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

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 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