Percent and Proportional Reasoning

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

Concept Review

Finding Percent of a Number: The Shopping Cart Challenge

You walk into your favorite store and see a huge sign: "25% OFF EVERYTHING!" Your eyes land on those sneakers you've been wanting — they're $80. But here's the question that stumps most shoppers: How much money will you actually save?

Finding the percent of a number is like being a detective with a calculator. You're hunting for a piece of the whole — but that piece is described as a percentage instead of a fraction.

The Percent Formula: Your Mathematical GPS

Every percent problem follows the same roadmap:

Percent × Whole Number = Part

(But first, convert the percent to a decimal!)

Let's solve that sneaker problem step by step. We want to find 25% of $80:

Convert percent to decimal: 25% = 25 ÷ 100 = 0.25

Multiply: 0.25 × $80 = $20

Answer: You save $20! The sneakers cost $60.

🔑 Key Insight

Here's something that might surprise you: Finding 25% of a number is exactly the same as finding ¼ of that number! That's because 25% = 25/100 = ¼. So 25% of $80 = ¼ × $80 = $80 ÷ 4 = $20. Percents and fractions are secret twins!

The Three Methods Toolbox

You can find 15% of 200 using any of these approaches:

Decimal Method

0.15 × 200 = 30

Fraction Method

15/100 × 200 = 30

Mental Math

10% = 20, so 15% = 20 + 10 = 30

Whether you're calculating tips at restaurants, figuring out test scores, or hunting for the best deals during sales, you're using this same fundamental skill. The numbers change, but the process stays exactly the same.

Key Takeaway

Remember those $80 sneakers? Finding the percent of a number turned a confusing store sign into concrete savings. Master this skill, and you'll never wonder "How much is that discount really worth?" again. You'll be the calculator-free shopper who knows the real deal!

Sample questions

1. What is 25% of 80?

✓ 20

○ 25

○ 30

○ 40

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

2. Find 60% of 45.

○ 18

✓ 27

○ 30

○ 36

Answer: 27 — 60% = 0.6, so 0.6 × 45 = 27.

3. What is 12.5% of 64?

○ 16

○ 24

✓ 8

○ 32

Answer: 8 — 12.5% = 1/8, so 64 ÷ 8 = 8.

Skills in this topic

Find the percent of a number
Find the whole given a part and the percent
Find what percent one number is of another
Use a proportion to solve percent problems
Solve real-world percent word problems

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