Understanding percentages is fundamental in math, finance, business, and daily life. One of the most common percentage calculations involves determining the percentage relationship between two values. Whether you’re figuring out a discount, calculating growth, or comparing data, mastering how to find the percentage of two values can empower you with a critical skill.
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This blog post covers everything you need to know about calculating percentages between two numbers — from basics and formulas to practical examples, applications, and common mistakes to avoid.
What Is a Percentage?
Before diving into the percentage of two values, let’s quickly recap what a percentage is.
A percentage is a way to express a number as a fraction of 100. The word “percent” literally means “per hundred.” For example:
- 50% means 50 out of 100,
- 25% means 25 out of 100,
- 120% means 120 out of 100 (which is more than the whole).
Percentages are a universal way to compare ratios or proportions, making it easier to understand parts of a whole.
Understanding Percentage Between Two Values
When you have two values, you often want to know what percentage one value is of the other. This is useful in many scenarios like:
- Calculating how much a sale price is a percentage of the original price.
- Understanding how much one number has increased or decreased relative to another.
- Comparing scores, profits, or measurements in terms of percentages.
The Basic Formula to Calculate the Percentage of Two Values
To find what percentage one value (let’s call it Value A) is of another value (Value B), you use this formula:
Percentage = (Value A ÷ Value B) × 100
Where:
- “÷” means divided by,
- “×” means multiplied by,
- The result is the percentage that Value A represents of Value B.
Explanation:
- Divide Value A by Value B to get the fraction of Value B that Value A represents.
- Multiply that fraction by 100 to convert it into a percentage.
Step-by-Step Example
Let’s say you want to find what percentage 45 is of 60.
- Value A = 45
- Value B = 60
Step 1: Divide 45 by 60:
45 ÷ 60 = 0.75
Step 2: Multiply by 100:
0.75 × 100 = 75
So, 45 is 75% of 60.
Common Use Cases
1. Discounts and Sales
If an item originally costs 80 dollars but is on sale for 60 dollars, you may want to calculate the percentage of the sale price compared to the original price.
Percentage of sale price relative to original price:
(60 ÷ 80) × 100 = 75%
So the sale price is 75% of the original price.
To find the discount percentage, subtract from 100:
100% – 75% = 25%
Hence, the item is sold at a 25% discount.
2. Exam Scores
If a student scores 72 marks out of 90, the percentage score is:
(72 ÷ 90) × 100 = 80%
So the student scored 80%.
3. Profit and Loss
If you bought a product for 150 dollars and sold it for 200 dollars, the profit percentage is calculated by:
Profit = Selling price – Cost price = 200 – 150 = 50
Profit percentage (relative to cost price):
(Profit ÷ Cost price) × 100 = (50 ÷ 150) × 100 = 33.33%
How to Calculate Percentage Increase or Decrease Between Two Values
Often, you want to know the percentage change between two values. This is a bit different from simply finding what percentage one value is of another.
Formula for Percentage Change:
Percentage Change = ((New Value – Old Value) ÷ Old Value) × 100
- Positive result = percentage increase,
- Negative result = percentage decrease.
Example:
If your salary increases from 2000 to 2500 dollars:
Percentage increase = ((2500 – 2000) ÷ 2000) × 100 = (500 ÷ 2000) × 100 = 25%
Using Percentage in Real Life Situations
Percentages help us understand proportions quickly and are used in countless areas:
- Finance: Interest rates, investment returns, inflation rates.
- Health: Body fat percentage, daily nutrient intake, medical test results.
- Education: Grades, attendance percentages.
- Business: Market shares, sales growth, profit margins.
- Everyday Shopping: Discounts, tax rates, tips.
Percentage to Decimal and Fraction Conversion
Understanding how to switch between percentages, decimals, and fractions makes math easier.
- To convert a percentage to a decimal: divide by 100.
- To convert a decimal to a percentage: multiply by 100.
- To convert a percentage to a fraction: write the percentage over 100 and simplify.
Example:
- 25% = 25/100 = 1/4 = 0.25 (decimal)
- 0.6 (decimal) = 0.6 × 100 = 60%
- 75% = 75/100 = 3/4
Tips for Accuracy in Percentage Calculations
- Always identify which value is the base or reference (denominator).
- Use a calculator for complex or large numbers to avoid errors.
- Remember to multiply by 100 after division.
- When calculating percentage change, subtract first before dividing.
- Watch out for negative values which might imply direction of change.
Frequently Asked Questions (FAQs)
Q1: What if Value B is zero?
You cannot divide by zero; this is undefined in mathematics. If Value B is zero, the percentage calculation is impossible.
Q2: How to calculate percentage difference between two numbers?
Use the formula:
Percentage Difference = (|Value A – Value B| ÷ ((Value A + Value B)/2)) × 100
This gives the relative difference compared to the average of the two values.
Q3: How to calculate percentage of a number?
To find x percent of a number n, use:
(x ÷ 100) × n
Example: 20% of 50 = (20 ÷ 100) × 50 = 10
Visual Representation: Percentage of Two Values Table
| Value A | Value B | Calculation (Value A ÷ Value B) | Percentage Result |
|---|---|---|---|
| 30 | 50 | 30 ÷ 50 = 0.6 | 60% |
| 15 | 60 | 15 ÷ 60 = 0.25 | 25% |
| 80 | 100 | 80 ÷ 100 = 0.8 | 80% |
| 200 | 400 | 200 ÷ 400 = 0.5 | 50% |
| 9 | 12 | 9 ÷ 12 = 0.75 | 75% |
How to Use Technology for Percentage Calculations
Calculators
Most basic calculators have a percentage button (%). Use it carefully to ensure you enter the correct numbers and operations.
Spreadsheets (Excel/Google Sheets)
Use formulas:
- To find percentage of two values:
= (ValueA / ValueB) * 100 - To calculate percentage increase:
= ((NewValue - OldValue) / OldValue) * 100
Example:
| Old Price | New Price | Percentage Change Formula | Result |
|---|---|---|---|
| 100 | 120 | =((B2 - A2) / A2) * 100 | 20% |
Common Mistakes in Percentage Calculations
- Mixing up which value to divide by — Always divide by the base or original value.
- Forgetting to multiply by 100 — Division gives a decimal fraction, multiply to get percentage.
- Confusing percentage increase and percentage of a value — Percentage increase looks at the difference relative to the original.
- Using percentage as a whole number — Remember 25% is 0.25 as a decimal.
- Misinterpreting percentages over 100% — Values over 100% mean more than the whole or original.
Practical Exercises to Improve Your Skills
Try these exercises:
- What percentage is 18 of 90?
- If a shirt costs 40 dollars and is sold for 30 dollars, what is the discount percentage?
- A population grew from 1500 to 1650, calculate the percentage increase.
- A student scored 48 out of 60. What is their percentage score?
Solutions:
- (18 ÷ 90) × 100 = 20%
- Discount = (40 – 30) = 10; Discount percentage = (10 ÷ 40) × 100 = 25%
- ((1650 – 1500) ÷ 1500) × 100 = 10%
- (48 ÷ 60) × 100 = 80%
Summary
- The percentage of two values is found by dividing one by the other and multiplying by 100.
- Percentages express proportions and comparisons in a simple form.
- Always identify your base value for division.
- Percentage increase or decrease measures change relative to the original.
- Avoid common mistakes by careful calculations and understanding concepts.
- Use calculators and spreadsheets to simplify computations.
- Practice regularly to master percentage calculations.
Mastering percentages opens the door to many real-world applications in finance, education, science, and daily decisions. Understanding how to calculate the percentage of two values accurately can help you make informed and confident decisions.