Sequential Division Problem: Finding the Sign in -12:-8 for Positive Result

Q: Why does negative divided by negative equal positive?

Think of division as repeated subtraction. When you divide $ -12 ÷ (-8) $, you're asking "how many times does -8 go into -12?" The answer is 1.5 times in the positive direction!

Q: How do I know what number to insert in the blank?

First calculate $ -12 ÷ (-8) = +1.5 $. Then you need a positive number that when divided by 1.5 gives a positive result. Any positive number works, like $ +\frac{1}{90} $!

Q: Can the missing number be negative?

No! Since $ -12 ÷ (-8) = +1.5 $ (positive), dividing by a negative number would give a negative result, but we need the final answer to be greater than zero.

Q: Why is the answer specifically +1/90?

The answer $ +\frac{1}{90} $ is just one example of a positive number that works. You could use +1, +2, +0.5, or any positive number - they all make the final result positive!

Q: What does the > 0 mean in this problem?

The $ > 0 $ symbol means "greater than zero" or positive. It's telling you that the final result of the entire expression must be a positive number.

Division Sign Rules with Sequential Operations

Insert the appropriate sign for the following expression:

$-12:-8:?>0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the missing value

00:06 Negative divided by negative is always positive

00:18 Let's assume the missing value is positive

00:24 Positive divided by positive is always positive

00:28 Positive is greater than 0, therefore the missing value must be positive

00:31 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

Insert the appropriate sign for the following expression:

$-12:-8:?>0$

Step-by-step solution

Let's begin by observing the exercise on the left side whilst paying particular attention to the plus and minus signs.

The exercise looks like this:

$-:-:?=$

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

$-:-=+$

The resulting exercise is as follows:

$+:\text{?=}$

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

Hence:

$+:+=+$

$+ > 0$

Therefore the answer is $+\frac{1}{90}$

Final Answer

$+\frac{1}{90}$

Key Points to Remember

Essential concepts to master this topic

Rule: Negative divided by negative always equals positive
Technique: Work left to right: $-12 ÷ (-8) = +1.5$
Check: Final result must be positive: $+1.5 ÷ (+\frac{1}{90}) = +135 > 0$ ✓

Common Mistakes

Avoid these frequent errors

Ignoring the order of operations in sequential division
Don't try to determine the final sign without calculating step by step = wrong logic! You must first solve $-12 ÷ (-8) = +1.5$ , then determine what positive number makes the final result positive. Always work sequentially from left to right.

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 negative divided by negative equal positive?

Think of division as repeated subtraction. When you divide $-12 ÷ (-8)$ , you're asking "how many times does -8 go into -12?" The answer is 1.5 times in the positive direction!

How do I know what number to insert in the blank?

First calculate $-12 ÷ (-8) = +1.5$ . Then you need a positive number that when divided by 1.5 gives a positive result. Any positive number works, like $+\frac{1}{90}$ !

Can the missing number be negative?

No! Since $-12 ÷ (-8) = +1.5$ (positive), dividing by a negative number would give a negative result, but we need the final answer to be greater than zero.

Why is the answer specifically +1/90?

The answer $+\frac{1}{90}$ is just one example of a positive number that works. You could use +1, +2, +0.5, or any positive number - they all make the final result positive!

What does the > 0 mean in this problem?

The $> 0$ symbol means "greater than zero" or positive. It's telling you that the final result of the entire expression must be a positive number.

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