BB.4 Convert and compare customary units of weight
What is weight?
Weight is a measure of how heavy an object is. In the United States, we use the customary system to measure weight. The main units of weight in this system are ounces (oz), pounds (lb), and tons (T). Understanding these units helps you compare and convert weights accurately.
- A slice of bread weighs about 1 ounce.
- A loaf of bread weighs about 1 pound.
- A small car weighs about 1 ton.
Weight is different from mass. Mass measures the amount of matter in an object, while weight measures how heavy that object is. In everyday life, we often use the word "weight" for both, but in math, we focus on the customary units of weight.
Customary units of weight
The customary system of weight uses three main units: ounces, pounds, and tons. Here are the key facts you must know:
- 1 pound (lb) = 16 ounces (oz)
- 1 ton (T) = 2,000 pounds (lb)
These relationships allow you to convert between units. When you convert, you change a measurement from one unit to another without changing the actual weight.
- 2 pounds = 2 × 16 = 32 ounces
- 3 tons = 3 × 2,000 = 6,000 pounds
- 48 ounces = 48 ÷ 16 = 3 pounds
Always write the unit after the number. For example, write "5 lb" or "5 pounds," not just "5." This helps avoid confusion and shows that you are measuring weight.
Converting ounces to pounds
To convert ounces to pounds, divide the number of ounces by 16. This is because there are 16 ounces in 1 pound.
Formula: pounds = ounces ÷ 16
- 32 oz = 32 ÷ 16 = 2 lb
- 64 oz = 64 ÷ 16 = 4 lb
- 8 oz = 8 ÷ 16 = 0.5 lb (or ½ pound)
When the number of ounces is not a multiple of 16, you may get a fraction or decimal. For example, 24 ounces is 1.5 pounds, which is also written as 1½ pounds. Fractions and decimals are both acceptable in math.
Converting pounds to ounces
To convert pounds to ounces, multiply the number of pounds by 16. This is because each pound has 16 ounces.
Formula: ounces = pounds × 16
- 5 lb = 5 × 16 = 80 oz
- 2.5 lb = 2.5 × 16 = 40 oz
- 10 lb = 10 × 16 = 160 oz
When you multiply a decimal by 16, line up the numbers carefully. For example, 2.5 × 16 = 40. You can also think of 2.5 pounds as 2 pounds plus 0.5 pound. 2 pounds = 32 ounces, and 0.5 pound = 8 ounces, so 32 + 8 = 40 ounces.
Converting pounds to tons
To convert pounds to tons, divide the number of pounds by 2,000. This is because 1 ton equals 2,000 pounds.
Formula: tons = pounds ÷ 2,000
- 4,000 lb = 4,000 ÷ 2,000 = 2 T
- 6,000 lb = 6,000 ÷ 2,000 = 3 T
- 1,000 lb = 1,000 ÷ 2,000 = 0.5 T (or ½ ton)
Use commas when writing large numbers. For example, write 4,000 not 4000. This makes the number easier to read and follows standard American English conventions.
Converting tons to pounds
To convert tons to pounds, multiply the number of tons by 2,000. This is because each ton has 2,000 pounds.
Formula: pounds = tons × 2,000
- 2 T = 2 × 2,000 = 4,000 lb
- 1.5 T = 1.5 × 2,000 = 3,000 lb
- 0.25 T = 0.25 × 2,000 = 500 lb
When multiplying by 2,000, you can think of it as multiplying by 2 and then adding three zeros. For example, 3 × 2 = 6, so 3 × 2,000 = 6,000. This trick works for whole numbers.
Comparing customary units of weight
To compare weights, you must first make sure they are in the same unit. If they are not, convert one or both measurements. Then compare the numbers using the symbols < (less than), > (greater than), or = (equal to).
- Compare 2 lb and 30 oz. Convert 2 lb to ounces: 2 × 16 = 32 oz. Since 32 oz > 30 oz, 2 lb > 30 oz.
- Compare 3,000 lb and 2 T. Convert 2 T to pounds: 2 × 2,000 = 4,000 lb. Since 3,000 lb < 4,000 lb, 3,000 lb < 2 T.
- Compare 48 oz and 3 lb. Convert 3 lb to ounces: 3 × 16 = 48 oz. Since 48 oz = 48 oz, 48 oz = 3 lb.
Always double-check your conversions before comparing. A common mistake is to compare numbers without converting, which can lead to incorrect answers. For example, 5 lb and 70 oz: 5 lb = 80 oz, so 5 lb > 70 oz.
Solving word problems with customary units of weight
Word problems often require you to convert units before adding, subtracting, multiplying, or dividing. Follow these steps:
- Read the problem carefully.
- Identify the units given and the unit you need.
- Convert all measurements to the same unit.
- Perform the operation.
- Check your answer and include the correct unit.
- A bag of apples weighs 3 pounds. A bag of oranges weighs 40 ounces. Which is heavier? Convert 3 lb to ounces: 3 × 16 = 48 oz. 48 oz > 40 oz, so the apples are heavier.
- A truck carries 2 tons of gravel. It unloads 1,500 pounds. How many pounds are left? Convert 2 T to pounds: 2 × 2,000 = 4,000 lb. 4,000 − 1,500 = 2,500 lb left.
- A recipe calls for 8 ounces of butter. You have 0.5 pound. Do you have enough? Convert 0.5 lb to ounces: 0.5 × 16 = 8 oz. Yes, you have exactly enough.
When solving word problems, pay attention to key words like "total," "difference," "heavier," "lighter," "left," and "remaining." These words tell you which operation to use.
Using a conversion table
A conversion table helps you quickly change between units. Here is a table for customary units of weight:
| Unit | Relationship |
|---|---|
| 1 pound (lb) | 16 ounces (oz) |
| 1 ton (T) | 2,000 pounds (lb) |
| 1 ton (T) | 32,000 ounces (oz) |
- How many ounces are in 2 tons? 2 × 32,000 = 64,000 oz.
- How many pounds are in 0.5 ton? 0.5 × 2,000 = 1,000 lb.
Memorizing the basic conversions (1 lb = 16 oz and 1 T = 2,000 lb) will help you solve problems faster. You can always figure out other conversions from these two facts.
Real-world applications of weight conversion
Converting and comparing customary units of weight is useful in many real-life situations, such as cooking, shipping, and shopping.
- Cooking: A recipe calls for 1.5 pounds of flour. You have a scale that measures in ounces. You need 1.5 × 16 = 24 ounces.
- Shipping: A package weighs 3,200 ounces. The shipping company charges by the pound. You need 3,200 ÷ 16 = 200 pounds.
- Shopping: A 5-pound bag of potatoes costs $4.00. A 80-ounce bag costs $3.50. Which is a better deal? Convert 5 lb to ounces: 5 × 16 = 80 oz. Both bags are 80 ounces, so the $3.50 bag is the better deal.
When comparing prices, make sure the weights are in the same unit. This helps you determine which item is the better value.
Common mistakes to avoid
Students often make mistakes when converting or comparing weights. Here are some common errors and how to avoid them:
- Forgetting to convert: Always convert to the same unit before comparing or calculating.
- Using the wrong operation: Remember, to go from a larger unit to a smaller unit, multiply. To go from a smaller unit to a larger unit, divide.
- Misplacing commas: Write large numbers with commas, such as 2,000 and 32,000.
- Ignoring units: Always include the unit in your answer. For example, write "48 oz," not just "48."
- Incorrect: 2 lb = 2 oz. Correct: 2 lb = 32 oz.
- Incorrect: 4,000 lb = 4 T. Correct: 4,000 lb = 2 T.
Practice regularly to avoid these mistakes. The more you convert, the more comfortable you will become with the process.
Common Core alignment: CCSS.MATH.CONTENT.4.MD.A.1 – Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.
Notes for teachers
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