Percent and Unit Conversion

Lesson 2 of 2: Special Applications of Rate Reasoning

In this lesson:

• Interpret percent as a rate per 100 — find the part and find the whole
• Convert measurement units by multiplying by a unit rate fraction

What You Will Learn Today

By the end of this lesson, you should be able to:

1. Interpret percent as a rate per 100 and find a percent of a quantity
2. Solve problems where part and percent are known, whole is unknown
3. Convert measurement units using a conversion factor so unwanted units cancel

Percent Is Already a Rate

Percent means: per hundred.

• "Per hour" = for every 1 hour
• "Per hundred" = for every 100 of the whole

Finding 30% of something means multiplying by .

Percent as Rate Per 100

30 out of every 100 squares are shaded — that is 30%.

Find the Part — Double Number Line

30% of 200 students passed. How many?

Double number line (percent on top, students below):

• Unit rate: per percent
• Part: students

Find the Whole — Reverse the Equation

60 students passed — that was 30% of the class. Total?

Double number line: 30% aligns with 60; unit rate ; whole

Applying Percent — Sale Price Example

Jacket 25% off; original price $48

Step 1 — discount:

Step 2 — sale price:

Shortcut: 25% off → pay 75% → ✓

Worked Example — Find the Whole

You saved $9, which was 15% off the original price. What was the original price?

Set up the equation:

Solve:

Check: ✓

One Equation for All Percent Problems

• Know percent and whole → multiply to find part
• Know percent and part → divide to find whole

Quick Check — Percent Both Problem Types

1 (find the part):
40% of 350 students prefer math. How many students?

2 (find the whole):
18 correct answers = 75% of the test. How many questions total?

Set up the equation before computing.

Percent Practice Answers — Both Types

1: students

2: → whole questions

Check: ✓

Conversion Factors Are Unit Rates Equaling One

12 inches = 1 foot, so:

Multiplying by 1 does not change a quantity — but changes the unit.

• Put the unit you want to eliminate in the denominator
• That unit cancels; the target unit remains

Feet to Inches — Unit Cancellation

A table is 4.5 feet long. How long in inches?

• "ft" in 4.5 ft cancels "ft" in the denominator ✓
• "I have feet; I want inches — put feet in denominator."

Inches to Feet — Flip the Fraction

A board is 78 inches long. How long in feet?

"I have inches; I want feet. Put inches in the denominator."

Two More Conversions — Distance and Rate

Miles to feet: 2.4 miles → feet?

Rate conversion: 60 mph → miles per minute?

Practice — Choose the Right Conversion Direction

1: A room is 15 feet wide. How wide in inches?

2: A shelf is 252 inches long. How long in feet?

Write the conversion factor as a fraction and show unit cancellation.

Unit Conversion Practice — Answers Revealed

1:

2:

ft × (in/ft) = in ✓ | in × (ft/in) = ft ✓

Key Takeaways — Lesson 2

✓ Percent means "per 100" — it is a unit rate like any other

✓ Find the part:

✓ Find the whole:

✓ Conversion factors equal 1 — choose the direction that cancels the unit you have

30% of 200 ≠ 30 × 200 = 6,000 — convert percent to 0.30 first

Unit check every conversion — wrong fraction direction gives a nonsense unit

Standard 6.RP.A.3 — All Five Sub-Parts Complete

1. Equivalent ratio tables — build, extend, find missing values
2. Coordinate plane — ratio pairs form a straight line
3. Unit rate problems — forward and backward
4. Percent as rate per 100 — find part and whole
5. Unit conversion — cancellation logic, any direction

Foundation for 7.RP.A.2 (proportional relationships) and 7.RP.A.3 (percent).