Solve the Expression: Finding the Correct Operator in -53 ? +3 > 0

Q: Why does dividing a negative by a negative give a positive?

Think of division as "how many groups" - when you divide -53 by $ -\frac{1}{4} $, you're asking "how many $ -\frac{1}{4} $ groups fit in -53?" The answer is positive: 212 groups!

Q: How do I know which operation symbol to test?

The colon (:) typically means division in many countries. So $ -53:?:+3 $ means $ -53 ÷ ? + 3 $. Always check what notation your textbook uses!

Q: Why can't the answer be +1 or +39?

Test them! $ -53 ÷ 1 + 3 = -50 $ (negative, not >0). $ -53 ÷ 39 + 3 ≈ -1.36 + 3 = 1.64 $ (this would work, but +39 isn't exact - check your calculation!)

Q: What if I get confused with the inequality sign?

Remember: $ > 0 $ means "greater than zero" or positive. Your final result after all operations must be a positive number. Work left to right, then check if your result is positive.

Q: How do I handle fractions in division?

Dividing by a fraction means multiplying by its reciprocal. So $ -53 ÷ (-\frac{1}{4}) = -53 × (-4) = 212 $. The negative signs cancel out!

Order of Operations with Inequality Signs

Insert the compatible sign for the following expression:

$-53:?:+3>0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Complete the unknown

00:05 Let's assume the unknown is positive

00:14 Negative divided by positive is always negative

00:25 Accordingly, the answer would be less than 0 so it doesn't fit

00:32 Therefore the unknown must be negative

00:36 Negative divided by negative is always positive

00:41 Positive divided by positive is always positive

00:44 Therefore the unknown must be negative

00:47 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 compatible sign for the following expression:

$-53:?:+3>0$

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:

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

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

$-:\text{?}$

Our result needs to be greater than zero, therefore our first operation must give us a positive number, so that in the final operation the resulting number will be positive.

Therefore:

$-:-:+=$

$+:+=+$

$+ > 0$

Therefore the answer is $-\frac{1}{4}$

Final Answer

$-\frac{1}{4}$

Key Points to Remember

Essential concepts to master this topic

Sign Analysis: Dividing negative by negative gives positive result
Technique: Check: $-53 ÷ (-\frac{1}{4}) + 3 = 212 + 3 = 215 > 0$
Verification: Test each answer choice by substituting into the full expression ✓

Common Mistakes

Avoid these frequent errors

Ignoring the sign when dividing negative numbers
Don't assume dividing -53 by any number automatically gives a negative result = wrong answer! Dividing negative by negative gives positive. Always consider both the sign and magnitude of the missing value.

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 dividing a negative by a negative give a positive?

Think of division as "how many groups" - when you divide -53 by $-\frac{1}{4}$ , you're asking "how many $-\frac{1}{4}$ groups fit in -53?" The answer is positive: 212 groups!

How do I know which operation symbol to test?

The colon (:) typically means division in many countries. So $-53:?:+3$ means $-53 ÷ ? + 3$ . Always check what notation your textbook uses!

Why can't the answer be +1 or +39?

Test them! $-53 ÷ 1 + 3 = -50$ (negative, not >0). $-53 ÷ 39 + 3 ≈ -1.36 + 3 = 1.64$ (this would work, but +39 isn't exact - check your calculation!)

What if I get confused with the inequality sign?

Remember: $> 0$ means "greater than zero" or positive. Your final result after all operations must be a positive number. Work left to right, then check if your result is positive.

How do I handle fractions in division?

Dividing by a fraction means multiplying by its reciprocal. So $-53 ÷ (-\frac{1}{4}) = -53 × (-4) = 212$ . The negative signs cancel out!

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