- Terms with different units are not like terms and cannot be combined.
- (a) 5 weeks and 2 cars are not like terms.
- (b) 7 tomatoes and 3 grams are not like terms.
- (c) 2 miles and 10 miles are like terms, and \(2 \text{ miles} + 10 \text{ miles} = \boxed{12 \text{ miles}}\).
Explanation
- Analysis of Like Terms
In algebra and basic arithmetic, "like terms" refer to quantities that share the same unit of measurement. This allows us to combine them through addition or subtraction. If quantities have different units, they represent different types of measures (such as time, mass, or length) and cannot be combined into a single meaningful value. We examine three cases to determine if they are like terms and perform the appropriate arithmetic operation.
- Evaluating the Expressions
A5 weeks and 2 cars: The units are "weeks" (a measurement of time) and "cars" (a count of discrete objects). Since these units are different, the terms are not like terms. Therefore, they cannot be subtracted.
B7 tomatoes and 3 grams: The units are "tomatoes" (a count of items) and "grams" (a measurement of mass). Since these units are different, the terms are not like terms. Therefore, they cannot be subtracted.
C2 miles and 10 miles: The units are "miles" and "miles" (both are measurements of length). Since the units are identical, these are like terms. We can perform the addition:
\[2 \text{ miles} + 10 \text{ miles} = (2 + 10) \text{ miles} = 12 \text{ miles}.\]
- Conclusion
In summary, for case (a), they are not like terms. For case (b), they are not like terms. For case (c), they are like terms, and the result is \(\boxed{12 \text{ miles}}\).
Examples
Understanding like terms is essential in everyday life to ensure we are adding or subtracting the right things. For example, if you are grocery shopping, you cannot simply add the number of apples to the total weight of potatoes to get a meaningful total quantity, as they have different units (items vs. weight). However, you can add the weights of two different bags of apples together because they are both measured in units like kilograms or pounds. This principle keeps our calculations accurate in cooking, budgeting, and science.