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

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

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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