Finding a Percent of a Quantity

Three Methods for Calculating Percents

Learning Objectives:

• Calculate percent of a number using decimals
• Calculate percent of a number using fractions
• Use proportions to find percent of a quantity
• Solve real-world percent problems

The Big Idea

"Of" means "multiply" in math

When you see: 30% of 80

It means: 30% × 80

The Decimal Method: Two Steps

Step 1: Convert percent to decimal (÷ 100)

Step 2: Multiply by the quantity

Example: Find 30% of 80

• Step 1: 30% = 0.30
• Step 2: 0.30 × 80 = 24

Example: Find 45% of 120

Step 1: Convert to decimal
45% = 0.45

Step 2: Multiply
0.45 × 120 = 54

Answer: 45% of 120 is 54

Example: Find 8% of 250

Step 1: Convert to decimal
8% = 0.08

Step 2: Multiply
0.08 × 250 = 20

Answer: 8% of 250 is 20

Example: Result with Decimals

Find 15% of 73

• 15% = 0.15
• 0.15 × 73 = 10.95

Answers can be decimals—that's okay!

Practice: Decimal Method

Calculate using the decimal method:

1. 20% of 150 = ?
2. 75% of 48 = ?
3. 6% of 500 = ?

Convert to decimal, then multiply

Answers: Decimal Method

1. 20% of 150 = 0.20 × 150 = 30
2. 75% of 48 = 0.75 × 48 = 36
3. 6% of 500 = 0.06 × 500 = 30

Benchmark Percents as Fractions

Example: Find 50% of 86

Using the fraction method:

50% = 1/2

86 ÷ 2 = 43

Much faster than 0.50 × 86!

Example: Find 25% of 60

Using the fraction method:

25% = 1/4

60 ÷ 4 = 15

The "Find 10%, Then Build" Strategy

Find 35% of 80

• Find 10%: 80 ÷ 10 = 8
• Find 30%: 3 × 8 = 24
• Find 5%: Half of 10% = 4
• Find 35%: 24 + 4 = 28

Build any percent from 10% and 5%!

Example: Find 15% of 200

Using the building strategy:

• 10% of 200 = 20
• 5% of 200 = 10 (half of 10%)
• 15% = 10% + 5% = 20 + 10 = 30

Practice: Fraction Method

Use mental math with fractions:

1. 50% of 124 = ?
2. 10% of 350 = ?
3. 25% of 80 = ?

Think: divide by 2, 10, or 4

Answers: Fraction Method

1. 50% of 124 = 124 ÷ 2 = 62
2. 10% of 350 = 350 ÷ 10 = 35
3. 25% of 80 = 80 ÷ 4 = 20

The Percent Proportion

Template: "Part is to whole as percent is to 100"

Example: Find 35% of 60

Set up the proportion:

Cross multiply:
100x = 35 × 60 = 2100

Solve:
x = 2100 ÷ 100 = 21

Example: Find 12% of 75

Set up:

Cross multiply:
100x = 12 × 75 = 900

Solve:
x = 900 ÷ 100 = 9

When to Use Each Method

All three methods give the same answer!

Practice: Proportion Method

Set up and solve using proportions:

1. Find 40% of 85
2. Find 65% of 120

Hint: x/whole = percent/100

Answers: Proportion Method

1. Find 40% of 85
x/85 = 40/100 → 100x = 3400 → x = 34

2. Find 65% of 120
x/120 = 65/100 → 100x = 7800 → x = 78

Application: Store Discounts

A jacket costs $45. It's on sale for 20% off. How much is the discount?

Find 20% of $45:

• Method: 0.20 × 45 = $9

The discount is $9.
Sale price: $45 - $9 = $36

Application: Restaurant Tips

Your meal costs $32. You want to leave a 15% tip. How much is the tip?

Using the building strategy:

• 10% of $32 = $3.20
• 5% of $32 = $1.60
• 15% = $3.20 + $1.60 = $4.80

Application: Test Scores

Maria got 85% of 40 questions correct. How many did she get right?

Find 85% of 40:

• 0.85 × 40 = 34 questions

Maria answered 34 questions correctly.

Check: Does Your Answer Make Sense?

Reasonableness check:

• Finding 30% of 80? Answer must be less than 80
• Finding 50% of something? Answer is exactly half
• Finding more than 100%? Answer is larger than the original

Always estimate first!

Key Takeaways

• "Of" means multiply — percent problems are multiplication
• Decimal method: Convert to decimal, then multiply
• Fraction method: Use benchmarks for mental math
• Proportion method: part/whole = percent/100
• Choose the best method for each problem

Common Mistakes to Avoid

Always ask: does my answer make sense?

What's Next?

Upcoming lessons:

• Finding the whole when given a part and percent
• Percent increase and decrease
• Multi-step percent problems

Practice all three methods until they feel natural!