The four-digit numeral 3AA1 is divisible by 9. What digit does A represent?
I just substituted in numbers from 0-9 to see what the answer was. "3AA1 is divisible by 9" means that the problem 3AA1 divided by 9 will equal an integral number. So, once you substitute in numbers you'll find that 3,771 divided by 9 equals 419, so A = 7. Hope this makes sense!
i thought that a number divisible to 9 has to have the number's digit add up to 9, like 9, 18, 27, 36, 45, 63, 72, 81
nv,cm f
the numbers 2 4 6 and 8 are a set of four consecutive even numbers. Suppose the sum of five consecutive even numbers is 320. What is the smallest of the of the five numbers.
What is the formula? and how did you get the answer 7?
To determine the value of the digit A, we first need to understand the divisibility rule for 9. A number is divisible by 9 if the sum of its digits is also divisible by 9.
In this case, the four-digit numeral is 3AA1. So, we need to find the value of A, which will make the sum of all the digits divisible by 9.
Let's analyze the problem step by step:
1. In the given numeral, we have two known digits, which are 3 and 1.
2. We also know that the numeral is divisible by 9, which means the sum of all four digits must also be divisible by 9.
3. The sum of the digits can be calculated as 3 + A + A + 1.
4. Simplifying this expression, we get 5 + 2A.
5. Now, to make this sum divisible by 9, we need to find the value of A that satisfies the equation 5 + 2A = 9n, where n is an integer.
6. Rearranging the equation, we have 2A = 9n - 5.
7. To find a solution where A satisfies this equation, we need to substitute different values of n and check if there is a whole number solution for A.
Let's try some values of n to find the solution:
If we substitute n = 1, the equation becomes 2A = 9 - 5 = 4. Here, 4 is not divisible by 2, so A = 1 is not the solution.
If we substitute n = 2, the equation becomes 2A = 2(9) - 5 = 13. Again, 13 is not divisible by 2, so A = 2 is not the solution.
If we substitute n = 3, the equation becomes 2A = 3(9) - 5 = 22. 22 is divisible by 2.
Therefore, A can be equal to 3.
Hence, the value of A that makes the four-digit numeral 3AA1 divisible by 9 is A = 3.