase, \(1-r/100\) to decrease.
  3. Multiply by the original value and round appropriately.