Simplify: 15 - 6 (mod 4)
Understand the Problem
The question is asking to simplify the expression 15 - 6 modulo 4. This involves performing the subtraction first and then applying the modulo operation to find the remainder when the result is divided by 4.
Answer
1
Answer for screen readers
The final answer is (1).
Steps to Solve
- Perform the subtraction
First, we subtract 6 from 15: $$ 15 - 6 = 9 $$
- Apply the modulo operation
Next, we find the remainder when 9 is divided by 4: $$ 9 \mod 4 $$
- Calculate the remainder
To calculate this, we divide 9 by 4:
- The closest multiple of 4 less than or equal to 9 is 8, which is $4 \times 2$.
- The remainder can be found by subtracting 8 from 9: $$ 9 - 8 = 1 $$
So, we have: $$ 9 \mod 4 = 1 $$
The final answer is (1).
More Information
This means that when you subtract 6 from 15 and then take that result modulo 4, the remainder is 1. Modulo operations are often used in computer science, cryptography, and mathematical proofs, as they help determine cyclic behaviors in numbers.
Tips
A common mistake is forgetting to perform the subtraction before applying the modulo operation. Ensure that the order is correct: subtraction first, then modulo.
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