What is 99 X 9?
The Correct Answer and Explanation is:
The correct answer to 99 × 9 is 891.
To explain this, we can break down the multiplication process using distributive property, which is a method of simplifying the multiplication of numbers by breaking one or both numbers into parts.
- Break down the numbers:
We can express 99 as the sum of 100 and -1:
[
99 = 100 – 1
] - Apply the distributive property:
Using the distributive property, we multiply both parts of 99 (which is 100 and -1) by 9:
[
99 \times 9 = (100 – 1) \times 9
]
We can now distribute the 9 to both terms:
[
= (100 \times 9) – (1 \times 9)
] - Simplify each term:
Now, we perform the multiplication of each term:
[
100 \times 9 = 900
]
[
1 \times 9 = 9
] - Subtract the results:
Finally, subtract 9 from 900:
[
900 – 9 = 891
]
Thus, the result of 99 × 9 is 891.
Why is this method helpful?
The distributive property is useful because it breaks down a seemingly difficult multiplication problem into smaller, simpler steps. Instead of multiplying 99 and 9 directly, we separate 99 into 100 and -1, making the multiplication easier to handle. This method helps reinforce understanding of how numbers relate to each other and how to manipulate them for easier calculations.
In a practical sense, this approach can be particularly helpful when performing mental math, as it allows us to work with round numbers (like 100) which are easier to multiply, and then correct for the small adjustment (subtracting 9) afterward.