Percentages- 6th Grade Math Practice Guide

What Are Percentages? The Basics You Need to Know

Let's get one thing straight: a percentage is just a fraction out of 100. That's it. 50% means 50 out of 100. 25% means 25 out of 100. Once you understand this, percentages stop being scary.

Think of it like cutting a pizza into 100 slices. If you eat 30 slices, you've eaten 30% of the pizza. Simple.

Why Percentages Matter in 6th Grade

By 6th grade, you're expected to do more than just find 10% of a number. You're working with:

• Converting between fractions, decimals, and percentages
• Solving real-world percentage problems
• Finding percent of change
• Discount, tax, and tip calculations

If any of this makes your head spin, you're in the right place. Let's fix that.

How to Convert Between Fractions, Decimals, and Percentages

This is where most students get stuck. The good news: there's one trick that makes everything easier.

The Magic Rule

Move the decimal point two places. That's it.

• To convert a decimal to a percentage: multiply by 100 (or move decimal right 2 places)
• To convert a percentage to a decimal: divide by 100 (or move decimal left 2 places)
• To convert a fraction to a percentage: divide the top by the bottom, then multiply by 100

Quick Examples

Decimal to Percentage: 0.75 = 75%

Percentage to Decimal: 45% = 0.45

Fraction to Percentage: 3/4 = 0.75 = 75%

See the pattern? The fraction 3/4 becomes the decimal 0.75, which becomes 75%. They're all the same number, just written differently.

Finding Percent of a Number

This is probably what your teacher assigns most often. Here's how to do it without guessing.

Method 1: Use Proportions

Set up this equation:

part/whole = percent/100

Example: What is 20% of 50?

part/50 = 20/100

Cross multiply: part × 100 = 50 × 20

part × 100 = 1000

part = 10

Method 2: Multiply Directly

Convert the percent to a decimal, then multiply.

20% of 50 = 0.20 × 50 = 10

Both methods give you the same answer. Use whichever feels more natural to you.

Common Percentage Problems You'll Face

1. "What percent is one number of another?"

Example: What percent of 80 is 20?

Set it up: 20/80 = x/100

20/80 = 0.25 = 25%

2. "A number is some percent of what number?"

Example: 15 is 30% of what number?

15/x = 30/100

15 = 0.30 × x

x = 50

3. Percent of Change

New value minus old value, divided by old value, times 100.

Price went from $40 to $50.

Change = (50 - 40) / 40 × 100 = 25% increase

Real-World Percentage Problems

Your teacher loves these because they actually matter in life.

Sales Tax

An item costs $60. Tax is 8%.

Tax amount = 0.08 × 60 = $4.80

Total = 60 + 4.80 = $64.80

Discounts

Jacket is $80, marked down 25%.

Discount = 0.25 × 80 = $20

Sale price = 80 - 20 = $60

Tips

Bill is $45. You want to leave 20%.

Tip = 0.20 × 45 = $9

Total = 45 + 9 = $54

Practice Problems: Test Yourself

Try these before checking the answers below.

1. Convert 3/5 to a percentage
2. What is 15% of 200?
3. 45 is what percent of 90?
4. A $120 item has 30% off. What's the sale price?
5. Your grade went from 70 to 91. What's the percent increase?

Answers

1. 60%
2. 30
3. 50%
4. $84
5. 30% increase

Percentages, Decimals, and Fractions Conversion Table

Keep this handy. You'll reference it constantly until these become second nature.

How to Get Better at Percentages

Practice is the only way to get faster. Here's what actually works:

• Drill the basics first: If converting fractions to percentages is slow, fix that before moving on
• Use mental math: 10% of any number is just divide by 10. 50% is divide by 2. Build from there
• Check your work: If 20% of 50 is 10, does that make sense? Yes, because 10/50 = 1/5 = 20%
• Don't rely on calculators: You won't always have one. Practice until you can do simple percentages in your head

Common Mistakes to Avoid

These trip up almost everyone:

• Forgetting to convert the percent to a decimal before multiplying
• Mixing up which number goes on top of a proportion
• Calculating the percent off instead of the sale price
• Rounding too early and losing accuracy

Quick Reference Formulas

Bookmark these. You'll need them.

• Percent of a number: (percent/100) × number
• Find the percent: (part/whole) × 100
• Find the whole: part ÷ (percent/100)
• Percent of change: ((new - old)/old) × 100

Master these formulas and percentage problems stop being a problem. They become automatic.