Customary Units of Weight (oz, lb, T): Fifth Grade Mathematics

Measuring weight in the customary system utilizes ounces, pounds, and tons, governed by conversions of 16 and 2,000.

The Customary Weight Units

Weight measures the gravitational pull on an object. The three customary units of weight are:
- Ounce (oz): A very light unit (e.g., a slice of bread or a pencil weighs approximately 1 oz).

- Pound (lb): The standard everyday weight unit (e.g., a loaf of bread or a soccer ball weighs about 1 lb).

- Ton (T): An extremely heavy industrial weight unit (e.g., a small car or a rhinoceros weighs about 1 to 2 tons).

+--------------------------------------------------------------------------+
|                  CUSTOMARY WEIGHT EQUIVALENCIES                          |
+---------------------+----------------------------+-----------------------+
| Smaller Unit        | Conversion Ratio           | Larger Unit           |
+---------------------+----------------------------+-----------------------+
| Ounces (oz)         | 16 ounces                  | = 1 pound (lb)        |
| Pounds (lb)         | 2,000 pounds               | = 1 ton (T)           |
| Ounces (oz)         | 32,000 ounces              | = 1 ton (T)           |
+---------------------+----------------------------+-----------------------+

Conversion Computations

Applying the conversion rules:
- Pounds to Ounces: Multiply by 16 (e.g., 5 lbs = 5 * 16 = 80 oz).

- Ounces to Pounds: Divide by 16 (e.g., 48 oz = 48 / 16 = 3 lbs).

- Tons to Pounds: Multiply by 2,000 (e.g., 3.5 T = 3.5 * 2,000 = 7,000 lbs).

- Pounds to Tons: Divide by 2,000 (e.g., 6,000 lbs = 6,000 / 2,000 = 3 T).

Decomposing Ounces to Pounds and Ounces:
  Convert 58 ounces:
  58 / 16 = 3 with a remainder of 10.
  58 oz = 3 pounds 10 ounces (or 3 10/16 lb = 3 5/8 lb).

Exercises and Solutions

Exercise 1: Weight Conversions Across Units. Perform the following conversions: Part A: Convert 7 1/4 pounds into ounces. Part B: Convert 9,500 pounds into tons.

Solution 1: For Part A: Converting from pounds to ounces requires multiplying by 16. Convert 7 1/4 to an improper fraction: 29/4. Multiply: (29/4) * 16 = 29 * 4 = 116 ounces. For Part B: Converting from pounds to tons requires dividing by 2,000. Divide: 9,500 / 2,000 = 95/20 = 4 15/20 = 4 3/4 tons (or 4.75 tons).

Exercise 2: Cargo Weight Word Problem. A shipping truck has a maximum carrying capacity of 4 tons. The truck is loaded with 45 crates that weigh 160 pounds each. How many pounds below or above the maximum weight capacity is the truck?

Solution 2: Step 1: Find the maximum truck capacity in pounds: 4 tons * 2,000 pounds per ton = 8,000 pounds. Step 2: Find the total weight of the crates: multiply 45 crates by 160 pounds: 45 * 160 = 7,200 pounds. Step 3: Compare cargo weight to maximum capacity: 8,000 - 7,200 = 800 pounds. The truck is 800 pounds below its maximum weight capacity.