A number is divided by 7 and gives a remainder of 3. If this number is increased by 4, what will be the new remainder when divided by 7?

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Q: A number is divided by 7 and gives a remainder of 3. If this number is increased by 4, what will be the new remainder when divided by 7?

Solution: The new number is (7k + 3 + 4) = 7k + 7, which gives a remainder of 0 when divided by 7.

Steps: 6

Step 1: Understand that when a number is divided by 7 and gives a remainder of 3, it can be written as '7k + 3', where 'k' is some whole number.
Step 2: Increase the number by 4. So, we take '7k + 3' and add 4 to it, which gives us '7k + 3 + 4'.
Step 3: Simplify the expression from Step 2. This becomes '7k + 7'.
Step 4: Notice that '7k + 7' can be factored as '7(k + 1)'.
Step 5: When '7(k + 1)' is divided by 7, it divides evenly with no remainder.
Step 6: Therefore, the new remainder when this number is divided by 7 is 0.