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

Solve the following exercise:

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

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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