If a number is expressed as 5k + 3 for some integer k, what is the remainder whe

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Question: If a number is expressed as 5k + 3 for some integer k, what is the remainder when this number is divided by 5? (2023)

Options:

Correct Answer: 3

Exam Year: 2023

Solution:

The term 5k is divisible by 5, so the remainder is solely from 3, which is 3.

If a number is expressed as 5k + 3 for some integer k, what is the remainder when this number is divided by 5? (2023)

If a number is expressed as 5k + 3 for some integer k, what is the remainder when this number is divided by 5? (2023)

Step 1: Understand that the number is written as 5k + 3, where k is any whole number (integer).
Step 2: Recognize that 5k means 5 times some integer k, which is always divisible by 5.
Step 3: When we divide 5k by 5, there is no remainder because it divides evenly.
Step 4: Now, look at the '+ 3' part. This means we are adding 3 to the number 5k.
Step 5: When we divide the entire expression (5k + 3) by 5, the 5k part gives a remainder of 0, and we only need to consider the + 3.
Step 6: The remainder when 3 is divided by 5 is simply 3, because 3 is less than 5.

Modular Arithmetic – Understanding how to find remainders when dividing numbers, particularly focusing on the properties of divisibility.
Linear Expressions – Recognizing that expressions of the form '5k + 3' can be analyzed by separating terms based on their divisibility.