Percents - Sixth Grade

Complete Notes & Formulas

1. What is a Percent?

Definition

Percent means "OUT OF 100"

% = per 100

Latin: "per centum" = by the hundred

Basic Formula

n% = n/100

Examples

• 50% = 50 out of 100 = 50/100 = 1/2

• 25% = 25 out of 100 = 25/100 = 1/4

• 100% = 100 out of 100 = the whole thing

• 10% = 10 out of 100 = 10/100 = 1/10

Remember: The % symbol is like a shortcut for "divide by 100"!

2. Benchmark Percents

Common Benchmark Percents to Memorize

Percent	Fraction	Decimal	Meaning
10%	1/10	0.1	One tenth
20%	1/5	0.2	One fifth
25%	1/4	0.25	One quarter
33⅓%	1/3	0.333...	One third
50%	1/2	0.5	One half
75%	3/4	0.75	Three quarters
100%	1/1	1.0	The whole

Visual Strip Model Example

100% Bar (10 equal parts = 10% each)

3. Converting Fractions to Percents

Method 1: Divide and Multiply

Step 1: Divide numerator by denominator

Step 2: Multiply by 100

Step 3: Add % symbol

Formula

Fraction → Percent: (Numerator ÷ Denominator) × 100%

Example: Convert 3/4 to percent

Step 1: 3 ÷ 4 = 0.75

Step 2: 0.75 × 100 = 75

Step 3: Add % symbol

Answer: 75%

Method 2: Equivalent Fraction with Denominator 100

Example: Convert 2/5 to percent

2/5 = ?/100

5 × 20 = 100, so multiply numerator by 20

2 × 20 = 40

2/5 = 40/100 = 40%

Answer: 40%

4. Converting Decimals to Percents

Quick Rule

Move decimal point TWO places to the RIGHT

Add % symbol

Formula

Decimal → Percent: Decimal × 100%

Examples

Example 1: 0.45 → Move decimal right 2 places → 45%

Example 2: 0.8 → 0.80 → Move decimal right 2 places → 80%

Example 3: 1.25 → Move decimal right 2 places → 125%

Example 4: 0.03 → Move decimal right 2 places → 3%

5. Converting Percents to Fractions

Steps

Step 1: Write the percent as numerator

Step 2: Write 100 as denominator

Step 3: Simplify the fraction

Formula

Percent → Fraction: n% = n/100 (then simplify)

Examples

Example 1: Convert 60% to fraction

60% = 60/100

Simplify: 60÷20 / 100÷20 = 3/5

Answer: 3/5

Example 2: Convert 75% to fraction

75% = 75/100

Simplify: 75÷25 / 100÷25 = 3/4

Answer: 3/4

6. Converting Percents to Decimals

Quick Rule

Move decimal point TWO places to the LEFT

Remove % symbol

Formula

Percent → Decimal: n% ÷ 100

Examples

Example 1: 35% → Move decimal left 2 places → 0.35

Example 2: 8% → 08% → Move decimal left 2 places → 0.08

Example 3: 150% → Move decimal left 2 places → 1.50 or 1.5

Example 4: 5.5% → Move decimal left 2 places → 0.055

7. Comparing Percents and Fractions

Methods to Compare

Method 1: Convert both to percents and compare

Method 2: Convert both to decimals and compare

Method 3: Convert both to fractions with common denominator

Example: Compare 3/5 and 55%

Method 1: Convert to percents

3/5 = (3÷5) × 100% = 0.6 × 100% = 60%

Compare: 60% vs 55%

60% > 55%

Answer: 3/5 is greater than 55%

8. Understanding Percents with Grid Models

100-Square Grid

• A 10×10 grid has 100 squares

• Each square = 1%

• Shaded squares = the percent

• Count shaded squares to find the percent

Example: 40% on a Grid

40 squares shaded = 40%

9. Word Problems with Percents

Example 1: Comparing Test Scores

Problem: Sarah scored 85% on her math test. Tom got 4/5 correct. Who scored higher?

Step 1: Convert Tom's fraction to percent

4/5 = (4÷5) × 100% = 0.8 × 100% = 80%

Step 2: Compare

Sarah: 85% vs Tom: 80%

85% > 80%

Answer: Sarah scored higher

Example 2: Shopping Discount

Problem: A store offers 25% off. What fraction discount is this?

25% = 25/100

Simplify: 25÷25 / 100÷25 = 1/4

Answer: 1/4 discount

Quick Reference: Conversion Formulas

Conversion	Formula/Rule
Fraction → Percent	(Numerator ÷ Denominator) × 100%
Decimal → Percent	Move decimal 2 right, add %
Percent → Fraction	n/100, then simplify
Percent → Decimal	Move decimal 2 left, remove %