Finding a Percent of a Number

Understanding Percent

Percent means "per hundred" or "out of 100."

50% means 50 out of 100, or 50/100, or 0.50 (half)

Converting Percent to Decimal

To calculate with percents, convert to a decimal first.

Rule: Move the decimal point two places left (or divide by 100)

Examples:

• 25% = 0.25
• 50% = 0.50 = 0.5
• 75% = 0.75
• 10% = 0.10 = 0.1
• 5% = 0.05
• 100% = 1.00 = 1
• 150% = 1.50 = 1.5

Method 1: Multiply by the Decimal

Formula: Part = Percent × Whole

Convert percent to decimal, then multiply.

Example: What is 30% of 80?

Step 1: Convert 30% to decimal: 0.30 Step 2: Multiply: 80 × 0.30 = 24

Answer: 24

Example: What is 15% of 60?

• 15% = 0.15
• 60 × 0.15 = 9

Answer: 9

Method 2: Use Fractions

Convert the percent to a fraction, then multiply.

Example: What is 25% of 200?

• 25% = 25/100 = 1/4
• 1/4 × 200 = 200 ÷ 4 = 50

Answer: 50

Example: What is 50% of 90?

• 50% = 50/100 = 1/2
• 1/2 × 90 = 90 ÷ 2 = 45

Answer: 45

Method 3: Use 10% as a Benchmark

Find 10% first (easy!), then multiply or divide.

10% of any number: Move decimal one place left

Example: What is 10% of 80?

• Move decimal: 80.0 → 8.0
• 10% of 80 = 8

Then use 10% to find other percents:

20% = 10% × 2

• 10% of 80 = 8
• 20% of 80 = 8 × 2 = 16

30% = 10% × 3

• 30% of 80 = 8 × 3 = 24

5% = 10% ÷ 2

• 5% of 80 = 8 ÷ 2 = 4

Common Percents to Know

Finding Percents Greater Than 100%

150% of 40:

• 150% = 1.5
• 40 × 1.5 = 60

200% of 30:

• 200% = 2.0
• 30 × 2 = 60 (double it!)

Finding Percents Less Than 1%

0.5% of 200:

• 0.5% = 0.005
• 200 × 0.005 = 1

Working Backwards

Problem: 30% of what number is 18?

Set up equation: 0.30 × n = 18

Solve: n = 18 ÷ 0.30 = 60

Answer: 60

Problem: What percent of 50 is 10?

Set up: n% of 50 = 10

• 50 × n = 10
• n = 10 ÷ 50 = 0.2 = 20%

Answer: 20%

Real-World Applications

Discounts: "30% off a $50 shirt"

• 30% of 50 = 0.30 × 50 = $15 off
• New price: $50 - $15 = $35

Tips: "15% tip on $40 meal"

• 15% of 40 = 0.15 × 40 = $6

Tax: "7% sales tax on $80"

• 7% of 80 = 0.07 × 80 = $5.60

Test scores: "You got 85% on a 60-question test"

• 85% of 60 = 0.85 × 60 = 51 questions correct

Mental Math Tricks

1% of a number: Move decimal two places left

• 1% of 300 = 3

50%: Divide by 2

• 50% of 66 = 33

25%: Divide by 4

• 25% of 80 = 20

75%: Find 25%, then multiply by 3

• 75% of 80 = 20 × 3 = 60

Practice