Solving Percentage Problems

Free sample questions, a clear explanation, and 5 practice skills with an AI tutor that guides without giving the answer away.

Concept Review

Finding a Percent of a Quantity: The Discount Detective

You walk into your favorite store and see a sign: "30% off everything!" Your eyes land on a $60 jacket. But here's the mystery — exactly how much money will you save? Welcome to the world of finding a percent of a quantity, where you become a discount detective.

A percent is just a fancy way of saying "parts out of 100." When we find 30% of something, we're really asking: "If I broke this into 100 equal pieces, what would 30 of those pieces be worth?"

The Percent Formula: Your Mathematical Toolbox

Finding a percent of a quantity follows one reliable pattern:

Percent × Quantity = Answer

(But remember: convert the percent to a decimal first!)

Let's solve that jacket mystery step by step:

Step 1 Convert 30% to a decimal: 30% = 0.30

Step 2 Multiply: 0.30 × $60 = letter: 'E', title: 'Solving Percentage Problems', concept: 8

Step 3 You save letter: 'E', title: 'Solving Percentage Problems', concept: 8! The jacket costs $60 - letter: 'E', title: 'Solving Percentage Problems', concept: 8 = $42

The "Move the Decimal" Trick

Here's a mind-bending shortcut: To convert any percent to a decimal, just move the decimal point two places to the left.

75%→ 0.75
8%→ 0.08
125%→ 1.25

Why does this work? Because percent literally means "per hundred," and dividing by 100 moves the decimal two places left!

Beyond Shopping: Percents Everywhere

This same process works for any situation. What's 15% of a $40 restaurant bill for the tip? 0.15 × $40 = $6. What about 85% of your class of 20 students who passed the test? 0.85 × 20 = 17 students.

🔑 Key Takeaway

That $60 jacket with a 30% discount? You're not just saving money — you're using the same mathematical thinking that helps calculate tips, test scores, population growth, and countless real-world scenarios. Every percent problem is just multiplication in disguise.

Sample questions

1. What is 25% of 80?

✓ 20

○ 25

○ 30

○ 40

Answer: 20 — 25% = 1/4, so 80 ÷ 4 = 20.

2. Find 40% of 90.

○ 36

○ 40

○ 45

✓ 36? 0.4 × 90 = 36

○ 36

Answer: 36? 0.4 × 90 = 36 — 40% = 0.4, so 0.4 × 90 = 36.

3. What is 15% of 200?

○ 30

○ 15

○ 20

✓ 30? 0.15 × 200 = 30

○ 30

Answer: 30? 0.15 × 200 = 30 — 0.15 × 200 = 30.

Skills in this topic

Find a percent of a given quantity (e.g., 30% of 50)
Find the whole given a part and the percent
Find the percent given the part and the whole
Solve real-world problems involving discounts and markups
Solve real-world problems involving tips and sales tax

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