Math  /  Numbers & Operations

QuestionChoose ALL of the operations for which the numbers in the operation must be like numbers, i.e., they must be expressed in the same unit.
Select Answer(s) multiplication subtraction exponentiation division addition

Studdy Solution

STEP 1

1. The problem requires identifying operations for which the operands must be expressed in the same unit.
2. We assume that "like numbers" implies that the quantities must be homogeneous, i.e., they must be directly comparable in terms of units.

STEP 2

1. Identify the operations that require operands to be in the same units: addition, subtraction.
2. Verify if multiplication requires operands to be in the same units.
3. Verify if division requires operands to be in the same units.
4. Verify if exponentiation requires operands to be in the same units.

STEP 3

Consider the operation of addition. For addition to be meaningful, the numbers being added must be expressed in the same unit, e.g., adding meters to meters or dollars to dollars.
a meters+b meters=(a+b) meters a \text{ meters} + b \text{ meters} = (a+b) \text{ meters}

STEP 4

Similarly, consider the operation of subtraction. For subtraction to be meaningful, the numbers being subtracted must be expressed in the same unit, e.g., subtracting meters from meters.
a metersb meters=(ab) meters a \text{ meters} - b \text{ meters} = (a-b) \text{ meters}

STEP 5

Consider the operation of multiplication. Multiplication does not require the numbers to be in the same unit. For example, multiplying speed (meters/second) by time (seconds) results in a distance (meters).
(a meters/second)×(b seconds)=(a×b) meters (a \text{ meters/second}) \times (b \text{ seconds}) = (a \times b) \text{ meters}

STEP 6

Consider the operation of division. Division does not require the numbers to be in the same unit. For example, dividing distance (meters) by time (seconds) results in speed (meters/second).
(a meters)/(b seconds)=(a/b) meters/second (a \text{ meters}) / (b \text{ seconds}) = (a / b) \text{ meters/second}

STEP 7

Consider the operation of exponentiation. Exponentiation usually involves raising a number to a power, and the units are typically not compatible in such a case. For example, (a meters)2 (a \text{ meters})^2 results in square meters, which is not the same unit as meters.
Solution: From the above steps, we conclude that the operations for which the numbers in the operation must be expressed in the same unit are: - Addition - Subtraction
Therefore, the correct answers are: - subtraction - addition

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