Sequential Division Problem: Tracking Position After Dividing by 3, 1/8, and 4

Q: Why does dividing by a fraction flip it to multiplication?

Dividing by a fraction is the same as multiplying by its reciprocal! When we divide by $ \frac{1}{8} $, we multiply by $ \frac{8}{1} = 8 $. This is a fundamental rule that makes fraction division much easier.

Q: How do I keep track of negative signs in multi-step problems?

Write down the sign of each result after every step. Remember: negative ÷ negative = positive, and negative ÷ positive = negative. Count your negatives - an even number gives positive, odd gives negative.

Q: Can I do all the divisions at once instead of step by step?

No! You must follow the sequence exactly as described. Each jump depends on the position from the previous jump. Doing them out of order will give you a completely different answer.

Q: What if I get confused about which operation to do next?

Read the problem word by word and number each step: 1) Start at 1, 2) Divide by -3, 3) Divide by $ +\frac{1}{8} $, 4) Divide by -4. Follow this exact order!

Q: How can I check if my final answer is correct?

Work backwards from your answer! Start with $ \frac{2}{3} $, multiply by -4, then by $ \frac{1}{8} $, then by -3. You should get back to 1.

Sequential Division with Negative Numbers and Fractions

A frog jumps on the number axis.

It starts with the digit 1. It first jumps to a value equal to the value it is set to, divided by 3-.

Then it jumps to a value equal to the value at which it is placed, divided by $+\frac{1}{8}$ .

Finally it jumps to a value equal to the value it is at, divided by 4-.

Where will you stop at the end of three jumps?

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A frog jumps on the number axis.

It starts with the digit 1. It first jumps to a value equal to the value it is set to, divided by 3-.

Then it jumps to a value equal to the value at which it is placed, divided by $+\frac{1}{8}$ .

Finally it jumps to a value equal to the value it is at, divided by 4-.

Where will you stop at the end of three jumps?

Step-by-step solution

To solve this problem, we will perform each division in sequence as described:

Step 1: Initial Position

- The frog starts at $x = 1$ .

Step 2: First Jump

- Divide by $-3$ :
$x = \frac{1}{-3} = -\frac{1}{3}$ .

Step 3: Second Jump

- Divide by $+\frac{1}{8}$ :
$x = \frac{-\frac{1}{3}}{\frac{1}{8}} = -\frac{1}{3} \times 8 = -\frac{8}{3}$ .

Step 4: Third Jump

- Divide by $-4$ :
$x = \frac{-\frac{8}{3}}{-4} = \frac{8}{3} \times \frac{1}{4} = \frac{8}{3} \times \frac{1}{4} = \frac{8}{12} = \frac{2}{3}$ .

Therefore, the frog stops at the position $+\frac{2}{3}$ .

Final Answer

$+\frac{2}{3}$

Key Points to Remember

Essential concepts to master this topic

Order: Perform each division operation in the exact sequence given
Technique: Dividing by $\frac{1}{8}$ equals multiplying by 8
Check: Trace backwards: $\frac{2}{3} \times (-4) \times \frac{1}{8} \times (-3) = 1$ ✓

Common Mistakes

Avoid these frequent errors

Treating negative signs incorrectly during division
Don't ignore the negative signs or apply them inconsistently = wrong final answer! Many students get $-\frac{2}{3}$ instead of $+\frac{2}{3}$ by missing that two negative divisions create a positive result. Always track each negative sign carefully through every step.

Practice Quiz

Test your knowledge with interactive questions

Convert $\frac{7}{2}$ into its reciprocal form:

FAQ

Everything you need to know about this question

Why does dividing by a fraction flip it to multiplication?

Dividing by a fraction is the same as multiplying by its reciprocal! When we divide by $\frac{1}{8}$ , we multiply by $\frac{8}{1} = 8$ . This is a fundamental rule that makes fraction division much easier.

How do I keep track of negative signs in multi-step problems?

Write down the sign of each result after every step. Remember: negative ÷ negative = positive, and negative ÷ positive = negative. Count your negatives - an even number gives positive, odd gives negative.

Can I do all the divisions at once instead of step by step?

No! You must follow the sequence exactly as described. Each jump depends on the position from the previous jump. Doing them out of order will give you a completely different answer.

What if I get confused about which operation to do next?

Read the problem word by word and number each step: 1) Start at 1, 2) Divide by -3, 3) Divide by $+\frac{1}{8}$ , 4) Divide by -4. Follow this exact order!

How can I check if my final answer is correct?

Work backwards from your answer! Start with $\frac{2}{3}$ , multiply by -4, then by $\frac{1}{8}$ , then by -3. You should get back to 1.

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