What times 9 equals 81?
The Correct Answer and Explanation is:
To determine what number multiplied by 9 equals 81, we can use the equation:
[
9 \times x = 81
]
To isolate ( x ), we divide both sides of the equation by 9:
[
x = \frac{81}{9}
]
Calculating this gives us:
[
x = 9
]
Therefore, the correct answer is ( 9 ).
Explanation
The problem involves basic multiplication and division concepts, foundational elements of arithmetic. Here’s a breakdown of the process:
- Understanding the Equation: The equation ( 9 \times x = 81 ) is an expression of a relationship between three numbers: 9, ( x ), and 81. The goal is to find the value of ( x ) that makes this equation true.
- Division as Inverse of Multiplication: Multiplication and division are inverse operations. To solve for ( x ), we can effectively “undo” the multiplication of 9 by dividing both sides of the equation by 9. This helps isolate ( x ) on one side of the equation.
- Performing the Division: When we divide 81 by 9, we are looking for how many times 9 fits into 81. This can also be visualized through repeated subtraction: if we subtract 9 from 81 repeatedly (9, 18, 27, 36, 45, 54, 63, 72, 81), we find that 9 can be subtracted 9 times before reaching zero. Thus, ( 81 \div 9 = 9 ).
- Verification: It’s always useful to verify our solution. By multiplying ( 9 \times 9 ), we can confirm that it equals 81. This verifies that our answer is correct.
- Practical Applications: This type of calculation has practical implications in daily life, from calculating prices during shopping to measuring distances and quantities, demonstrating the importance of mastering basic arithmetic operations.
In conclusion, the number that multiplied by 9 equals 81 is 9. This exercise illustrates not only the arithmetic involved but also reinforces the foundational understanding of how multiplication and division interact.