Concepts
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Customary Units of Length
- Inch (in), Foot (ft), Yard (yd), Mile (mi)
- 1 ft = 12 in, 1 yd = 3 ft = 36 in, 1 mi = 1,760 yd = 5,280 ft
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Customary Units of Liquid Volume
- Cup (c), Pint (pt), Quart (qt), Gallon (gal)
- 1 pt = 2 c, 1 qt = 2 pt = 4 c, 1 gal = 4 qt = 8 pt = 16 c
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Customary Units of Weight
- Ounce (oz), Pound (lb), Ton (T)
- 1 lb = 16 oz, 1 T = 2,000 lb
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Perimeter
- Distance around a shape. For rectangles:
P = 2(l + w)
- Distance around a shape. For rectangles:
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Area
- Space inside a shape. For rectangles:
A = l × w
- Space inside a shape. For rectangles:
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Volume of a Solid
- Space inside a 3D object. For rectangular prisms:
V = l × w × h
- Space inside a 3D object. For rectangular prisms:
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Time
- Seconds (s), Minutes (min), Hours (h), Days (d), Weeks, Months, Years
- 1 min = 60 s, 1 h = 60 min, 1 d = 24 h, 1 wk = 7 d
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Temperature
- Measured in degrees Fahrenheit (°F) in customary system, Celsius (°C) in metric
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Metric Units of Length
- Millimeter (mm), Centimeter (cm), Meter (m), Kilometer (km)
- 1 m = 100 cm = 1,000 mm, 1 km = 1,000 m
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Metric Units of Liquid Volume
- Milliliter (mL), Liter (L)
- 1 L = 1,000 mL
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Metric Units of Mass
- Milligram (mg), Gram (g), Kilogram (kg)
- 1 g = 1,000 mg, 1 kg = 1,000 g
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Perimeter, Area, and Volume (Metric)
- Formulas are the same. Units: meters (m), square meters (m²), cubic meters (m³)
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Changing from Customary Units to Metric Units
- Length: 1 in ≈ 2.54 cm, 1 ft ≈ 30.48 cm, 1 mi ≈ 1.609 km
- Volume: 1 gal ≈ 3.785 L
- Weight: 1 lb ≈ 0.454 kg
- Temperature: °C = (°F - 32) × 5/9
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Changing from Metric Units to Customary Units
- Length: 1 cm ≈ 0.394 in, 1 m ≈ 3.281 ft, 1 km ≈ 0.621 mi
- Volume: 1 L ≈ 0.264 gal
- Weight: 1 kg ≈ 2.205 lb
- Temperature: °F = (°C × 9/5) + 32
Examples
Example 1: Customary Length
How many inches are in 4 feet?
Solution: 1 ft = 12 in, so 4 ft = 4 × 12 = 48 in.
How many inches are in 4 feet?
Solution: 1 ft = 12 in, so 4 ft = 4 × 12 = 48 in.
Example 2: Metric Mass
Convert 2,500 grams to kilograms.
Solution: 1 kg = 1,000 g, so 2,500 g = 2,500 ÷ 1,000 = 2.5 kg.
Convert 2,500 grams to kilograms.
Solution: 1 kg = 1,000 g, so 2,500 g = 2,500 ÷ 1,000 = 2.5 kg.
Example 3: Area
What is the area of a rectangle with length 8 cm and width 6 cm?
Solution: Area = 8 × 6 = 48 cm².
What is the area of a rectangle with length 8 cm and width 6 cm?
Solution: Area = 8 × 6 = 48 cm².
Example 4: Convert Gallons to Liters
Convert 3 gallons to liters (1 gal ≈ 3.785 L).
Solution: 3 × 3.785 = 11.355 L.
Convert 3 gallons to liters (1 gal ≈ 3.785 L).
Solution: 3 × 3.785 = 11.355 L.
Example 5: Temperature Conversion
Convert 68°F to Celsius.
Solution: (68-32)×5/9 = 36×5/9 = 20°C.
Convert 68°F to Celsius.
Solution: (68-32)×5/9 = 36×5/9 = 20°C.