A number is divided by 9 and gives a remainder of 5. If this number is increased
Practice Questions
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A number is divided by 9 and gives a remainder of 5. If this number is increased by 4, what will be the new remainder when divided by 9? (2023)
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Questions & Step-by-Step Solutions
A number is divided by 9 and gives a remainder of 5. If this number is increased by 4, what will be the new remainder when divided by 9? (2023)
Step 1: Start with a number that, when divided by 9, gives a remainder of 5. This means the number can be written as '9k + 5' for some integer k.
Step 2: Increase this number by 4. So, the new number is '(9k + 5) + 4'.
Step 3: Simplify the new number: '9k + 5 + 4' becomes '9k + 9'.
Step 4: Notice that '9k + 9' can be factored as '9(k + 1)'.
Step 5: Now, when you divide '9(k + 1)' by 9, it divides evenly, which means there is no remainder.
Step 6: Therefore, the remainder when the new number is divided by 9 is 0.
Remainders and Modular Arithmetic – Understanding how remainders work when dividing numbers and how to manipulate them through addition or subtraction.
