Understanding Percent

Lesson 1: What Percent Means and Connecting to Fractions

Learning Objectives:

• Define percent as "per hundred"
• Represent percents using hundred grids
• Convert between percents and fractions

Where Do You See Percents?

• Sales: "30% off!"
• Weather: "70% chance of rain"
• Grades: "Scored 85%"
• Sports: "Made 60% of free throws"

Percents are everywhere in daily life.

What Does "Percent" Mean?

The word percent comes from Latin:

• per = for each, out of
• cent = hundred

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

45% Means "45 Out of 100"

When we write 45%, we mean:

• 45 out of every 100
• 45 per hundred
• 45/100

The % symbol is a shorthand for "/100"

Visualizing Percent: The Hundred Grid

A hundred grid has exactly 100 squares (10 × 10).

Each square represents 1% of the whole.

Showing 25% on a Hundred Grid

25% means 25 out of 100.

Shade 25 squares to show 25%.

Showing 50% on a Hundred Grid

50% means 50 out of 100.

Shade 50 squares — exactly half the grid.

Showing 100% on a Hundred Grid

100% means 100 out of 100.

Shade all 100 squares — the whole grid.

Your Turn: Hundred Grid Practice

What percent is shown?

Count the shaded squares...

Answer: 75%

75 squares are shaded out of 100.

75 out of 100 = 75%

Percent IS a Fraction

The % symbol means "divided by 100" or "over 100"

Converting Percent to Fraction

Step 1: Write the percent as a fraction over 100

Step 2: Simplify if possible

Example: Convert 50% to a fraction

• Step 1: 50% = 50/100
• Step 2: 50/100 = 1/2 (divide both by 50)

50% = 1/2

Example: Convert 25% to a Fraction

Step 1: 25% = 25/100

Step 2: Simplify 25/100

• Both 25 and 100 are divisible by 25
• 25 ÷ 25 = 1
• 100 ÷ 25 = 4

25% = 1/4

Example: Convert 75% to a Fraction

Step 1: 75% = 75/100

Step 2: Simplify 75/100

• GCF of 75 and 100 is 25
• 75 ÷ 25 = 3
• 100 ÷ 25 = 4

75% = 3/4

Common Percent-Fraction Equivalents

Memorize these—you'll use them often!

Going the Other Way: Fraction to Percent

To convert a fraction to a percent:

Find an equivalent fraction with denominator 100

Example: Convert 1/4 to a percent

• 1/4 = ?/100
• 4 × 25 = 100, so multiply top by 25 too
• 1 × 25 = 25

1/4 = 25/100 = 25%

Example: Convert 3/5 to a Percent

Find equivalent fraction with denominator 100

• 3/5 = ?/100
• 5 × 20 = 100
• 3 × 20 = 60

3/5 = 60/100 = 60%

Practice: Convert to Fractions

Convert each percent to a simplified fraction:

1. 40% = ?
2. 80% = ?
3. 5% = ?

Try these before the next slide

Answers: Convert to Fractions

1. 40% = 40/100 = 2/5
2. 80% = 80/100 = 4/5
3. 5% = 5/100 = 1/20

Practice: Convert to Percents

Convert each fraction to a percent:

1. 1/2 = ?%
2. 1/5 = ?%
3. 7/10 = ?%

Find equivalent fractions with denominator 100

Answers: Convert to Percents

1. 1/2 = 50/100 = 50%
2. 1/5 = 20/100 = 20%
3. 7/10 = 70/100 = 70%

Key Takeaways

• Percent means "per hundred" or "out of 100"
• A hundred grid visualizes percents perfectly
• Percent to fraction: write over 100, then simplify
• Fraction to percent: find equivalent with denominator 100

Watch Out For...

45 and 45% are NOT the same!

• 45 means forty-five (whole number)
• 45% means 45 out of 100 = 0.45 (less than 1)

Always include the % symbol when you mean percent.

Coming Up Next

Lesson 2: Decimals and Benchmark Percents

• Convert between percents and decimals
• Master the common benchmark percents
• See how percent, fraction, and decimal connect

Practice your percent-fraction conversions!