Which of the following is a valid remainder for the expression 12 mod 9? A) 15 B) 3 C) 9 D) -6
Understand the Problem
The question is asking us to determine which of the provided options can be a valid remainder when 12 is divided by 9. To solve this, we will find out the actual remainder of the expression '12 mod 9' and then check each option to see if it matches the valid remainders that can be produced from this operation.
Answer
3
Answer for screen readers
The valid remainder when 12 is divided by 9 is 3.
Steps to Solve
- Calculate the remainder of 12 divided by 9
We will find the remainder when 12 is divided by 9. This can be done using the modulo operation.
The division is: $$ 12 \div 9 = 1.3333... $$ The whole number part is 1, which means 9 goes into 12 one time.
Now, we calculate the product of 9 and 1: $$ 9 \times 1 = 9 $$
- Find the remainder
Next, we subtract this product from 12 to find the remainder: $$ 12 - 9 = 3 $$
Thus, the remainder when 12 is divided by 9 is 3.
- List possible remainders
When dividing by 9, valid remainders can be any integer from 0 to 8. Therefore, the possible remainders when dividing a number by 9 are: $$ 0, 1, 2, 3, 4, 5, 6, 7, 8 $$
Since we found that the remainder is 3, we will check if 3 is part of these possible remainders.
The valid remainder when 12 is divided by 9 is 3.
More Information
This means that if you divide 12 by 9, you will have a quotient of 1 and a remainder of 3. The modulo operation, denoted as $12 \mod 9$, confirms this result.
Tips
- Confusing the quotient with the remainder. Remember, the quotient is how many times the divisor fits into the dividend, while the remainder is what is left over after the division.
- Forgetting that remainders can only be between 0 and one less than the divisor.
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