Determine all possible digits to fill in the blanks to make each of the following true.
9 |482____ 6|24____35 4 |63____
I have no idea what they are asking for, nor what your | symbols represent. Fractions?
To determine the possible digits that can be placed in the blanks to make each statement true, we need to consider the properties and rules of numbers.
1) 9 | 482 ____
In this case, we are looking for a digit to fill in the blank to make 482 divisible by 9. The rule for divisibility by 9 is that the sum of the digits of the number should be divisible by 9.
To find the possible options, we can calculate the sum of the digits in 482 and then determine which digit(s) can be added to make the new sum divisible by 9.
Sum of the digits in 482 = 4 + 8 + 2 = 14
To make this number divisible by 9, we need to find a digit x such that:
14 + x ≡ 0 (mod 9)
By checking different values of x, we find that x = 4 makes the sum divisible by 9:
14 + 4 = 18
Therefore, to make 482 divisible by 9, we can fill in the blank with the digit 4.
2) 6 | 24 ____ 35
Similar to the previous case, we need to find a digit that can be placed in the blank to make 24X35 divisible by 6. The rule for divisibility by 6 is that the number must be divisible by both 2 and 3.
To check divisibility by 2, the digit in the ones place must be an even number. Therefore, we can replace the blank with any even digit: 0, 2, 4, 6, or 8.
Next, we need to consider divisibility by 3. To check if a number is divisible by 3, we can calculate the sum of its digits and see if it is divisible by 3.
Sum of the digits in 24X35 = 24 + X + 3 + 5 = 32 + X
To make this number divisible by 3, we need to find a digit x such that:
32 + x ≡ 0 (mod 3)
By checking different values of x, we find that x = 1 makes the sum divisible by 3:
32 + 1 = 33
Therefore, to make 24X35 divisible by 3, we can fill in the blank with the digit 1.
3) 4 | 63 ____
Again, we are looking for a digit that can be placed in the blank to make 63X divisible by 4. The rule for divisibility by 4 is that the number formed by the last two digits must be divisible by 4.
To find the possible options, we can find the remainder when 63X is divided by 4.
By trying different digits in the place of X, we find that X = 2 makes 632 divisible by 4:
632 ÷ 4 = 158
Therefore, to make 63X divisible by 4, we can fill in the blank with the digit 2.