5x divided by 5 =???????
The Correct Answer and Explanation is:
To solve the expression (5x \div 5), we follow the basic principles of algebra, specifically the rules concerning division.
Step 1: Understand the Expression
The expression (5x \div 5) consists of a term, (5x), that represents five times a variable (x), and we are dividing this term by (5). In algebra, division is the process of determining how many times one number is contained within another.
Step 2: Apply the Division Rule
According to the rules of division, when we divide a product by a number, we can divide each factor separately. This means that we can simplify (5x \div 5) as follows:
[
5x \div 5 = \frac{5x}{5}
]
Step 3: Simplify the Expression
Next, we simplify the fraction (\frac{5x}{5}). The number (5) in the numerator and the denominator cancels out, because dividing a number by itself (except zero) equals (1):
[
\frac{5x}{5} = x
]
Conclusion
Therefore, the simplified form of the expression (5x \div 5) is simply (x).
Practical Implications
This result, (x), indicates that no matter the value of (x), the operation of dividing (5x) by (5) effectively reduces the coefficient from (5) to (1), leaving the variable (x) intact. This operation is particularly useful in algebra when solving equations or simplifying expressions.
For instance, if we had an equation like (5x = 15), dividing both sides by (5) would lead us to (x = 3), demonstrating how this simplification process is foundational in algebraic manipulation. Overall, the operation emphasizes the importance of understanding variable manipulation and the properties of numbers within algebra.