Basic Percentage Calculations- Math Fundamentals Tutorial

What Percentages Actually Are

A percentage is just a fraction out of 100. That's it. 45% means 45 out of every 100 units. You're not learning rocket science here.

The symbol % is shorthand for "divided by 100." So when you see 25%, read it as 25/100 or 0.25. This single insight makes every percentage calculation easier.

The Three Percentage Calculations You Need to Know

Every percentage problem in existence fits into one of these three categories. Learn them, and you're covered.

1. Finding X% of a Number

This is the most common calculation. "What is 20% of 150?"

Formula: (Percentage ÷ 100) × Number

Example: 20% of 150 = (20 ÷ 100) × 150 = 0.20 × 150 = 30

2. Finding What Percent One Number Is of Another

This answers: "30 is what percent of 150?"

Formula: (Part ÷ Whole) × 100

Example: (30 ÷ 150) × 100 = 0.20 × 100 = 20%

3. Finding the Whole When You Know the Part and Percentage

This answers: "30 is 20% of what number?"

Formula: Part ÷ (Percentage ÷ 100)

Example: 30 ÷ 0.20 = 150

Quick Mental Math Tricks

You don't always need a calculator. These shortcuts work fast.

• 10% of any number: Move the decimal one place left. 10% of 240 = 24
• 50% of any number: Cut it in half. 50% of 88 = 44
• 25% of any number: Divide by 4. 25% of 80 = 20
• 1% of any number: Move decimal two places left. 1% of 350 = 3.5
• Finding 5%: Find 10%, then halve it. 5% of 60 = 6 ÷ 2 = 3

Chain these together for more complex percentages. 15%? That's 10% plus 5%. 30%? That's three times 10%.

Common Mistakes That Ruin Your Answers

• Forgetting to divide the percentage by 100 before multiplying. 30% × 50 is not 30 × 50. It is 0.30 × 50.
• Mixing up which number is the part and which is the whole in percentage-of problems. The whole is what comes after "of."
• Rounding too early in multi-step problems. Keep full precision until the final answer.

The Three Calculations Side by Side

How to Solve Percentage Problems Step by Step

Here's the process that works every time.

Step 1: Identify What You're Looking For

Ask yourself: Do I need a part, a percentage, or the original whole number?

Step 2: Plug Into the Right Formula

Use the table above. Pick the formula that matches your situation.

Step 3: Do the Math

Convert the percentage to decimal form first. Then multiply or divide as needed.

Step 4: Check Your Work

Does 30 being 20% of 150 make sense? Yes. Is 30 roughly 1/5 of 150? Yes. Does 20% equal 1/5? Yes.

Where You'll Actually Use This

• Shopping: 30% off a $90 jacket. 0.30 × 90 = $27 savings.
• Tips: 20% tip on an $85 dinner. 0.20 × 85 = $17.
• Test scores: Got 42 out of 56 questions right. (42 ÷ 56) × 100 = 75%.
• Interest rates: 5% annual interest on $2000. Year one = $100.
• Sales commissions: You earn 12% on $5,000 in sales. 0.12 × 5000 = $600.

These aren't classroom exercises. They're everyday math you encounter constantly.