A number is divided by 15 and gives a remainder of 9. If this number is decrease

A number is divided by 15 and gives a remainder of 9. If this number is decreased by 4, what will be the new remainder when divided by 15? (2023)

A number is divided by 15 and gives a remainder of 9. If this number is decreased by 4, what will be the new remainder when divided by 15? (2023)

Step 1: Understand that when a number is divided by 15 and gives a remainder of 9, it can be expressed as '15k + 9', where 'k' is some integer.
Step 2: Decrease the original number by 4. This means we calculate '15k + 9 - 4'.
Step 3: Simplify the expression from Step 2: '15k + 9 - 4' becomes '15k + 5'.
Step 4: Now, we need to find the remainder when '15k + 5' is divided by 15.
Step 5: When dividing '15k + 5' by 15, the '15k' part divides evenly (giving a remainder of 0), and we are left with the remainder of 5 from the '+ 5'.
Step 6: Therefore, the new remainder when the number decreased by 4 is divided by 15 is 5.

Modular Arithmetic – Understanding how remainders work when dividing numbers.
Algebraic Manipulation – Ability to manipulate expressions to find new values based on given conditions.