Converting Units & Converting Rates Lesson

Lesson Overview

• What Are Units and Rates?
• Why Do We Need to Convert Them?
• How to Convert Simple Units
• Converting Between Metric and Customary Units
• How to Convert Rates
• Common Conversion Factors Table
• Multi-Step Word Problems
• Key Concepts and Summary

Imagine you're following a recipe that calls for cups, but your measuring jug only shows liters. Or you're reading a road sign in miles, but your speedometer is in kilometers per hour. These real-life situations show why understanding converting units and converting rates is so important.

In this lesson, you'll learn how to switch between different units and compare rates with ease, giving you the skills to solve problems confidently-whether you're baking a cake or calculating travel time.

What Are Units and Rates?

• Units are standard measurements for things like length, volume, or time (e.g., meters, cups, hours).
  
• Rates are comparisons between two different units (e.g., miles per hour, cups per day).
  

Real-Life Examples:

Why Do We Need to Convert Them?

You may need to:

• Use consistent units to solve problems.
  
• Compare two values with different units.
  
• Translate unfamiliar measurements into ones you understand.
  

Take This Quiz:

How to Convert Simple Units

Steps:

1. Identify the unit you have and the unit you need.
   
2. Find the conversion factor (e.g., 1 gallon = 16 cups).
   
3. Multiply or divide to cancel out the old unit and get the new one.
   

Example:

Convert 5 gallons to cups:

5×16=80 cups5 \times 16 = 80 \text{ cups}5×16=80 cups

✔ Gallons cancel out, you're left with cups.

Converting Between Metric and Customary Units

Metric Conversion Table:

Customary Conversion Table:

Example:

Convert 150 cm to meters:

150÷100=1.5 m150 \div 100 = 1.5 \text{ m}150÷100=1.5 m

How to Convert Rates

Rates involve two units (e.g., distance/time, volume/day).
To convert a rate:

• Convert both the numerator and the denominator.
  

Example:

Convert 70 miles/hour to feet/second:

70×52801×13600=102.67 ft/sec70 \times \frac{5280}{1} \times \frac{1}{3600} = 102.67 \text{ ft/sec}70×15280​×36001​=102.67 ft/sec

Another Example:

Convert 5 cups/day to gallons/year:

5×116×365=114.06 gal/year5 \times \frac{1}{16} \times 365 = 114.06 \text{ gal/year}5×161​×365=114.06 gal/year

Common Conversion Factors Table

Multi-Step Word Problems

Problem 1:

How many feet in 3 miles?

3×5280=15,840 feet3 \times 5280 = 15,840 \text{ feet}3×5280=15,840 feet

Problem 2:

You drink 5 cups of water daily. How many gallons a year?

5×116×365=114.06 gallons/year5 \times \frac{1}{16} \times 365 = 114.06 \text{ gallons/year}5×161​×365=114.06 gallons/year

Problem 3:

Convert 100 mi/hr to feet/second:

100×5280÷3600=146.6 ft/sec100 \times 5280 \div 3600 = 146.6 \text{ ft/sec}100×5280÷3600=146.6 ft/sec

Key Concepts and Summary

• Always multiply or divide using a conversion factor.
  
• Cancel out units to isolate the one you need.
  
• For rates, convert both the top and bottom units.
  
• Real-life problems become much easier with strong conversion skills.
  

Take This Quiz: