Solve Division Sequence: -12 ÷ (-1/4) with Positive Result

Q: Why does dividing two negatives give a positive?

Sign rule: When you divide numbers with the same sign (both positive or both negative), the result is always positive. Think of it as: negative ÷ negative = positive!

Q: How do I divide by a negative fraction?

Dividing by a fraction means multiplying by its reciprocal. So $ -12 ÷ (-\frac{1}{4}) = -12 × (-4) = +48 $

Q: What does the >0 condition mean?

The >0 condition means your final answer must be positive. Since we already have +48 ÷ ? > 0, we need a positive number to keep the result positive.

Q: How do I find the missing number in the sequence?

First solve $ -12 ÷ (-\frac{1}{4}) = +48 $. Then find what positive number makes $ +48 ÷ ? > 0 $. Any positive divisor works!

Q: Why is +35 the correct answer?

After getting +48 from the first division, we need $ +48 ÷ ? > 0 $. Since $ +48 ÷ 35 = \frac{48}{35} > 0 $, the answer +35 satisfies the condition!

Division Sequences with Sign Analysis

$-12:-\frac{1}{4}:?>0$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the missing value

00:11 Negative divided by negative is always positive

00:23 Positive divided by positive is always positive

00:30 Therefore the missing value must be positive

00:34 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$-12:-\frac{1}{4}:?>0$

Step-by-step solution

Let's pay attention to the exercise on the left side in terms of plus and minus signs.

The exercise looks like this:

$-:-\text{:?}=$

If we solve the equation from left to right, we can see that we first divide a negative number by a negative number.

This means the result we get is a positive number:

$-:-=+$

Now the remaining exercise is:

$+:?=$

Our result needs to be greater than zero, and therefore we need a positive number, in order to get a positive number in the exercise.

Therefore:

$+:+=+$

$+ > 0$

Therefore the answer is $+35$

Final Answer

$+35$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Negative divided by negative equals positive result
Technique: Calculate $-12 ÷ (-\frac{1}{4}) = +48$ first
Check: Verify $+48 ÷ ? > 0$ requires positive divisor ✓

Common Mistakes

Avoid these frequent errors

Ignoring sign changes during division sequence
Don't calculate numbers without tracking signs = wrong final sign! When you divide -12 by -1/4, you get +48, not -48. Always determine the sign of each step before finding the missing number.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

$(+6)\cdot(+9)=$

FAQ

Everything you need to know about this question

Why does dividing two negatives give a positive?

Sign rule: When you divide numbers with the same sign (both positive or both negative), the result is always positive. Think of it as: negative ÷ negative = positive!

How do I divide by a negative fraction?

Dividing by a fraction means multiplying by its reciprocal. So $-12 ÷ (-\frac{1}{4}) = -12 × (-4) = +48$

What does the >0 condition mean?

The >0 condition means your final answer must be positive. Since we already have +48 ÷ ? > 0, we need a positive number to keep the result positive.

How do I find the missing number in the sequence?

First solve $-12 ÷ (-\frac{1}{4}) = +48$ . Then find what positive number makes $+48 ÷ ? > 0$ . Any positive divisor works!

Why is +35 the correct answer?

After getting +48 from the first division, we need $+48 ÷ ? > 0$ . Since $+48 ÷ 35 = \frac{48}{35} > 0$ , the answer +35 satisfies the condition!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Signed Numbers (Positive and Negative) questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime