A number is divided by 11 and gives a remainder of 4. If this number is multipli

A number is divided by 11 and gives a remainder of 4. If this number is multiplied by 3, what will be the remainder when the result is divided by 11?

A number is divided by 11 and gives a remainder of 4. If this number is multiplied by 3, what will be the remainder when the result is divided by 11?

Step 1: Understand that when a number is divided by 11 and gives a remainder of 4, we can express this number as 11k + 4, where k is some integer.
Step 2: Multiply the entire expression (11k + 4) by 3. This gives us 3 * (11k + 4) = 33k + 12.
Step 3: Now, we need to find the remainder when 33k + 12 is divided by 11.
Step 4: Notice that 33k is a multiple of 11, so it will leave a remainder of 0 when divided by 11.
Step 5: Now, focus on the 12. We need to find 12 mod 11, which means we want to find the remainder when 12 is divided by 11.
Step 6: When we divide 12 by 11, the quotient is 1 and the remainder is 1 (since 12 - 11 = 1).
Step 7: Therefore, the remainder when 33k + 12 is divided by 11 is the same as the remainder when 12 is divided by 11, which is 1.

Modular Arithmetic – Understanding how remainders work when dividing numbers, particularly in the context of multiplication and addition.
Properties of Remainders – Applying properties of remainders when performing operations like multiplication.