Repeated Division by 5: Calculate Bank Balance After 3 Weeks Starting at $245

Repeated Division with Negative Numbers

Alejandra checks her bank account once a week.

The first time you checked you had 245 $.

With each passing week, the value is divided by 5-.

How much money will Alejandra have when she reviews the account after 3 weeks?

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Alejandra checks her bank account once a week.

The first time you checked you had 245 $.

With each passing week, the value is divided by 5-.

How much money will Alejandra have when she reviews the account after 3 weeks?

2

Step-by-step solution

To solve this problem, we'll follow the steps of dividing the account balance by -5 for each of the three weeks:

Step-by-step Calculation:

  • Initial balance: \245 \)
  • Week 1: Calculate 245÷(5)=49 245 \div (-5) = -49 .
    This indicates that after the first week, the account has a negative balance of 49-49, meaning a debt or overdraft of \49.
  • Week 2: Calculate \((-49) \div (-5) = 9.8 .
    Since negative divided by negative gives a positive, Alejandra's balance is \9.8 \), recovering part of the overdraft.
  • Week 3: Calculate 9.8÷(5)=1.969.8 \div (-5) = -1.96.
    This results in a negative balance of 1.96-1.96, indicating Alejandra is again in debt or overdraft of slightly less than \$2.

Convert 1.96-1.96 to a mixed number: 12425 -1\frac{24}{25} .

Conclusion: After 3 weeks, Alejandra will have 12425-1\frac{24}{25} in her account, reflecting an overdraft.

3

Final Answer

12425 -1\frac{24}{25}

Key Points to Remember

Essential concepts to master this topic
  • Division Rule: Negative divided by negative gives positive result
  • Technique: Track signs carefully: 245 ÷ (-5) = -49
  • Check: Convert final decimal to fraction: -1.96 = 12425 -1\frac{24}{25}

Common Mistakes

Avoid these frequent errors
  • Forgetting to track negative signs through multiple divisions
    Don't ignore the negative sign in -5 during each division = wrong signs throughout! This leads to all positive results when some should be negative. Always track whether each division involves positive or negative numbers to get correct signs.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

\( (-2)\cdot(-4)= \)

FAQ

Everything you need to know about this question

Why does the balance become negative in some weeks?

+

When you divide by a negative number (-5), the sign of your result flips! A positive balance becomes negative (debt), and a negative balance becomes positive (recovery from debt).

How do I convert -1.96 to a mixed number?

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First, separate the whole number: -1. Then convert the decimal part: 0.96 = 96100=2425 \frac{96}{100} = \frac{24}{25} . So -1.96 = 12425 -1\frac{24}{25} .

What does a negative bank balance mean in real life?

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A negative balance means overdraft or debt - you owe the bank money! For example, 12425 -1\frac{24}{25} means Alejandra owes about $1.96 to the bank.

Why do we keep dividing by -5 instead of +5?

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The problem states "divided by 5-" which means negative 5. This creates the alternating positive/negative pattern in the account balance each week.

How can I check my work at each step?

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  • Week 1: 245 ÷ (-5) = -49
  • Week 2: (-49) ÷ (-5) = 9.8
  • Week 3: 9.8 ÷ (-5) = -1.96

Each step should follow the division sign rules!

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