Finding Percentage of a Number
Finding a percentage of a number means calculating a certain part of a given number. For example, 25% of 200 means finding one-quarter of 200, which is 50.
This is one of the most useful calculations in daily life — discounts, marks, tips, tax, and interest all involve finding percentages of numbers.
What is Finding Percentage of a Number - Grade 7 Maths (Comparing Quantities)?
Formula:
x% of a number = (x/100) × number
The word “of” means multiply.
Finding Percentage of a Number Formula
Quick percentage shortcuts:
- 10% of a number = divide by 10.
- 25% of a number = divide by 4.
- 50% of a number = divide by 2.
- 1% of a number = divide by 100.
- 20% = 10% × 2. 5% = 10% ÷ 2.
Types and Properties
Types of problems:
- Direct calculation: Find 35% of 600.
- Finding the whole: If 40% of a number is 80, find the number.
- Real-life applications: Discount, tax, marks scored.
Solved Examples
Example 1: Basic Calculation
Problem: Find 15% of 300.
Solution:
- 15% of 300 = (15/100) × 300 = 15 × 3 = 45
Answer: 45.
Example 2: Discount Problem
Problem: A shirt costs ₹800. A 20% discount is offered. Find the discount amount and selling price.
Solution:
- Discount = 20% of 800 = (20/100) × 800 = ₹160
- Selling price = 800 − 160 = ₹640
Answer: Discount = ₹160, Selling price = ₹640.
Example 3: Finding the Whole
Problem: 30% of a number is 45. Find the number.
Solution:
- 30% × N = 45
- N = 45 × 100/30 = 4500/30 = 150
Answer: The number is 150.
Example 4: Marks Problem
Problem: Riya scored 72 out of 80 in Maths. Find her percentage.
Solution:
- Percentage = (72/80) × 100 = 90%
Answer: 90%.
Real-World Applications
Real-world uses:
- Shopping: Calculating discounts (“30% off”).
- Exams: Converting marks to percentage.
- Tax: GST is a percentage of the price.
- Banking: Interest rates are percentages.
Key Points to Remember
- x% of a number = (x/100) × number.
- 10% of any number = number ÷ 10.
- To find the whole from a percentage: number = (given value × 100) ÷ percentage.
- Percentage = (part/whole) × 100.
Practice Problems
- Find 45% of 500.
- Find 12.5% of 240.
- If 60% of a number is 90, find the number.
- A book costs ₹350 with 10% discount. Find the selling price.
Frequently Asked Questions
Q1. How do you find x% of a number?
Multiply the number by x and divide by 100: x% of N = (x/100) × N.
Q2. What is a quick way to find 10%?
Divide the number by 10. For example, 10% of 450 = 45.
Q3. How do you find the original number if percentage is given?
If x% of N = value, then N = (value × 100) ÷ x. For example, if 25% of N = 50, then N = 50 × 100 ÷ 25 = 200.
Related Topics
- Introduction to Percentage
- Percentage Increase and Decrease
- Profit and Loss
- Discount Calculation
- Simple Interest
- Compound Interest
- Applications of Compound Interest
- Sales Tax and VAT
- Growth and Decay
- Converting Between %, Fraction and Decimal
- Word Problems on Comparing Quantities
- Word Problems on Profit and Loss
- Converting Percentage to Fraction
- Compound Interest (Half-Yearly & Quarterly)
