A number is divided by 9 and leaves a remainder of 5. If this number is increase

A number is divided by 9 and leaves a remainder of 5. If this number is increased by 4, what will be the new remainder when divided by 9? (2023)

A number is divided by 9 and leaves a remainder of 5. If this number is increased by 4, what will be the new remainder when divided by 9? (2023)

Step 1: Understand that when a number is divided by 9 and leaves a remainder of 5, it can be expressed as '9k + 5', where 'k' is some integer.
Step 2: Increase the original number by 4. This gives us the new number: '9k + 5 + 4'.
Step 3: Simplify the new number: '9k + 5 + 4' becomes '9k + 9'.
Step 4: Notice that '9k + 9' can be factored as '9(k + 1)', which means it is a multiple of 9.
Step 5: Since '9(k + 1)' is a multiple of 9, when this new number is divided by 9, the remainder is 0.

Remainders and Modular Arithmetic – Understanding how remainders work when dividing numbers and how they change with arithmetic operations.