Solve Division Inequality: -45 ÷ x < 0

Q: Why does dividing -45 by a positive number give a negative result?

Because of sign rules! When you divide a negative number by a positive number, the result is always negative. Think: $ -45 \div 5 = -9 $

Q: What would happen if I chose a negative number instead?

If you divide $ -45 $ by a negative number, you'd get a positive result! For example: $ -45 \div (-3) = 15 > 0 $, which doesn't satisfy our inequality.

Q: Can zero be the answer?

No! You cannot divide by zero - it's undefined in mathematics. Also, zero wouldn't satisfy our inequality since $ -45 \div 0 $ doesn't exist.

Q: Is +78 the only correct answer?

Actually, any positive number would work! +78 is just one example. The solution is all positive numbers: $ x > 0 $

Division Inequalities with Sign Analysis

$-45:?<0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the missing value

00:08 Negative divided by positive always equals negative

00:16 Negative is less than 0, so it fits

00:20 Therefore the missing value must be negative

00:23 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

$-45:?<0$

Step-by-step solution

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

The exercise looks like this:

$-:\text{?}=$

Our result needs to be less than zero, and therefore we need a positive number in order to get a negative result.

Therefore:

$-:+=-$

$- < 0$

So the answer is $+78$

Final Answer

$+78$

Key Points to Remember

Essential concepts to master this topic

Rule: Negative divided by positive gives negative result
Technique: For $-45 \div x < 0$ , need x > 0
Check: $-45 \div 78 = -0.58 < 0$ ✓

Common Mistakes

Avoid these frequent errors

Ignoring the sign rules when dividing
Don't just pick any number without considering signs = wrong inequality direction! When dividing a negative by a positive, you always get negative. Always analyze: negative ÷ positive = negative, which satisfies < 0.

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 -45 by a positive number give a negative result?

Because of sign rules! When you divide a negative number by a positive number, the result is always negative. Think: $-45 \div 5 = -9$

What would happen if I chose a negative number instead?

If you divide $-45$ by a negative number, you'd get a positive result! For example: $-45 \div (-3) = 15 > 0$ , which doesn't satisfy our inequality.

How do I know which sign to choose for the unknown?

Look at what the inequality requires! Since we need the result to be less than zero, and we're dividing -45, we need the divisor to be positive to get a negative quotient.

Can zero be the answer?

No! You cannot divide by zero - it's undefined in mathematics. Also, zero wouldn't satisfy our inequality since $-45 \div 0$ doesn't exist.

Is +78 the only correct answer?

Actually, any positive number would work! +78 is just one example. The solution is all positive numbers: $x > 0$

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