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SSAT Middle Level: Quantitative • Fractions, Decimals, and Percents

Find a percent of a number.

Master calculating discounts, tips, and scores with this key skill.

Explore the lesson 4 min read
SSAT Middle Level illustration with a test notebook, quantitative function, and reading book
Inside this lesson 10 sections 5 questions 6 figures

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.

1

Percent as Fraction

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

Decimal Form

25% = 0.25. Drop the % and divide by 100.
3

Key Formula

Part = (percent ÷ 100) × whole number.
4

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

See Percents in Action A 10 × 10 grid represents 100% — each small square is 1% TOTAL SQUARES 100 SHADED SQUARES 25 PERCENT SHADED 25% 25 ÷ 100 = 0.25 0.25 = 25% = Shaded (1%) = Unshaded (1%) 10 10 5 25 💡 Each square = 1 out of 100 = 1%
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)×wholepart = (percent ÷ 100) × whole

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

EXAMPLE DECIMAL

2525% = 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

Finding 20% of $50 Visualizing a percent discount on a number line Total Price Bar $10 20% off $40 remaining to pay $0 $10 $50 20% 80% Step-by-Step Breakdown 1 Convert percent to decimal 20% = 0.20 2 Multiply to find the discount 0.20 × $50 = $10 3 Subtract to find amount remaining $50 − $10 = $40 You pay $40
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!

  1. 1

    Step 1: Convert Percent

    35% = 35 ÷ 100 = 0.35
    0.35
  2. 2

    Step 2: Multiply

    0.35 × 200 = 70 (35 × 2 = 70)
    70

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

SECTION 7

Strengths and Common Mistakes

MethodStrengthWatch Out
Decimal WayFast for any percent.Don't forget ÷100.
10% TrickEasy: move decimal left once.Only works for 10%.
50% TrickJust divide by 2.Great for even numbers.

Quick ways to compute without paper.

★

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 LessonAdvanced
Part = p% × wholePercent change = (new − old)/old × 100%
Simple discountsCompound interest

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

SECTION 9

Practice Problems

Question 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
Show answer
B is correct because percent means parts per 100. A is wrong (that's 100%). C is 40% but not the definition. D and E use larger numbers but equal 4% and 10%.

Question 2: BASIC CALCULATION

What is 10% of 50? A) 5 B) 10 C) 50 D) 500 E) 0.5
Show answer
A is correct: 10% = 0.1, 0.1 × 50 = 5. B is 20%. C is 100%. D too big (1000%). E is 1%.

Question 3: INTERMEDIATE

Find 25% of 80. A) 10 B) 20 C) 20 D) 30 E) 40
Show answer
B is correct: 25% = 0.25, 0.25 × 80 = 20 (quarter of 80). A is 12.5%. C wrong label. D=37.5%, E=50%.

Question 4: APPLIED

You buy a $60 game on 30% sale. Savings? A) $12 B) $18 C) $30 D) $42 E) $90
Show answer
B is correct: 0.30 × 60 = 18. A=20%, C=50%, D=70% (too much), E=150% (impossible).

Question 5: CRITICAL THINKING

40% of a number is 24. What is 10% of it? A) 4 B) 6 C) 10 D) 24 E) 60
Show answer
B is correct: Whole=24/(0.4)=60, 10%=6. A too small, C=16.7%, D=40%, E=100%.

SUMMARY

Quick Review

Summary

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!

Varsity Tutors • SSAT Middle Level • Find a percent of a number.