What times 8 equals 36
The Correct Answer and Explanation is:
To find out what number multiplied by 8 equals 36, we can represent this mathematically with the equation:
[
x \times 8 = 36
]
To solve for (x), we can isolate it by dividing both sides of the equation by 8:
[
x = \frac{36}{8}
]
Now, simplifying the fraction:
[
x = \frac{36 \div 4}{8 \div 4} = \frac{9}{2} = 4.5
]
Thus, the answer is 4.5.
Explanation
The process of solving for (x) in the equation (x \times 8 = 36) involves understanding basic algebraic operations, specifically multiplication and division. In algebra, we often need to isolate the variable (in this case, (x)) to determine its value.
- Understanding the Equation: The equation (x \times 8 = 36) states that some unknown value (x) multiplied by 8 results in 36. To find (x), we need to reverse the operation of multiplication.
- Isolating the Variable: To isolate (x), we perform the opposite operation of multiplication, which is division. We divide both sides of the equation by 8, ensuring we maintain equality.
- Performing the Division: By dividing 36 by 8, we find the value of (x). This division can also be expressed as a fraction (\frac{36}{8}). To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 4 in this case.
- Simplifying the Fraction: Simplifying (\frac{36}{8}) gives us (\frac{9}{2}), which is equivalent to 4.5 in decimal form.
- Conclusion: Therefore, the solution reveals that (x), the unknown number that when multiplied by 8 equals 36, is 4.5. This problem exemplifies fundamental algebraic principles that are applicable in various mathematical contexts, from simple arithmetic to more complex equations.