A number leaves a remainder of 7 when divided by 10. If this number is decreased

A number leaves a remainder of 7 when divided by 10. If this number is decreased by 3, what will be the new remainder when divided by 10? (2023)

A number leaves a remainder of 7 when divided by 10. If this number is decreased by 3, what will be the new remainder when divided by 10? (2023)

Step 1: Understand that the original number leaves a remainder of 7 when divided by 10. This means it can be written as 10k + 7, where k is some integer.
Step 2: Decrease the original number by 3. So, we calculate (10k + 7) - 3.
Step 3: Simplify the expression: (10k + 7) - 3 = 10k + 4.
Step 4: Now, we need to find the remainder when 10k + 4 is divided by 10.
Step 5: When dividing 10k + 4 by 10, the 10k part gives a remainder of 0, and the 4 gives a remainder of 4.
Step 6: Therefore, the new remainder when the decreased number is divided by 10 is 4.

Remainders – Understanding how remainders work when dividing numbers.
Algebraic Manipulation – Using algebra to express the original number in terms of a variable.
Modular Arithmetic – Applying the concept of modular arithmetic to find new remainders after modifications.