Customary Units of Measurement - Fifth Grade
Complete Notes & Formulas
1. Compare and Convert Customary Units of Length
Customary Units of Length
| Unit | Symbol | Used For |
|---|---|---|
| Inch | in | Small lengths (paperclip, pencil) |
| Foot | ft | Medium lengths (desk, door height) |
| Yard | yd | Larger lengths (room, football field) |
| Mile | mi | Very long distances (roads, travel) |
Length Conversion Formulas
1 foot (ft) = 12 inches (in)
1 yard (yd) = 3 feet (ft)
1 yard (yd) = 36 inches (in)
1 mile (mi) = 1,760 yards (yd)
1 mile (mi) = 5,280 feet (ft)
Conversion Rules
LARGER Unit → SMALLER Unit: MULTIPLY ×
SMALLER Unit → LARGER Unit: DIVIDE ÷
Examples
Example 1: Convert 7 feet to inches
• Larger to smaller → Multiply
• 1 ft = 12 in
• 7 × 12 = 84 inches
Example 2: Convert 36 inches to yards
• Smaller to larger → Divide
• 1 yd = 36 in
• 36 ÷ 36 = 1 yard
Example 3: Convert 2 miles to feet
• Larger to smaller → Multiply
• 1 mi = 5,280 ft
• 2 × 5,280 = 10,560 feet
2. Compare and Convert Customary Units of Weight
Customary Units of Weight
| Unit | Symbol | Used For |
|---|---|---|
| Ounce | oz | Light objects (letter, slice of bread) |
| Pound | lb | Medium weight (book, bag of apples) |
| Ton | T | Very heavy objects (car, elephant) |
Weight Conversion Formulas
1 pound (lb) = 16 ounces (oz)
1 ton (T) = 2,000 pounds (lb)
Examples
Example 1: Convert 5 pounds to ounces
• Larger to smaller → Multiply
• 1 lb = 16 oz
• 5 × 16 = 80 ounces
Example 2: Convert 64 ounces to pounds
• Smaller to larger → Divide
• 1 lb = 16 oz
• 64 ÷ 16 = 4 pounds
Example 3: Convert 3 tons to pounds
• Larger to smaller → Multiply
• 1 T = 2,000 lb
• 3 × 2,000 = 6,000 pounds
3. Compare and Convert Customary Units of Volume (Capacity)
Customary Units of Volume/Capacity
| Unit | Symbol | Used For |
|---|---|---|
| Fluid Ounce | fl oz | Very small liquid amounts |
| Cup | c | Cooking measurements, drinks |
| Pint | pt | Ice cream container, milk |
| Quart | qt | Large milk container |
| Gallon | gal | Large jugs, gas tank |
Volume Conversion Formulas
1 cup (c) = 8 fluid ounces (fl oz)
1 pint (pt) = 2 cups (c)
1 quart (qt) = 2 pints (pt)
1 gallon (gal) = 4 quarts (qt)
Quick Reference Chart
• 1 pint = 2 cups = 16 fl oz
• 1 quart = 2 pints = 4 cups = 32 fl oz
• 1 gallon = 4 quarts = 8 pints = 16 cups = 128 fl oz
Examples
Example 1: Convert 6 pints to cups
• Larger to smaller → Multiply
• 1 pt = 2 c
• 6 × 2 = 12 cups
Example 2: Convert 8 quarts to gallons
• Smaller to larger → Divide
• 1 gal = 4 qt
• 8 ÷ 4 = 2 gallons
Example 3: Convert 3 gallons to cups
• Larger to smaller → Multiply
• 1 gal = 16 cups
• 3 × 16 = 48 cups
4. Conversion Tables - Customary Units
Complete Conversion Table
LENGTH
| 1 foot | = | 12 inches |
| 1 yard | = | 3 feet or 36 inches |
| 1 mile | = | 1,760 yards or 5,280 feet |
WEIGHT
| 1 pound | = | 16 ounces |
| 1 ton | = | 2,000 pounds |
VOLUME/CAPACITY
| 1 cup | = | 8 fluid ounces |
| 1 pint | = | 2 cups or 16 fl oz |
| 1 quart | = | 2 pints or 4 cups |
| 1 gallon | = | 4 quarts or 16 cups |
5. Compare Customary Units by Multiplying
How to Compare Different Units
To compare measurements in different units, convert them to the same unit first, then compare.
Steps to Compare
Step 1: Look at both measurements
Step 2: Convert one or both to the same unit
Step 3: Compare the numbers
Step 4: Use > (greater), < (less), or = (equal)
Examples
Example 1: Compare: 5 feet ___ 55 inches
Convert to same unit (inches):
• 5 feet × 12 = 60 inches
Compare: 60 inches vs 55 inches
• Answer: 5 feet > 55 inches
Example 2: Compare: 48 ounces ___ 3 pounds
Convert to same unit (ounces):
• 3 pounds × 16 = 48 ounces
Compare: 48 ounces vs 48 ounces
• Answer: 48 ounces = 3 pounds
6. Convert Customary Units Involving Fractions
Why Fractions?
Sometimes measurements include fractions like ½ foot, ¼ pound, or ⅔ gallon. You must convert these carefully!
Steps to Convert with Fractions
Step 1: Identify the fraction
Step 2: Multiply the fraction by the conversion factor
Step 3: Simplify if needed
Formula
Fraction × Conversion Factor = Answer
Examples
Example 1: Convert ½ foot to inches
• 1 foot = 12 inches
• ½ × 12 = 12 ÷ 2 = 6 inches
Example 2: Convert ¾ pound to ounces
• 1 pound = 16 ounces
• ¾ × 16 = (3 × 16) ÷ 4 = 48 ÷ 4 = 12 ounces
Example 3: Convert 2½ gallons to quarts
• 1 gallon = 4 quarts
• 2 gallons = 2 × 4 = 8 quarts
• ½ gallon = ½ × 4 = 2 quarts
• Total: 8 + 2 = 10 quarts
7. Convert Mixed Customary Units
What are Mixed Units?
Mixed units combine two units together, like 3 feet 7 inches or 2 pounds 5 ounces.
Two Types of Conversion
Type 1: Mixed Units → Single Unit
Steps:
1. Convert the larger unit to the smaller unit
2. Add the remaining smaller units
Type 2: Single Unit → Mixed Units
Steps:
1. Divide to find the larger unit
2. The remainder is the smaller unit
Examples
Example 1: Convert 5 feet 8 inches to inches
Step 1: Convert feet to inches
5 feet × 12 = 60 inches
Step 2: Add the remaining inches
60 + 8 = 68 inches
Example 2: Convert 50 inches to feet and inches
Step 1: Divide by 12
50 ÷ 12 = 4 remainder 2
Step 2: Write as mixed units
4 feet 2 inches
Example 3: Convert 3 pounds 12 ounces to ounces
• 3 pounds × 16 = 48 ounces
• 48 + 12 = 60 ounces
8. Add and Subtract Mixed Customary Units
Steps to Add Mixed Units
Step 1: Add the larger units together
Step 2: Add the smaller units together
Step 3: If smaller units ≥ conversion factor, convert to larger unit
Step 4: Simplify the answer
Steps to Subtract Mixed Units
Step 1: If you can't subtract smaller units, borrow from larger unit
Step 2: Subtract the smaller units
Step 3: Subtract the larger units
Examples
Addition Example: Add 3 ft 8 in + 2 ft 7 in
Step 1: Add feet: 3 + 2 = 5 ft
Step 2: Add inches: 8 + 7 = 15 in
Step 3: 15 in = 1 ft 3 in
Step 4: 5 ft + 1 ft 3 in = 6 ft 3 in
Subtraction Example: Subtract 5 ft 2 in - 2 ft 8 in
Problem: Can't subtract 8 in from 2 in
Step 1: Borrow 1 ft = 12 in from 5 ft
5 ft 2 in becomes 4 ft 14 in
Step 2: Now subtract inches: 14 - 8 = 6 in
Step 3: Subtract feet: 4 - 2 = 2 ft
Answer: 2 ft 6 in
9. Multi-Step Problems with Customary Unit Conversions
What are Multi-Step Problems?
These problems require multiple conversions or operations (add, subtract, multiply, divide) to solve.
Strategy
Step 1: Read the problem carefully
Step 2: Identify what you need to find
Step 3: Convert all measurements to the same unit
Step 4: Perform the necessary operations
Step 5: Convert back if needed
Step 6: Check if your answer makes sense
Examples
"A recipe calls for 3 cups of milk. If Sarah makes 4 batches, how many quarts of milk does she need?"
Step 1: Find total cups needed
3 cups × 4 batches = 12 cups
Step 2: Convert cups to quarts
1 quart = 4 cups
12 cups ÷ 4 = 3 quarts
Answer: Sarah needs 3 quarts of milk
"Tom walks 2 miles to school and back each day. How many feet does he walk in 5 days?"
Step 1: Find daily distance
To school and back = 2 miles × 2 = 4 miles per day
Step 2: Find distance for 5 days
4 miles × 5 days = 20 miles
Step 3: Convert miles to feet
1 mile = 5,280 feet
20 × 5,280 = 105,600 feet
Answer: Tom walks 105,600 feet in 5 days
"A bag contains 80 ounces of flour. If a baker uses 3 pounds, how many ounces are left?"
Step 1: Convert pounds to ounces
3 pounds × 16 = 48 ounces
Step 2: Subtract from total
80 - 48 = 32 ounces
Answer: 32 ounces of flour are left
Quick Conversion Reference Chart
LENGTH
1 ft = 12 in
1 yd = 3 ft
1 yd = 36 in
1 mi = 5,280 ft
WEIGHT
1 lb = 16 oz
1 T = 2,000 lb
VOLUME
1 c = 8 fl oz
1 pt = 2 c
1 qt = 2 pt
1 gal = 4 qt
💡 Important Tips to Remember
✓ MULTIPLY when converting from LARGER to SMALLER units
✓ DIVIDE when converting from SMALLER to LARGER units
✓ Memorize the basic conversion factors (12 in = 1 ft, 16 oz = 1 lb, etc.)
✓ Always convert to the same unit before comparing
✓ When adding/subtracting mixed units, regroup when needed
✓ In multi-step problems, write out each step
✓ Check if your answer makes sense (Is 100 feet reasonable?)
✓ Include correct units in your final answer
🧠 Memory Tricks
For Length: "The Football player has 12 (F looks like 1 and 2)"
For Weight: "A Pound has 16 ounces (P looks like 16 upside down)"
For Volume: "Gallon Queen Puts Crown on" = Gal → Qt → Pt → Cup (each divided by 2 or 4)
Direction Tip: "When numbers get BIGGER, you MULTIPLY. When they get SMALLER, you DIVIDE."
Master Customary Units! 📏⚖️🥤
Practice converting units daily - cooking, measuring, and building!