📏 Customary Units of Measurement - Complete Notes & Formulas 📐
🎯 MASTER CONVERSION RULE 🎯
LARGER → SMALLER: MULTIPLY (×)
SMALLER → LARGER: DIVIDE (÷)
1. Compare and Convert Customary Units of Length
📏 Customary Units of Length:
| Unit | Abbreviation | Conversion |
|---|---|---|
| Inch | in | Smallest unit |
| Foot | ft | 1 ft = 12 in |
| Yard | yd | 1 yd = 3 ft = 36 in |
| Mile | mi | 1 mi = 1,760 yd = 5,280 ft |
1 foot = 12 inches
1 yard = 3 feet = 36 inches
1 mile = 1,760 yards = 5,280 feet
Converting Larger to Smaller (MULTIPLY):
Example 1: Convert 5 feet to inches
1 Identify: Feet → Inches (larger to smaller)
2 Formula: Feet × 12 = Inches
3 Calculate: 5 × 12 = 60 inches
Example 2: Convert 3 yards to feet
Solution: 3 × 3 = 9 feet
Example 3: Convert 2 miles to feet
Solution: 2 × 5,280 = 10,560 feet
Converting Smaller to Larger (DIVIDE):
Example 4: Convert 72 inches to feet
1 Identify: Inches → Feet (smaller to larger)
2 Formula: Inches ÷ 12 = Feet
3 Calculate: 72 ÷ 12 = 6 feet
Example 5: Convert 15 feet to yards
Solution: 15 ÷ 3 = 5 yards
Comparing Lengths:
Example 6: Which is longer: 48 inches or 3 feet?
Solution: Convert to the same unit:
3 feet = 3 × 12 = 36 inches
Compare: 48 inches > 36 inches
Answer: 48 inches is longer
- Going DOWN the chart (miles→yards→feet→inches) = MULTIPLY
- Going UP the chart (inches→feet→yards→miles) = DIVIDE
- Always convert to the same unit before comparing
- Remember: 1 foot = 12 inches (like 12 months in a year!)
2. Compare and Convert Customary Units of Weight
⚖️ Customary Units of Weight:
| Unit | Abbreviation | Conversion |
|---|---|---|
| Ounce | oz | Smallest unit |
| Pound | lb | 1 lb = 16 oz |
| Ton | T or t | 1 ton = 2,000 lb |
1 pound = 16 ounces
1 ton = 2,000 pounds
1 ton = 32,000 ounces
Converting Larger to Smaller (MULTIPLY):
Example 1: Convert 4 pounds to ounces
1 Identify: Pounds → Ounces (larger to smaller)
2 Formula: Pounds × 16 = Ounces
3 Calculate: 4 × 16 = 64 ounces
Example 2: Convert 3 tons to pounds
Solution: 3 × 2,000 = 6,000 pounds
Converting Smaller to Larger (DIVIDE):
Example 3: Convert 80 ounces to pounds
1 Identify: Ounces → Pounds (smaller to larger)
2 Formula: Ounces ÷ 16 = Pounds
3 Calculate: 80 ÷ 16 = 5 pounds
Example 4: Convert 8,000 pounds to tons
Solution: 8,000 ÷ 2,000 = 4 tons
Comparing Weights:
Example 5: Which is heavier: 100 ounces or 5 pounds?
Solution: Convert to the same unit:
5 pounds = 5 × 16 = 80 ounces
Compare: 100 ounces > 80 ounces
Answer: 100 ounces is heavier
- Tons → Pounds → Ounces (going down = multiply)
- Ounces → Pounds → Tons (going up = divide)
- 1 pound = 16 ounces (remember: sweet sixteen!)
- 1 ton = 2,000 pounds (think: a car weighs about 2 tons)
3. Compare and Convert Customary Units of Volume
🥤 Customary Units of Volume (Capacity):
| Unit | Abbreviation | Conversion |
|---|---|---|
| Fluid Ounce | fl oz | Smallest unit |
| Cup | c | 1 c = 8 fl oz |
| Pint | pt | 1 pt = 2 c = 16 fl oz |
| Quart | qt | 1 qt = 2 pt = 4 c = 32 fl oz |
| Gallon | gal | 1 gal = 4 qt = 8 pt = 16 c = 128 fl oz |
1 cup = 8 fluid ounces
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
Remember: C-P-Q-G → Cups, Pints, Quarts, Gallons
Converting Larger to Smaller (MULTIPLY):
Example 1: Convert 3 pints to cups
1 Identify: Pints → Cups (larger to smaller)
2 Formula: Pints × 2 = Cups
3 Calculate: 3 × 2 = 6 cups
Example 2: Convert 5 quarts to pints
Solution: 5 × 2 = 10 pints
Example 3: Convert 2 gallons to quarts
Solution: 2 × 4 = 8 quarts
Converting Smaller to Larger (DIVIDE):
Example 4: Convert 24 cups to pints
1 Identify: Cups → Pints (smaller to larger)
2 Formula: Cups ÷ 2 = Pints
3 Calculate: 24 ÷ 2 = 12 pints
Example 5: Convert 16 quarts to gallons
Solution: 16 ÷ 4 = 4 gallons
Comparing Volumes:
Example 6: Which is more: 6 cups or 2 pints?
Solution: Convert to the same unit:
2 pints = 2 × 2 = 4 cups
Compare: 6 cups > 4 cups
Answer: 6 cups is more
- Gallons → Quarts → Pints → Cups → Fluid Ounces (going down = multiply)
- Remember the pattern: Each step DOUBLES (2×) until you reach gallons
- 1 gallon = 4 quarts (think: 4 quarter gallons!)
- Use measuring cups in the kitchen to practice!
4. Compare and Convert All Customary Units
To compare measurements with different units:
1 Convert both measurements to the SAME unit
2 Compare the numbers
3 State which is larger/smaller or if they're equal
Mixed Unit Type Comparisons:
Example 1 - Length: Compare: 5 feet __ 70 inches
Solution:
Convert 5 feet to inches: 5 × 12 = 60 inches
Compare: 60 inches < 70 inches
Answer: 5 feet < 70 inches
Example 2 - Weight: Compare: 3 pounds __ 40 ounces
Solution:
Convert 3 pounds to ounces: 3 × 16 = 48 ounces
Compare: 48 ounces > 40 ounces
Answer: 3 pounds > 40 ounces
Example 3 - Volume: Compare: 3 quarts __ 10 cups
Solution:
Convert 3 quarts to cups: 3 × 4 = 12 cups
Compare: 12 cups > 10 cups
Answer: 3 quarts > 10 cups
📊 Quick Reference - All Conversions
LENGTH:
1 ft = 12 in | 1 yd = 3 ft = 36 in | 1 mi = 1,760 yd = 5,280 ft
WEIGHT:
1 lb = 16 oz | 1 ton = 2,000 lb = 32,000 oz
VOLUME:
1 c = 8 fl oz | 1 pt = 2 c | 1 qt = 2 pt = 4 c | 1 gal = 4 qt = 8 pt = 16 c
5. Conversion Tables - Customary Units
How to Use Conversion Tables:
Example: Complete this conversion table for feet and inches
| Feet | Inches |
|---|---|
| 1 | 12 |
| 2 | 24 |
| 3 | 36 |
| 4 | 48 |
| 5 | 60 |
Pattern: Each foot equals 12 inches, so multiply feet by 12!
Example: Complete this conversion table for pounds and ounces
| Pounds | Ounces |
|---|---|
| 1 | 16 |
| 2 | 32 |
| 3 | 48 |
| 4 | 64 |
| 5 | 80 |
Pattern: Each pound equals 16 ounces, so multiply pounds by 16!
- Look for patterns in the numbers
- Identify the multiplication factor (conversion rate)
- Each row shows equivalent measurements
- Use the table to quickly find conversions
- Check your work by dividing larger units by conversion factor
6. Compare Customary Units by Multiplying
To compare: Multiply the larger unit by the conversion factor, then compare
Example 1: Compare: 4 yards __ 10 feet
Solution:
1 Multiply yards by 3: 4 × 3 = 12 feet
2 Compare: 12 feet > 10 feet
Answer: 4 yards > 10 feet
Example 2: Compare: 6 pounds __ 100 ounces
Solution:
1 Multiply pounds by 16: 6 × 16 = 96 ounces
2 Compare: 96 ounces < 100 ounces
Answer: 6 pounds < 100 ounces
Example 3: Compare: 5 quarts __ 20 cups
Solution:
1 Multiply quarts by 4: 5 × 4 = 20 cups
2 Compare: 20 cups = 20 cups
Answer: 5 quarts = 20 cups
- Multiplication is faster than division
- Avoids decimals and remainders
- Always convert the larger unit to match the smaller unit
- Use your conversion factors (12, 16, 3, 2, 4, etc.)
7. Convert Customary Units Involving Fractions
Whole × Conversion Factor + (Fraction × Conversion Factor)
Converting Whole Numbers with Fractions:
Example 1: Convert 2½ feet to inches
Solution:
1 Convert whole number: 2 × 12 = 24 inches
2 Convert fraction: ½ × 12 = 6 inches
3 Add: 24 + 6 = 30 inches
Example 2: Convert 3¼ pounds to ounces
Solution:
1 Convert whole: 3 × 16 = 48 ounces
2 Convert fraction: ¼ × 16 = 4 ounces
3 Add: 48 + 4 = 52 ounces
Example 3: Convert 1½ gallons to quarts
Solution:
1 Convert whole: 1 × 4 = 4 quarts
2 Convert fraction: ½ × 4 = 2 quarts
3 Add: 4 + 2 = 6 quarts
Converting Back to Mixed Numbers:
Example 4: Convert 30 inches to feet and inches
Solution:
1 Divide: 30 ÷ 12 = 2 remainder 6
2 Write as mixed unit: 2 feet 6 inches
Or as mixed number: 2½ feet (since 6 ÷ 12 = ½)
Example 5: Convert 50 ounces to pounds and ounces
Solution:
1 Divide: 50 ÷ 16 = 3 remainder 2
2 Write: 3 pounds 2 ounces
Or: 3⅛ pounds (since 2 ÷ 16 = ⅛)
- Convert whole numbers and fractions separately, then add
- Common fractions: ½, ¼, ¾, ⅓, ⅔, ⅕
- When converting back, use division with remainders
- Practice fraction multiplication first!
8. Convert Mixed Customary Units
Converting Mixed Units to Single Units:
Example 1: Convert 4 feet 9 inches to inches
Solution:
1 Convert feet: 4 × 12 = 48 inches
2 Add remaining inches: 48 + 9 = 57 inches
Example 2: Convert 3 pounds 5 ounces to ounces
Solution:
1 Convert pounds: 3 × 16 = 48 ounces
2 Add remaining ounces: 48 + 5 = 53 ounces
Example 3: Convert 2 gallons 3 quarts to quarts
Solution:
1 Convert gallons: 2 × 4 = 8 quarts
2 Add remaining quarts: 8 + 3 = 11 quarts
Converting Single Units to Mixed Units:
Example 4: Convert 75 inches to feet and inches
Solution:
1 Divide: 75 ÷ 12 = 6 remainder 3
2 Write: 6 feet 3 inches
Example 5: Convert 100 ounces to pounds and ounces
Solution:
1 Divide: 100 ÷ 16 = 6 remainder 4
2 Write: 6 pounds 4 ounces
Example 6: Convert 25 cups to gallons, quarts, and cups
Solution:
1 Cups to quarts: 25 ÷ 4 = 6 remainder 1
2 Quarts to gallons: 6 ÷ 4 = 1 remainder 2
3 Write: 1 gallon 2 quarts 1 cup
Total = (Large Unit × Conversion Factor) + Small Unit
9. Add and Subtract Mixed Customary Units
1 Add or subtract the smaller units first
2 Add or subtract the larger units
3 Regroup/convert if necessary
Adding Mixed Units:
Example 1: Add: 3 feet 7 inches + 2 feet 8 inches
Solution:
1 Add inches: 7 + 8 = 15 inches
2 Add feet: 3 + 2 = 5 feet
3 Regroup: 15 inches = 1 foot 3 inches
4 Final: 5 feet + 1 foot 3 inches = 6 feet 3 inches
Example 2: Add: 4 pounds 10 ounces + 3 pounds 9 ounces
Solution:
1 Add ounces: 10 + 9 = 19 ounces
2 Add pounds: 4 + 3 = 7 pounds
3 Regroup: 19 ounces = 1 pound 3 ounces
4 Final: 7 pounds + 1 pound 3 ounces = 8 pounds 3 ounces
Subtracting Mixed Units:
Example 3: Subtract: 5 feet 4 inches − 2 feet 7 inches
Solution:
1 Can't subtract 7 from 4, so regroup:
5 feet 4 inches = 4 feet 16 inches
2 Subtract inches: 16 − 7 = 9 inches
3 Subtract feet: 4 − 2 = 2 feet
Answer: 2 feet 9 inches
Example 4: Subtract: 6 pounds 3 ounces − 2 pounds 10 ounces
Solution:
1 Can't subtract 10 from 3, so regroup:
6 pounds 3 ounces = 5 pounds 19 ounces
2 Subtract ounces: 19 − 10 = 9 ounces
3 Subtract pounds: 5 − 2 = 3 pounds
Answer: 3 pounds 9 ounces
Example 5: Add: 2 gallons 3 quarts + 1 gallon 2 quarts
Solution:
1 Add quarts: 3 + 2 = 5 quarts
2 Add gallons: 2 + 1 = 3 gallons
3 Regroup: 5 quarts = 1 gallon 1 quart
4 Final: 4 gallons 1 quart
- Always regroup when the smaller unit is ≥ conversion factor
- For subtraction, borrow from the larger unit if needed
- Line up units vertically to stay organized
- Check your answer by converting to single units
- Remember: 1 foot = 12 inches, 1 pound = 16 ounces, etc.
10. Multi-Step Problems with Customary Unit Conversions
1 Read the problem carefully and identify all units
2 Determine what conversions are needed
3 Solve step by step
4 Check if your answer makes sense
Example 1 - Length:
Maria has 3 pieces of ribbon. The first is 2 feet 6 inches, the second is 18 inches, and the third is 1 yard. What is the total length in inches?
Solution:
1 Convert piece 1: 2 feet 6 inches
2 × 12 = 24 inches, plus 6 = 30 inches
2 Piece 2 already in inches: 18 inches
3 Convert piece 3: 1 yard = 3 × 12 = 36 inches
4 Add all: 30 + 18 + 36 = 84 inches
Example 2 - Weight:
A bakery uses 8 pounds of flour for cakes and 96 ounces for cookies. How many total pounds of flour are used?
Solution:
1 Cakes: 8 pounds (already in pounds)
2 Convert cookies: 96 ÷ 16 = 6 pounds
3 Add: 8 + 6 = 14 pounds
Example 3 - Volume:
A recipe calls for 3 cups of milk. You have 1 pint of milk. Do you have enough? If so, how much extra do you have?
Solution:
1 Convert pint to cups: 1 × 2 = 2 cups
2 Compare: Need 3 cups, have 2 cups
3 Not enough: Short by 3 − 2 = 1 cup
Example 4 - Combined Operations:
A rope is 10 feet long. You cut off 2 pieces: one is 3 feet 4 inches and another is 2 feet 9 inches. How much rope is left?
Solution:
1 Convert original: 10 feet = 120 inches
2 Convert piece 1: (3 × 12) + 4 = 40 inches
3 Convert piece 2: (2 × 12) + 9 = 33 inches
4 Total cut: 40 + 33 = 73 inches
5 Remaining: 120 − 73 = 47 inches
6 Convert back: 47 ÷ 12 = 3 remainder 11
Answer: 3 feet 11 inches
Example 5 - Real-World Problem:
A truck can carry 3 tons. It already has 2,500 pounds loaded. How many more pounds can it carry?
Solution:
1 Convert capacity: 3 tons = 3 × 2,000 = 6,000 pounds
2 Already loaded: 2,500 pounds
3 Remaining: 6,000 − 2,500 = 3,500 pounds
- Convert all measurements to the SAME unit first
- Write down each step clearly
- Use the smallest unit to avoid fractions during calculations
- Convert back to the requested unit at the end
- Draw pictures or diagrams if helpful
- Always ask: "Does my answer make sense?"
📚 Master Conversion Chart - Quick Reference
| LENGTH CONVERSIONS | ||
|---|---|---|
| 1 foot | = | 12 inches |
| 1 yard | = | 3 feet = 36 inches |
| 1 mile | = | 1,760 yards = 5,280 feet |
| WEIGHT CONVERSIONS | ||
|---|---|---|
| 1 pound | = | 16 ounces |
| 1 ton | = | 2,000 pounds = 32,000 ounces |
| VOLUME CONVERSIONS | ||
|---|---|---|
| 1 cup | = | 8 fluid ounces |
| 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 |
🎯 REMEMBER THE GOLDEN RULE! 🎯
LARGER → SMALLER = MULTIPLY (×)
SMALLER → LARGER = DIVIDE (÷)
🌟 Practice these conversions daily and you'll master them in no time! 🌟