A number is divided by 12 and gives a remainder of 7. If this number is increase

A number is divided by 12 and gives a remainder of 7. If this number is increased by 5, what will be the new remainder when divided by 12? (2023)

A number is divided by 12 and gives a remainder of 7. If this number is increased by 5, what will be the new remainder when divided by 12? (2023)

Step 1: Understand that when a number is divided by 12 and gives a remainder of 7, it can be written as '12k + 7', where 'k' is some integer.
Step 2: Increase the original number by 5. This means we calculate '12k + 7 + 5'.
Step 3: Simplify the expression from Step 2: '12k + 7 + 5' becomes '12k + 12'.
Step 4: Notice that '12k + 12' can be factored as '12(k + 1)', which means it is a multiple of 12.
Step 5: When a number is a multiple of 12, the remainder when divided by 12 is 0.

Modular Arithmetic – Understanding how remainders work when dividing numbers.
Algebraic Manipulation – Using algebra to express the original number in terms of a variable.