Solve Division Inequality: -73 ÷ ? < 0

Q: Why can't the answer be 0?

Division by zero is undefined in mathematics! You can never divide any number by 0, so 0 is not a valid option for any division problem.

Q: How do I remember the sign rules for division?

Think of it like multiplication: same signs give positive, different signs give negative. So negative ÷ positive = negative, but negative ÷ negative = positive!

Q: What if I chose -1 as the answer?

$ -73 ÷ (-1) = +73 $, which is positive and greater than 0! This doesn't satisfy our inequality \( .

Q: Does the size of the positive number matter?

No! Any positive number will work as the divisor. Whether it's 1, 4, 100, or 0.5, dividing -73 by any positive number always gives a negative result.

Q: How can I check my answer quickly?

Just do the division: $ -73 ÷ 4 = -18.25 $. Since -18.25 , the inequality is satisfied! Always verify your final result.

Division Inequalities with Negative Numbers

$-73:?<0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the missing value

00:04 Negative divided by positive always equals negative

00:14 Therefore the missing value must be positive

00:19 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

$-73:?<0$

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:

$-:\text{?}=$

In other words, we need to divide by a number that will give us a result smaller than 0, therefore:

$-:+=-$

$- < 0$

So the answer is $+4$

Final Answer

$+4$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Negative divided by positive always gives negative result
Technique: For $-73 ÷ ? < 0$ , divisor must be positive
Check: Verify $-73 ÷ 4 = -18.25 < 0$ ✓

Common Mistakes

Avoid these frequent errors

Choosing negative divisors thinking they make the result more negative
Don't pick negative numbers like -4 because -73 ÷ (-4) = +18.25 > 0! Dividing two negatives gives a positive result, which breaks the inequality. Always remember: negative ÷ positive = negative, but negative ÷ negative = positive.

Practice Quiz

Test your knowledge with interactive questions

Convert $\frac{7}{2}$ into its reciprocal form:

FAQ

Everything you need to know about this question

Why can't the answer be 0?

Division by zero is undefined in mathematics! You can never divide any number by 0, so 0 is not a valid option for any division problem.

How do I remember the sign rules for division?

Think of it like multiplication: same signs give positive, different signs give negative. So negative ÷ positive = negative, but negative ÷ negative = positive!

What if I chose -1 as the answer?

$-73 ÷ (-1) = +73$ , which is positive and greater than 0! This doesn't satisfy our inequality $< 0$ .

Does the size of the positive number matter?

No! Any positive number will work as the divisor. Whether it's 1, 4, 100, or 0.5, dividing -73 by any positive number always gives a negative result.

How can I check my answer quickly?

Just do the division: $-73 ÷ 4 = -18.25$ . Since -18.25 < 0, the inequality is satisfied! Always verify your final result.

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