Blank divided by 9 equals 6
The Correct Answer and Explanation is :
To solve the equation:
[
\frac{\text{Blank}}{9} = 6
]
The term “Blank” is the unknown variable that we need to solve for. To isolate the Blank, we can reverse the division operation by multiplying both sides of the equation by 9. This gives us:
[
\text{Blank} = 6 \times 9
]
Simplifying the multiplication:
[
\text{Blank} = 54
]
So, the correct answer is 54.
Explanation:
The equation (\frac{x}{9} = 6) represents a division where (x) is the unknown value that, when divided by 9, gives a result of 6. To solve for (x), we use the inverse operation of division, which is multiplication. Here’s the step-by-step reasoning:
- Start with the given equation:
[
\frac{x}{9} = 6
]
This tells us that some number (x), when divided by 9, equals 6. - Multiply both sides by 9:
To undo the division by 9 on the left side, we multiply both sides of the equation by 9. This is an application of the multiplication property of equality, which states that if you multiply both sides of an equation by the same non-zero number, the equality still holds:
[
9 \times \frac{x}{9} = 9 \times 6
]
The left side simplifies to (x), since (9 \div 9 = 1), and the right side simplifies to (54):
[
x = 54
] - Conclusion:
Thus, the value of the Blank (or (x)) is 54. This is the number that, when divided by 9, results in 6. So, the equation holds true: (\frac{54}{9} = 6).
This demonstrates how basic algebraic operations—multiplying both sides of an equation—are used to isolate the unknown variable and find the solution.