A number is divided by 7 and gives a remainder of 3. If this number is increased

A number is divided by 7 and gives a remainder of 3. If this number is increased by 4, what will be the new remainder when divided by 7?

A number is divided by 7 and gives a remainder of 3. If this number is increased by 4, what will be the new remainder when divided by 7?

Step 1: Understand that when a number is divided by 7 and gives a remainder of 3, it can be written as '7k + 3', where 'k' is some whole number.
Step 2: Increase the number by 4. So, we take '7k + 3' and add 4 to it, which gives us '7k + 3 + 4'.
Step 3: Simplify the expression from Step 2. This becomes '7k + 7'.
Step 4: Notice that '7k + 7' can be factored as '7(k + 1)'.
Step 5: When '7(k + 1)' is divided by 7, it divides evenly with no remainder.
Step 6: Therefore, the new remainder when this number is divided by 7 is 0.

Modular Arithmetic – Understanding how remainders work when dividing numbers.
Algebraic Manipulation – Ability to manipulate expressions involving variables and constants.