percentages

• What does the term "per-cent" mean?

  "Per-cent" means " ÷ 100" or "out of 100"
• How can a percentage be viewed in relation to fractions?

  A percentage is a standardized way of expressing a fraction by always expressing it "out of 100"
• What is the percentage equivalent of the fraction $\frac{1}{2}$?


  50%
• What is the percentage equivalent of the fraction $\frac{2}{5}$?


  40%
• What is the percentage equivalent of the fraction $\frac{3}{4}$?


  75%
• How can you calculate basic percentages of amounts without a calculator?

  • 50% = divide by 2
  • 25% = divide by 4
  • 20% = divide by 5
  • 10% = divide by 10
  • 5% = find 10% then divide by 2
  • 1% = divide by 100
• How can you express 17% using simpler percentages?

  17% can be expressed as 10% + 5% + 2 x 1%
• How do you find 23% of 40 using Method 1?

  Divide 40 by 100 to get 0.4, then multiply by 23 to get 9.2
• How do you find 23% of 40 using Method 2?


  Multiply 40 by the decimal equivalent of 23%, which is 0.23, to get 9.2
• How do you find "A as a percentage of B"?

  Calculate A ÷ B to get a decimal, then multiply by 100
• How do you express 26 as a percentage of 40?

  First do 26 ÷ 40 = 0.65, then multiply by 100 to get 65%
• How do you express an agent's commission as a percentage of earnings?

  Divide the commission by the earnings and multiply by 100
• How do you increase or decrease an amount by a percentage?

  • Identify "before" and "after" quantities
  • For increase: Add the percentage to 100
  • For decrease: Subtract the percentage from 100
  • Use multipliers for calculations

  
• What is the multiplier for a percentage increase of 25%?

  The multiplier is 1 + 0.25 = 1.25
• What is the multiplier for a percentage decrease of 25%?

  The multiplier is 1 - 0.25 = 0.75
• How are the "before" and "after" amounts related in percentage changes?

  They are related by the formula "before" × p = "after", where p is the multiplier
• How do you find the percentage change using the formula?

  Percentage change = (after - before) ÷ before × 100

  
• What does a positive value indicate in percentage change?

  A positive value indicates a percentage increase
• What does a negative value indicate in percentage change?

  A negative value indicates a percentage decrease
• What is the formula for percentage profit or loss?

  • Percentage profit (or loss) = (selling price - cost price) ÷ cost price × 100
  • Identify profit or loss:
  • Cost price < selling price = profit
  • Cost price > selling price = loss

  
• How do you increase £200 by 18%?

  Multiply £200 by 1.18 to get £236
• How do you decrease 500 kg by 23%?

  Multiply 500 by 0.77 to get 385 kg
• How do you describe a percentage change when the number of students in a school goes from 250 to 310?

  The percentage change is calculated as a positive value indicating a percentage increase of 24%

  
• What is a reverse percentage question?

  • A question where the value after a percentage change is given
  • The goal is to find the value before the change
• How do you find the "before" quantity in a reverse percentage question?

  Divide the "after" quantity by the multiplier, p
• What does a percentage increase of 4% mean in terms of the multiplier?

  A percentage increase of 4% means p = 1 + 0.04 = 1.04
• What does a percentage decrease of 5% mean in terms of the multiplier?

  A percentage decrease of 5% means p = 1 - 0.05 = 0.95
• How do you find Jennie's pay before a 5% increase if she is now paid £31,500?

  Divide £31,500 by 1.05 to find she was paid £30,000 before the pay rise
• What was Jennie's pay before the pay rise?

  £30,000