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)

1 question

1 item

Q: 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)

Solution: The new number is (original number + 4) = (9k + 5 + 4) = 9k + 9, which leaves a remainder of 0.

Steps: 5

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.