Percents of Numbers - Sixth Grade
Complete Notes & Formulas
1. Finding Percent of a Number
The Formula
Percent of Number = (Percent/100) × Number
OR
Percent × Number ÷ 100
Method 1: Convert to Decimal
Step 1: Convert percent to decimal (move decimal 2 places left)
Step 2: Multiply the decimal by the number
Example: Find 25% of 80
Method 1: Using decimal
25% = 0.25
0.25 × 80 = 20
Method 2: Using formula
(25/100) × 80
= 0.25 × 80 = 20
Answer: 20
Quick Tip: "Of" means multiply in percent problems!
2. Three Types of Percent Problems
Type A: Finding the Part
What number is 15% of 60?
Formula: Part = (Percent/100) × Whole
Solution:
Part = (15/100) × 60
Part = 0.15 × 60
Part = 9
Answer: 9
Type B: Finding the Percent
What percent of 50 is 10?
Formula: Percent = (Part/Whole) × 100
Solution:
Percent = (10/50) × 100
Percent = 0.2 × 100
Percent = 20
Answer: 20%
Type C: Finding the Whole
15 is 30% of what number?
Formula: Whole = Part ÷ (Percent/100)
OR: Whole = (Part × 100) ÷ Percent
Solution:
Whole = 15 ÷ (30/100)
Whole = 15 ÷ 0.3
Whole = 50
Answer: 50
3. Estimating Percents of Numbers
Use Benchmark Percents
10%: Divide by 10 (move decimal left 1 place)
25%: Divide by 4 (one quarter)
50%: Divide by 2 (half)
75%: Find 50% and add 25%
1%: Divide by 100 (move decimal left 2 places)
Example: Estimate 26% of 198
Step 1: Round 26% to 25% (benchmark)
Step 2: Round 198 to 200
Step 3: 25% of 200 = 200 ÷ 4 = 50
Estimate: About 50
(Actual: 51.48)
4. Solving Percent Problems Using Grid Models
How Grid Models Work
• Use a 10×10 grid = 100 squares
• Each square = 1%
• Shade squares to represent the percent
• Count shaded squares to find the answer
Example: Find 30% of 50 using grid
Step 1: The whole grid represents 50
Step 2: Shade 30 squares (30%)
Step 3: Each square = 50 ÷ 100 = 0.5
Step 4: 30 squares × 0.5 = 15
Answer: 15
5. Solving Percent Problems Using Strip Models
What is a Strip Model?
A strip (bar) model is a rectangle divided into equal parts
Used to visualize percent relationships
Helps solve problems by showing parts and wholes
Example: 40% of students = 20 students. How many total?
Step 1: Draw a strip for 100%
Step 2: Divide into 10 equal parts (each = 10%)
Step 3: 40% = 4 parts = 20 students
Step 4: So 1 part (10%) = 5 students
Step 5: 10 parts (100%) = 50 students
Answer: 50 students total
6. Percents of Money Amounts
Same Process - Just Add $ Symbol!
Convert percent to decimal
Multiply by the money amount
Round to 2 decimal places (cents)
Example 1: Find 20% of $45.00
20% = 0.20
0.20 × $45.00 = $9.00
Answer: $9.00
Example 2: Sales Tax (6% of $28.50)
6% = 0.06
0.06 × $28.50 = $1.71
Answer: $1.71 tax
7. Fractional and Decimal Percents
What are They?
Fractional Percent: 33⅓%, 66⅔%, 12½%
Decimal Percent: 5.5%, 12.75%, 3.25%
Example 1: Find 12.5% of 80
12.5% = 0.125
0.125 × 80 = 10
Answer: 10
Example 2: Find 33⅓% of 90
33⅓% = 1/3
90 × 1/3 = 90 ÷ 3 = 30
Answer: 30
8. Finding What Percent One Number is of Another
The Formula
Percent = (Part ÷ Whole) × 100
Example: 18 is what percent of 72?
Step 1: Identify part (18) and whole (72)
Step 2: Divide: 18 ÷ 72 = 0.25
Step 3: Multiply by 100: 0.25 × 100 = 25
Answer: 25%
Tip: The number after "of" is usually the whole (denominator)!
9. Solving Percent Word Problems
Key Words to Look For
"of" → multiply
"is" → equals (=)
"what" → unknown (variable)
"percent" → divide by 100 or convert to decimal
Example 1: Shopping Problem
Problem: A jacket costs $80. It's on sale for 25% off. How much is the discount?
Step 1: Find 25% of $80
25% = 0.25
0.25 × $80 = $20
Answer: $20 discount
Sale price = $80 - $20 = $60
Example 2: Test Score
Problem: Maria got 36 out of 40 questions correct. What percent did she score?
Step 1: Part = 36, Whole = 40
Step 2: (36 ÷ 40) × 100
0.9 × 100 = 90
Answer: 90%
Example 3: Finding the Whole
Problem: 30% of students walk to school. If 24 students walk, how many students are there in total?
Step 1: 30% of what = 24?
Step 2: Whole = 24 ÷ 0.30
Whole = 80
Answer: 80 students total
Quick Reference: Percent Formulas
| Problem Type | Formula |
|---|---|
| Find the Part | Part = (Percent/100) × Whole |
| Find the Percent | Percent = (Part/Whole) × 100 |
| Find the Whole | Whole = Part ÷ (Percent/100) |
| Quick Percent Conversion | Percent = Decimal × 100 |
💡 Important Tips to Remember
✓ "Of" means multiply in percent problems
✓ "Is" means equals (=)
✓ Convert percent to decimal: divide by 100
✓ To find part: multiply percent (as decimal) by whole
✓ To find percent: divide part by whole, multiply by 100
✓ To find whole: divide part by percent (as decimal)
✓ 10% shortcut: move decimal left 1 place
✓ 1% shortcut: divide by 100
✓ Round money to 2 decimal places
✓ Check your answer - does it make sense?
🧠 Memory Tricks & Strategies
The Three Types:
"Part, Percent, Whole - remember your role!"
Finding the Part:
"Percent OF means multiply, that's how you get the part, no lie!"
Finding the Percent:
"Part over whole, times one hundred - percent found, question conquered!"
Finding the Whole:
"Part divided by percent decimal - gives you the whole, it's not mythical!"
Benchmark Percents:
"10% is easy, divide by ten please! 25% divide by four, that's the score!"
Word Problems:
"Read it twice, identify the price - part, percent, or whole, that's your goal!"
Master Percents of Numbers! 💯 🎯 ✨
Remember: "Of" = Multiply, "Is" = Equals!