Division Sign Problem: Solve +2 ? +12 < 0

Q: Why does the unknown number need to be negative?

Since we start with +2 (positive) and need a final result less than 0, we need the middle operation to flip the sign. Dividing a positive by a negative gives a negative result.

Q: How do I work through division chains like this?

Work left to right! First: +2 ÷ (-40) = -1/20. Then: (-1/20) ÷ (+12) = -1/240. Since -1/240

Q: Could any of the other answer choices work?

Let's check: If we use +309, we get +2 ÷ 309 ÷ 12 = positive result. Only negative numbers will make the final result negative when starting with +2.

Q: What if I picked a different negative number?

Any negative number would make the inequality true! But $ -40 $ is the only negative option given in the answer choices, making it the correct selection.

Q: Why is the final result so small?

We're dividing +2 by two numbers: first by -40, then by +12. This creates a very small fraction: $ \frac{2}{-40 \times 12} = \frac{-1}{240} $, which is still less than 0!

Sign Determination with Division Inequalities

Select the compatible sign for the following expression:

$+2:?:+12<0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the missing value

00:05 Find the number signs

00:17 Positive divided by negative always equals negative

00:24 Negative divided by positive always equals negative

00:29 Therefore the missing value must be negative

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

Select the compatible sign for the following expression:

$+2:?:+12<0$

Step-by-step solution

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

The exercise looks like this:

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

If we solve the equation from left to right, we observe that we first divide a positive number by an unidentified integer:

$+:\text{?}$

Since the next operation is also division by a positive number, we need a negative number in order for the result to be less than 0:

$+:-:+=$

$-:+=-$

$- < 0$

Therefore the answer is $-40$

Final Answer

$-40$

Key Points to Remember

Essential concepts to master this topic

Rule: Division by negative changes positive to negative result
Technique: Work left to right: +2 ÷ (-40) ÷ (+12) = negative
Check: Verify final result is less than zero: -1/240 < 0 ✓

Common Mistakes

Avoid these frequent errors

Ignoring the order of operations in division chains
Don't just focus on making any negative result = wrong answer choice! Division operations must be performed left to right, so +2 ÷ ? ÷ +12 means first divide +2 by the unknown, then divide that result by +12. Always follow proper order of operations.

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 unknown number need to be negative?

Since we start with +2 (positive) and need a final result less than 0, we need the middle operation to flip the sign. Dividing a positive by a negative gives a negative result.

How do I work through division chains like this?

Work left to right! First: +2 ÷ (-40) = -1/20. Then: (-1/20) ÷ (+12) = -1/240. Since -1/240 < 0, our answer works!

Could any of the other answer choices work?

Let's check: If we use +309, we get +2 ÷ 309 ÷ 12 = positive result. Only negative numbers will make the final result negative when starting with +2.

What if I picked a different negative number?

Any negative number would make the inequality true! But $-40$ is the only negative option given in the answer choices, making it the correct selection.

Why is the final result so small?

We're dividing +2 by two numbers: first by -40, then by +12. This creates a very small fraction: $\frac{2}{-40 \times 12} = \frac{-1}{240}$ , which is still less than 0!

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