Percentage Chapter Notes | Mathematics Class 6 ICSE PDF Download

Percentages are a fun and practical way to understand how parts relate to a whole, like figuring out how much of your pocket money you spent on snacks or what portion of a pizza you ate! The concept comes from the Latin term "per centum," meaning "by the hundred," making it a simple way to express numbers out of 100. Whether you're calculating discounts, test scores, or even how many marbles in a jar are your favourite colour, percentages make it easy to compare and understand quantities. Let’s dive into this exciting world of percentages with clear steps and examples to make it super easy to grasp!

Percentage

• Percentage means "out of hundred" or "for every hundred."
• It is represented by the symbol %.
• A percentage shows how many parts out of 100 something represents.
• Percentages can be written as fractions with a denominator of 100.
• Steps to understand percentage:
  • Take a quantity and compare it to 100.
  • Express the quantity as a fraction with 100 as the denominator.
  • Add the % symbol to show it’s a percentage.
• Formula: A% = A/100
• Example: If 85 out of 100 marbles are green, the percentage of green marbles is:
  85/100 = 85% (read as 85 percent).

Expressing One Quantity as a Percentage of the Other

• This concept helps compare two quantities by expressing one as a percentage of the other.
• Steps to express x as a percentage of y:
  • Ensure x and y are in the same units (if not, convert them).
  • Divide x by y (i.e., x/y).
  • Multiply the result by 100 and add the % symbol.
• Formula:Percentage = (x/y) × 100%
• Example 1: Find 30 m as a percentage of 600 m.
  Step 1: Both are in meters, so no conversion needed.
  Step 2: Divide 30 by 600: 30/600 = 0.05.
  Step 3: Multiply by 100: 0.05 × 100 = 5%.
  So, 30 m is 5% of 600 m.
• Example 2: What is ₹50 as a percentage of ₹250?
  Step 1: Divide 50 by 250: 50/250 = 0.2.
  Step 2: Multiply by 100: 0.2 × 100 = 20%.
  So, ₹50 is 20% of ₹250.

Finding Percentage of a Given Quantity

• This is about finding a certain percentage of a given number.
• Steps to find A% of a number:
  • Convert the percentage to a fraction by dividing by 100 (A% = A/100).
  • Multiply this fraction by the given number.
• Formula:A% of N = (A/100) × N
• Example 1: Find 35% of ₹600.
  Step 1: Convert 35% to a fraction: 35/100.
  Step 2: Multiply by 600: (35/100) × 600 = 210.
  So, 35% of ₹600 is ₹210.
• Example 2: Out of 110 pens, 40% are blue. Find the number of blue and red pens.
  Step 1: Find blue pens: 40% of 110 = (40/100) × 110 = 44.
  Step 2: Find red pens: Total pens - blue pens = 110 - 44 = 66.
  Alternate Method: Red pens = (100 - 40)% of 110 = 60% of 110 = (60/100) × 110 = 66.
  So, there are 44 blue pens and 66 red pens.

Finding the Number from its Given Percentage

• This involves finding the original number when a percentage of it is given.
• Steps to find the number when A% of it is N:
  • Convert the percentage to a fraction: A% = A/100.
  • Divide the given number (N) by this fraction.
• Formula: Number = N ÷ (A/100) = (N × 100)/A
• Example 1: If 25% of a number is 25, find the number.
  Step 1: Convert 25% to a fraction: 25/100.
  Step 2: Divide 25 by (25/100): 25 ÷ (25/100) = 25 × (100/25) = 100.
  So, the number is 100.
• Example 2: If 13½ % of a number is 54, find the number.
  Step 1: Convert 13½ % to a fraction: 13½ % = (27/2)% = 27/(2 × 100) = 27/200.
  Step 2: Divide 54 by (27/200): 54 ÷ (27/200) = 54 × (200/27) = 400.
  So, the number is 400.

Applications of Percentage

• Percentages are used in real-life situations like calculating salaries, scores, or quantities.
• Steps to apply percentages:
  • Identify the percentage and the quantity it relates to.
  • Use the appropriate formula (e.g., finding percentage, finding number, etc.).
  • Calculate step-by-step to find the answer.
• Example 1: Rohan’s salary is 3% more than Rahul’s salary of ₹17,000. Find Rohan’s salary.
  Step 1: Find 3% of Rahul’s salary: (3/100) × 17,000 = ₹510.
  Step 2: Add to Rahul’s salary: 17,000 + 510 = ₹17,510.
  So, Rohan’s salary is ₹17,510.
• Example 2: A team needs 60% of a given score to win. They score 115 runs but lose by 5 runs. Find the given score.
  Step 1: Required score to win = 115 + 5 = 120 runs.
  Step 2: 60% of given score = 120, so given score = 120 ÷ (60/100) = 120 × (100/60) = 200.
  So, the given score is 200 runs.
• Example 3: In a basket of 120 apples, 24 are rotten. Find the percentage of edible apples.
  Step 1: Eatable apples = 120 - 24 = 96.
  Step 2: Percentage of eatable apples = (96/120) × 100% = 80%.
  Alternate Method: Rotten apples = (24/120) × 100% = 20%.
  Eatable apples = (100 - 20)% = 80%.
  So, 80% of the apples are edible.