A number leaves a remainder of 6 when divided by 11. If this number is multiplie
Practice Questions
Q1
A number leaves a remainder of 6 when divided by 11. If this number is multiplied by 3, what will be the new remainder when divided by 11?
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Questions & Step-by-Step Solutions
A number leaves a remainder of 6 when divided by 11. If this number is multiplied by 3, what will be the new remainder when divided by 11?
Step 1: Understand that the original number can be expressed as '11k + 6', where 'k' is any whole number. This means when you divide this number by 11, you get a remainder of 6.
Step 2: Multiply the entire expression '11k + 6' by 3. This gives you '3 * (11k + 6)'.
Step 3: Distribute the 3: '3 * 11k + 3 * 6' which simplifies to '33k + 18'.
Step 4: Now, we need to find the remainder when '33k + 18' is divided by 11.
Step 5: Notice that '33k' is a multiple of 11 (since 33 is 3 times 11), so it will leave a remainder of 0 when divided by 11.
Step 6: Now, focus on the '18'. When you divide 18 by 11, you get 1 with a remainder of 7 (because 18 - 11 = 7).
Step 7: Combine the results: since '33k' gives a remainder of 0 and '18' gives a remainder of 7, the total remainder when '33k + 18' is divided by 11 is 7.
Modular Arithmetic – Understanding how remainders work when dividing numbers.
Multiplication and Remainders – Applying multiplication to a number and determining the new remainder.
