Percentage Formulas: Complete Guide with Worked Steps

All fundamental percentage formulas clearly explained with mathematical derivations, conversion tables, visual memory aids, and solved practice problems.

Percentage Value (W)

W = (G × p) ÷ 100

"What is p% of G?" – Calculates the specific portion.

Percentage Rate (p)

p = (W ÷ G) × 100

"W is what % of G?" – Solves for the rate per hundred.

Base Value (G)

G = (W × 100) ÷ p

"W is p% of what?" – Calculates the whole (100%).

In-Depth Guide to the 3 Core Formulas

1. Calculate Percentage Value (W)

W = (G × p) ÷ 100

Use this formula when you know the total amount and the percentage rate, and want to find the exact portion.

📝 Worked Example:

What is 15% of $240?

Base Value (G) = $240

Percentage Rate (p) = 15%

W = ($240 × 15) ÷ 100 = $3,600 ÷ 100 = $36.00

2. Calculate Percentage Rate (p)

p = (W ÷ G) × 100

Use this formula when you know both the portion and the whole, and want to express the relationship as a percentage.

📝 Worked Example:

$45 is what percentage of $300?

Part (W) = $45

Whole (G) = $300

p = ($45 ÷ $300) × 100 = 0.15 × 100 = 15%

3. Calculate Base Value (G)

G = (W × 100) ÷ p

Use this formula when you know a portion and its corresponding percentage, and need to reconstruct the original 100% total.

📝 Worked Example:

$60 represents 25% of what total budget?

Portion (W) = $60

Rate (p) = 25%

G = ($60 × 100) ÷ 25 = $6,000 ÷ 25 = $240.00

The Percentage Triangle: Visual Memory Shortcut

Similar to Ohm's Law in physics (V = I × R) or speed formulas (Distance = Speed × Time), the Percentage Triangle makes it impossible to forget how to rearrange the terms:

W (Percentage Value)

G (Base)×p% (Rate ÷ 100)

To find W: Cover W with your finger. You see G × p%.

To find G: Cover G with your finger. You see W ÷ p%.

To find p: Cover p with your finger. You see (W ÷ G) × 100.

Fraction, Decimal & Percentage Conversion Chart

Memorizing standard fraction equivalents dramatically speeds up everyday math:

Fraction	Decimal	Percentage	Everyday Meaning
1/2	0.50	50%	Exactly half
1/3	0.3333...	33.33%	One third
1/4	0.25	25%	One quarter
1/5	0.20	20%	One fifth
1/8	0.125	12.5%	One eighth
1/10	0.10	10%	One tenth
3/4	0.75	75%	Three quarters

Solved Practice Questions & Step-by-Step Solutions

Practice 1: What is 8% sales tax on a $125 purchase?

W = ($125 × 8) ÷ 100 = $1,000 ÷ 100 = $10.00 tax

Total checkout price: $125 + $10 = $135.00

Practice 2: A student scores 68 out of 85 points on a test. What is their percentage score?

p = (68 ÷ 85) × 100 = 0.80 × 100 = 80.0% (Grade B)

Practice 3: A flight ticket costs $360 after a 20% discount. What was the original fare?

Discounted price represents 80% (0.80) of original.

G = $360 ÷ 0.80 = $450.00 original ticket fare

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