A number leaves a remainder of 7 when divided by 11. If we subtract 3 from this

A number leaves a remainder of 7 when divided by 11. If we subtract 3 from this number, what will be the new remainder when divided by 11? (2023)

A number leaves a remainder of 7 when divided by 11. If we subtract 3 from this number, what will be the new remainder when divided by 11? (2023)

Step 1: Understand that the original number leaves a remainder of 7 when divided by 11.
Step 2: Write the original number in a form that shows the remainder: original number = 11k + 7, where k is some integer.
Step 3: Subtract 3 from the original number: new number = (11k + 7) - 3.
Step 4: Simplify the new number: new number = 11k + 4.
Step 5: Now, find the remainder when the new number (11k + 4) is divided by 11.
Step 6: Since 11k is divisible by 11, the remainder comes from the 4.
Step 7: Therefore, the new remainder when the new number is divided by 11 is 4.

Remainders and Modular Arithmetic – Understanding how remainders work when performing arithmetic operations on numbers in modular systems.