-38 divided by 2.
The Correct Answer and Explanation is :
The result of dividing (-38) by (2) is (-19).
Explanation of Division
Division is one of the four basic operations in arithmetic, alongside addition, subtraction, and multiplication. It involves determining how many times one number (the divisor) can be subtracted from another number (the dividend) before reaching zero. In this case, we are dividing the negative number (-38) by the positive number (2).
When dividing negative numbers by positive numbers, the rule is straightforward: the result will always be negative. This is because dividing a negative quantity into positive groups yields a deficit, or a negative result. In mathematical terms:
[
\text{Dividend} \div \text{Divisor} = \text{Quotient}
]
Here, (-38) is the dividend and (2) is the divisor. When we divide (-38) by (2), we can think of it as asking how many times (2) fits into (-38).
To solve this, we can perform the division as if both numbers were positive:
[
38 \div 2 = 19
]
Since our original dividend was negative, we apply the rule regarding the signs:
[
-38 \div 2 = -19
]
This indicates that if you were to take (-19) groups of (2), you would arrive at (-38). This calculation can also be visualized on a number line, where moving to the left (indicating negative values) shows how many steps of (2) it takes to reach (-38).
In summary, the operation of dividing a negative number by a positive number will always yield a negative quotient. Thus, the answer to (-38 \div 2) is (-19). Understanding these basic principles helps clarify the behavior of numbers during division, especially when negative values are involved.