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Class 5 Maths Adventure

Percentages

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🔵Understanding Percent as "Out of 100"

What is Percent?

Percent means "per hundred" (cent = 100 in Latin). The symbol % means "out of 100."

50% = 50 out of 100 = 50/100 = ½
25% = 25 out of 100 = 25/100 = ¼
100% = all of it = 1 whole

Real-Life Examples:

"I got 90% on my test" = answered 90 out of 100 correctly
"This shirt is 20% off" = save 20 for every100
"75% of students like pizza" = 75 out of 100 students

PERCENT AS A 100-GRID (10×10):

    0%                              100%
    ┌─────────────────────────────────┐
    │                                 │
    │    25% shaded (25 squares)      │
    │    ░░░░░░░░░░░░░░░░░░░░░░░      │
    │    ░░░░░░░░░░░░░░░░░░░░░░░      │
    │                                 │
    │    50% shaded (50 squares)      │
    │    ░░░░░░░░░░░░░░░░░░░░░░░░░░░░ │
    │    ░░░░░░░░░░░░░░░░░░░░░░░░░░░░ │
    │                                 │
    │    75% shaded (75 squares)      │
    │    ░░░░░░░░░░░░░░░░░░░░░░░░░░░░ │
    │    ░░░░░░░░░░░░░░░░░░░░░░░░░░░░ │
    │    ░░░░░░░░░░░░░░░░░░░░░░░░░░░░ │
    └─────────────────────────────────┘

    100% = all 100 squares shaded


PERCENT PIE CHARTS:

    25% (¼)        50% (½)        75% (¾)
      ┌─┐            ┌─┐            ┌─┐
     ╱   ╲         ╱   ╲         ╱   ╲
    │  ░  │       │░░░░░│       │░░░░░│
    │ ░░  │       │░░░░░│       │░░░░░│
     ╲   ╱         ╲   ╱         ╲   ╱
      └─┘            └─┘            └─┘

👀 See a worked example

What percent is shaded if 45 out of 100 squares are shaded?

Percent = (part/whole) × 100
Part = 45, Whole = 100
45/100 × 100 = 45%
Answer: 45%

Write 60% as a fraction in simplest form

60% = 60/100
Simplify: divide both by 20 → (3)/(5)
Answer: (3)/(5)

What is 30% of 50?

Method 1: 30% = 30/100 = 0.3, 0.3 × 50 = 15
Method 2: 30% of 50 = (30/100) × 50 = 1500/100 = 15
Answer: 15

🤖 Vidi's Key Points

% means "out of 100"
To convert % to fraction: put over 100, simplify
To convert % to decimal: divide by 100
To find % of a number: multiply by the decimal or fraction

🟢Converting Between Fractions, Decimals, Percents

The Conversion Triangle:

        PERCENT
           %
        ↗     ↖
       /       \
    FRACTION   DECIMAL

Conversion Rules:

From	To	Method
Percent	Fraction	Put over 100, simplify
Percent	Decimal	Divide by 100
Fraction	Decimal	Divide numerator by denominator
Decimal	Percent	Multiply by 100
Decimal	Fraction	Write decimal as fraction, simplify
Fraction	Percent	Convert to decimal first, then ×100

CONVERSION FLOWCHART:

    FRACTION ──────divide───→ DECIMAL
         ↑                        │
         │                        │
      simplify                multiply
         │                        │
         │                        ↓
    ┌───┴───────────────────    PERCENT
    │   put over 100              │
    │                        divide by 100
    │                        multiply by 100
    ↓                              │
    DECIMAL ←─────write as fraction──┘


COMMON EQUIVALENTS (MEMORIZE!):

    Fraction    Decimal    Percent
    ───────────────────────────────
    ½          0.5        50%
    ¼          0.25       25%
    ¾          0.75       75%
    ⅕          0.2        20%
    ⅖          0.4        40%
    ⅗          0.6        60%
    ⅘          0.8        80%
    ⅓          0.333...   33⅓%
    ⅔          0.666...   66⅔%
    ⅛          0.125      12.5%
    ⅜          0.375      37.5%
    ⅝          0.625      62.5%
    ⅞          0.875      87.5%

👀 See a worked example

Convert (3)/(5) to percent

Method A: (3)/(5) = 0.6, 0.6 × 100 = 60%
Method B: (3)/(5) = 60/100 = 60%
Answer: 60%

Convert 0.375 to fraction and percent

Fraction: 0.375 = 375/1000 = simplify divide 125 → (3)/(8)
Percent: 0.375 × 100 = 37.5%
Answer: (3)/(8) and 37.5%

Convert 120% to decimal and fraction

Decimal: 120% ÷ 100 = 1.2
Fraction: 120/100 = 12/10 = 6/5 = 1⅕
Answer: 1.2 and 6/5

🤖 Vidi's Key Points

Decimal → Percent: multiply by 100 (move decimal 2 places right)
Percent → Decimal: divide by 100 (move decimal 2 places left)
Fraction → Decimal: numerator ÷ denominator
Fraction → Percent: numerator ÷ denominator × 100
Memorize common conversions (½=50%, ¼=25%, etc.)

🟣Finding Percent of a Quantity

Three Methods to Find Percent of a Number:

Method 1: Convert to Decimal

20% of 60 = 0.2 × 60 = 12

Method 2: Use Fraction

20% = (1)/(5), so (1)/(5) of 60 = 12

Method 3: Use Proportion

20/100 = x/60
Cross multiply: 100x = 1200, x = 12

Real-World Applications:

Sales tax: 8% tax on 50 = 0.08 × 50 =4
Tips: 15% tip on 40 = 0.15 × 40 =6
Discounts: 25% off 80 = 0.25 × 80 =20 saved

FINDING 20% OF 60 (VISUAL):

 0% 20% 100%
 ├──────────────────────┼──────────────────────┤
 │ │ │
 0 12 60
 
 20% of 60 = 12


PERCENT OF A NUMBER - BAR MODEL:

 60 total (100%)
 ┌────┬────┬────┬────┬────┐
 │ 12 │ 12 │ 12 │ 12 │ 12 │
 └────┴────┴────┴────┴────┘
 20% 20% 20% 20% 20%
 
 Each 20% = 12


DISCOUNT CALCULATION:

 Original Price: 80 (100%)
 
 25% Discount = 20 saved
 ┌─────────────┬─────────────┐
 │ 20 saved │ 60 pay │
 │ (25%) │ (75%) │
 └─────────────┴─────────────┘
 
 Final Price: 60

👀 See a worked example

Find 15% of 200

Decimal: 0.15 × 200 = 30
Fraction: 15/100 × 200 = 3000/100 = 30
Answer: 30

A shirt costs 40. It is 30% off. How much do you save?

30% of 40 = 0.3 × 40 = 12
Answer: 12 saved

There are 25 students. 40% are girls. How many are girls?

40% = 0.4
0.4 × 25 = 10
Answer: 10 girls

🤖 Vidi's Key Points

"Percent of" means multiply
Convert percent to decimal or fraction first
Of = multiplication (×)
Is = equals (=)
Check if answer makes sense (part < whole for % < 100%)

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