Lesson 3: Equivalence with Customary Units of Weight

Property

The customary system uses ounces, pounds, and tons to measure weight.

Property

To solve word problems with different units of weight, first convert all measurements to a single, common unit. Then, perform the necessary operations (addition, subtraction, multiplication, division).
Key conversions:

Examples

A recipe calls for $1\frac{1}{2}$ pounds of potatoes and $12$ ounces of carrots. What is the total weight of the vegetables in ounces?

• First, convert pounds to ounces: $1\frac{1}{2} \text{ lb} = 1.5 \times 16 \text{ oz} = 24 \text{ oz}$.
• Then, add the weights: $24 \text{ oz} + 12 \text{ oz} = 36 \text{ oz}$.

A truck is carrying $\frac{3}{4}$ of a ton of gravel. After a delivery, it has $500$ pounds of gravel left. How many pounds of gravel were delivered?

• First, convert tons to pounds: $\frac{3}{4} \text{ T} = \frac{3}{4} \times 2,000 \text{ lb} = 1,500 \text{ lb}$.
• Then, subtract the remaining amount: $1,500 \text{ lb} - 500 \text{ lb} = 1,000 \text{ lb}$.

Explanation

These problems require you to apply your knowledge of weight conversions to real-world scenarios. The first step is always to ensure all weights are in the same unit, which may involve converting fractions or mixed numbers of larger units (like tons or pounds) into smaller units (like pounds or ounces). Once all quantities share a common unit, you can perform the required calculations such as adding, subtracting, or comparing the values. This multi-step process combines your skills in fractions, operations, and measurement conversions.