Find a percent of a number.

SECTION 1

The Story Behind Percents

Long ago, people needed a way to compare parts of a whole easily. Percent comes from Latin words meaning "per hundred." It helps with things like sharing food or trading goods. Today, you use it for sales and grades!

3000 BC

Ancient Fractions

Egyptians used fractions like 1/10 to mean 10 parts out of 100.

1425

Percent Symbol Born

Italian merchants created the % sign for quick math in business.

1786

Science Adopts It

Chemists used percents to measure elements in compounds.

Today

Everyday Tool

You see percents in games, shopping, and school scores.

Percents solved the problem of comparing different sizes quickly. Now you can find any part of a number! Get ready to learn how.

SECTION 2

Core Principles of Percents

A percent is a part out of 100. For example, 25% means 25 out of 100. Think of it like slices of a pizza cut into 100 pieces.

Percent as Fraction

50% = 50/100 = 1/2. Always simplify!

Decimal Form

25% = 0.25. Drop the % and divide by 100.

Key Formula

Part = (percent ÷ 100) × whole number.

Benchmark Percents

10% = move decimal one left. 50% = half.

🍕 Pizza Party Analogy

Finding 30% of 10 pizzas is like taking 3 slices if each pizza is 10 slices. Easy and yummy math!

SECTION 3

See Percents in Action

This grid shows 100 squares. The shaded ones are 25%, or 25 squares. See how percents fill parts of the whole?

Look at the diagram above. It makes percents easy to see, like coloring in graph paper. Visuals help you understand before calculating.You can always picture it this way!

SECTION 4

The Math Formula

To find a percent of a number, use this simple rule. First, change the percent to a decimal by dividing by 100. Then multiply by the whole number.

FIND THE PART

part = (percent ÷ 100) × whole

percent: like 25 (no % sign). whole: the total number, like 200.

EXAMPLE DECIMAL

25% = 25 ÷ 100 = 0.25

Move decimal two places left: 25.0% → 0.25.

These steps work every time. Practice them, and you'll get faster. You're doing great!

SECTION 5

Step-by-Step Breakdown

Bar shows $50 price with 20% ($10) discount. Arrow points to savings section.

The diagram breaks down a real shopping example. See how 20% fills part of the bar? This model works for tips or taxes too.Draw your own bars to practice!

SECTION 6

Worked Example: 35% of 200

Let's find 35% of 200 step by step. This is like calculating your game score if you got 35% boosts on 200 points.

Solve It!

Step 1: Convert Percent35% = 35 ÷ 100 = 0.35

0.35

Step 2: Multiply0.35 × 200 = 70 (35 × 2 = 70)

Great job following along! 35% of 200 is 70. You can do this on any problem now.

SECTION 7

Strengths and Common Mistakes

Quick ways to compute without paper.

Method	Strength	Watch Out
Decimal Way	Fast for any percent.	Don't forget ÷100.
10% Trick	Easy: move decimal left once.	Only works for 10%.
50% Trick	Just divide by 2.	Great for even numbers.

✦ KEY TAKEAWAY

Percents are strong for real life, like sports stats. Use tricks to save time on tests!

SECTION 8

Beyond Basics

Finding a percent is step one. Next, you'll solve 'what percent' or increase/decrease problems.

This Lesson	Advanced
Part = p% × whole	Percent change = (new − old)/old × 100%
Simple discounts	Compound interest

Master this, then tackle taxes and growth. You're building a strong math toolbox!

SECTION 9

Practice Problems

PROBLEM 1 — CONCEPTUAL

What does 40% mean? A) 40 out of 40 B) 40 out of 100 C) 4 out of 10 D) 400 out of 1000 E) 40 out of 400

PROBLEM 2 — BASIC CALCULATION

What is 10% of 50? A) 5 B) 10 C) 50 D) 500 E) 0.5

PROBLEM 3 — INTERMEDIATE

Find 25% of 80. A) 10 B) 20 C) 20 D) 30 E) 40

PROBLEM 4 — APPLIED

You buy a $60 game on 30% sale. Savings? A) $12 B) $18 C) $30 D) $42 E) $90

PROBLEM 5 — CRITICAL THINKING

40% of a number is 24. What is 10% of it? A) 4 B) 6 C) 10 D) 24 E) 60

SUMMARY

Quick Review

You can now find a percent of a number using part = (p/100) × whole. Visualize with grids or bars for intuition.

Practice benchmarks like 10%, 25%, 50%. You're ready for SSAT success! Keep practicing—you've got this!