Converting Units of Measurement

Why Convert Units?

Sometimes we need to change measurements from one unit to another:

• Your height: 4 feet = ? inches
• A recipe: 2 cups = ? pints
• Your weight: 70 pounds = ? ounces

Converting means changing from one unit to another without changing the actual amount!

Customary Length Units

Remember these:

• 1 foot (ft) = 12 inches (in)
• 1 yard (yd) = 3 feet (ft)
• 1 yard (yd) = 36 inches (in)
• 1 mile (mi) = 5,280 feet (ft)

Converting Larger to Smaller Units

Rule: When going from a LARGER unit to a SMALLER unit, MULTIPLY!

Example: 3 feet = ? inches

Think: 1 foot = 12 inches, so 3 feet = ?

• 3 × 12 = 36 inches ✓

Example: 2 yards = ? feet

Think: 1 yard = 3 feet, so 2 yards = ?

• 2 × 3 = 6 feet ✓

Converting Smaller to Larger Units

Rule: When going from a SMALLER unit to a LARGER unit, DIVIDE!

Example: 24 inches = ? feet

Think: 12 inches = 1 foot, so 24 inches = ?

• 24 ÷ 12 = 2 feet ✓

Example: 9 feet = ? yards

Think: 3 feet = 1 yard, so 9 feet = ?

• 9 ÷ 3 = 3 yards ✓

Customary Weight Units

Remember these:

• 1 pound (lb) = 16 ounces (oz)
• 1 ton (T) = 2,000 pounds (lb)

Weight Conversions

Example: 3 pounds = ? ounces

• Larger → smaller, so multiply!
• 3 × 16 = 48 ounces ✓

Example: 32 ounces = ? pounds

• Smaller → larger, so divide!
• 32 ÷ 16 = 2 pounds ✓

Example: 4,000 pounds = ? tons

• Smaller → larger, so divide!
• 4,000 ÷ 2,000 = 2 tons ✓

Customary Capacity (Liquid) Units

Remember these:

• 1 cup (c) = 8 fluid ounces (fl oz)
• 1 pint (pt) = 2 cups (c)
• 1 quart (qt) = 2 pints (pt)
• 1 quart (qt) = 4 cups (c)
• 1 gallon (gal) = 4 quarts (qt)

Capacity Conversions

Example: 3 cups = ? fluid ounces

• Larger → smaller, multiply!
• 3 × 8 = 24 fluid ounces ✓

Example: 2 quarts = ? pints

• Larger → smaller, multiply!
• 2 × 2 = 4 pints ✓

Example: 16 cups = ? quarts

• Smaller → larger, divide!
• 16 ÷ 4 = 4 quarts ✓

Example: 8 quarts = ? gallons

• Smaller → larger, divide!
• 8 ÷ 4 = 2 gallons ✓

Memory Tricks

For Capacity (Liquid Measurements):

Think of the word "G-Q-P-C" (Gallons, Quarts, Pints, Cups)

• Going DOWN the list (big → small): Multiply
• Going UP the list (small → big): Divide

Gallon Man (visual helper):

        G
    ----+----
    Q   |   Q
   -----|-----
   P P  |  P P
  ------+------
 C C C C|C C C C

• 1 Gallon = 4 Quarts
• 1 Quart = 2 Pints
• 1 Pint = 2 Cups

Two-Step Conversions

Sometimes you need to convert twice!

Example: 2 yards = ? inches

Step 1: Yards to feet

• 2 yards × 3 = 6 feet

Step 2: Feet to inches

• 6 feet × 12 = 72 inches ✓

Example: 48 fluid ounces = ? pints

Step 1: Fluid ounces to cups

• 48 ÷ 8 = 6 cups

Step 2: Cups to pints

• 6 ÷ 2 = 3 pints ✓

Real-World Problems

Height: Your little brother is 40 inches tall. How tall is he in feet?

• 40 ÷ 12 = 3 feet 4 inches
• (40 ÷ 12 = 3 remainder 4)
• Answer: 3 feet 4 inches ✓

Recipe: A recipe needs 3 cups of milk. How many pints is that?

• 3 cups ÷ 2 = 1.5 pints
• Or: 1 pint 1 cup ✓

Swimming Pool: A pool holds 200 gallons. How many quarts is that?

• 200 × 4 = 800 quarts ✓

Metric System (Introduction)

Length:

• 1 meter (m) = 100 centimeters (cm)
• 1 kilometer (km) = 1,000 meters (m)

Mass:

• 1 kilogram (kg) = 1,000 grams (g)

Capacity:

• 1 liter (L) = 1,000 milliliters (mL)

Metric is easier because everything is based on 10s!

Metric Conversions

Example: 3 meters = ? centimeters

• 3 × 100 = 300 centimeters ✓

Example: 5,000 grams = ? kilograms

• 5,000 ÷ 1,000 = 5 kilograms ✓

Time Conversions

Remember these:

• 1 minute (min) = 60 seconds (sec)
• 1 hour (hr) = 60 minutes (min)
• 1 day = 24 hours (hr)
• 1 week = 7 days
• 1 year = 365 days (366 in leap years)
• 1 year = 52 weeks
• 1 year = 12 months

Time Examples

Example: 3 minutes = ? seconds

• 3 × 60 = 180 seconds ✓

Example: 120 minutes = ? hours

• 120 ÷ 60 = 2 hours ✓

Example: 2 hours = ? minutes

• 2 × 60 = 120 minutes ✓

Conversion Strategy Chart

Question to ask: Am I going from big to small, or small to big?

BIG unit → SMALL unit = MULTIPLY (more of them!)
Examples:
- Feet → Inches (multiply by 12)
- Yards → Feet (multiply by 3)
- Gallons → Quarts (multiply by 4)

SMALL unit → BIG unit = DIVIDE (fewer of them!)
Examples:
- Inches → Feet (divide by 12)
- Feet → Yards (divide by 3)
- Quarts → Gallons (divide by 4)

Practice Tips

Before converting:

1. Identify the units (what you have, what you want)
2. Ask: Bigger to smaller or smaller to bigger?
3. Remember the conversion fact (like 1 ft = 12 in)
4. Choose multiply or divide

Check your answer:

• Does it make sense?
• Should it be bigger or smaller than you started?
• 5 feet = 60 inches ✓ (more inches than feet makes sense!)

Common Conversions to Memorize

Length:

• 1 ft = 12 in
• 1 yd = 3 ft
• 1 yd = 36 in

Weight:

• 1 lb = 16 oz
• 1 ton = 2,000 lb

Capacity:

• 1 gal = 4 qt
• 1 qt = 2 pt
• 1 pt = 2 c
• 1 c = 8 fl oz

Time:

• 1 hr = 60 min
• 1 min = 60 sec

Word Problems

Problem 1: A rope is 5 yards long. How many feet is that?

• 5 × 3 = 15 feet ✓

Problem 2: You buy 2 gallons of juice. How many quarts is that?

• 2 × 4 = 8 quarts ✓

Problem 3: A movie is 120 minutes long. How many hours?

• 120 ÷ 60 = 2 hours ✓

Problem 4: You need 4 cups of water for a recipe. How many pints?

• 4 ÷ 2 = 2 pints ✓

Comparing Measurements

Which is more: 50 inches or 4 feet?

Convert to same unit:

• 4 feet = 4 × 12 = 48 inches
• 50 inches > 48 inches
• So 50 inches is more! ✓

Which is less: 3 cups or 1 pint?

Convert to same unit:

• 1 pint = 2 cups
• 3 cups > 2 cups
• So 1 pint is less! ✓

Common Mistakes

❌ Multiplying when you should divide

• Going smaller to bigger needs division!

❌ Dividing when you should multiply

• Going bigger to smaller needs multiplication!

❌ Using wrong conversion fact

• Make sure you know: 1 foot = 12 inches (not 10!)

❌ Not checking if answer makes sense

• 2 gallons should equal MORE quarts (not fewer!)

✅ Remember: Big → Small = Multiply ✅ Small → Big = Divide ✅ Memorize key conversions ✅ Check your answer makes sense

Quick Reference Table

| From → To | Operation | Conversion | |-----------|-----------|------------| | Feet → Inches | Multiply | × 12 | | Inches → Feet | Divide | ÷ 12 | | Yards → Feet | Multiply | × 3 | | Feet → Yards | Divide | ÷ 3 | | Pounds → Ounces | Multiply | × 16 | | Ounces → Pounds | Divide | ÷ 16 | | Gallons → Quarts | Multiply | × 4 | | Quarts → Gallons | Divide | ÷ 4 | | Pints → Cups | Multiply | × 2 | | Cups → Pints | Divide | ÷ 2 |

Remember: The key to conversions is knowing your facts and whether to multiply or divide!