Solve (-2²)-(-3¾): Order of Operations with Negative Numbers

Q: What's the difference between -2² and (-2)²?

Great question! -2² means "negative of 2 squared" = -(2²) = -4. But (-2)² means "negative 2, all squared" = (-2)×(-2) = +4. The parentheses make a huge difference!

Q: Why do I need to convert the mixed number to an improper fraction?

Converting $ -3\frac{3}{4} $ to $ -\frac{15}{4} $ makes subtraction much easier! It's hard to subtract mixed numbers directly, but fractions with the same denominator are simple to work with.

Q: How do I remember the order of operations with negative signs?

Think PEMDAS! Exponents come before addition/subtraction. So in -2², do the exponent first (2² = 4), then apply the negative sign (-4). The negative isn't part of what gets squared.

Q: What does subtracting a negative number really mean?

Subtracting a negative is the same as adding a positive! So $ -(-\frac{15}{4}) $ becomes $ +\frac{15}{4} $. Think "two negatives make a positive."

Q: How do I add fractions with different denominators?

Convert both fractions to have the same denominator! Here, -4 becomes $ -\frac{16}{4} $, so you can add $ -\frac{16}{4} + \frac{15}{4} = -\frac{1}{4} $.

Exponent Notation with Mixed Number Subtraction

$(-2^2)-(-3\frac{3}{4})=$

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Understand the problem

$(-2^2)-(-3\frac{3}{4})=$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Simplify $(-2^2)$ .
Step 2: Convert $-3\frac{3}{4}$ to an improper fraction.
Step 3: Subtract the results from Step 1 and Step 2.

Now, let's work through each step:
Step 1: $-2^2$ means square the 2 first and then apply the negative: $-2^2 = -(2^2) = -4$ .

Step 2: Convert $-3\frac{3}{4}$ into an improper fraction:
A mixed fraction $-3\frac{3}{4}$ can be represented as $-\left(3 + \frac{3}{4}\right) = -\left(\frac{12}{4} + \frac{3}{4}\right) = -\frac{15}{4}$ .

Step 3: Subtract the results:
Subtract $-(-\frac{15}{4})$ from $-4$ :
This is equivalent to $-4 + \frac{15}{4}$ . To add these, convert $-4$ to a fraction with the same denominator: $-4 = -\frac{16}{4}$ .
Now, $-\frac{16}{4} + \frac{15}{4} = -\frac{16 - 15}{4} = -\frac{1}{4}$ .

Therefore, the solution to the problem is $-\frac{1}{4}$ .

Final Answer

$-\frac{1}{4}$

Key Points to Remember

Essential concepts to master this topic

Order: Evaluate exponents before applying negative signs
Technique: Convert $-3\frac{3}{4}$ to $-\frac{15}{4}$ for easier calculation
Check: Verify $-\frac{16}{4} + \frac{15}{4} = -\frac{1}{4}$ ✓

Common Mistakes

Avoid these frequent errors

Treating -2² as (-2)²
Don't calculate (-2)² = 4 instead of -2² = -4! The negative sign is NOT part of the base being squared. Always square the number first, then apply the negative: -2² = -(2²) = -4.

Practice Quiz

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What is the additive inverse number of $$ 87 $$

FAQ

Everything you need to know about this question

What's the difference between -2² and (-2)²?

Great question! -2² means "negative of 2 squared" = -(2²) = -4. But (-2)² means "negative 2, all squared" = (-2)×(-2) = +4. The parentheses make a huge difference!

Why do I need to convert the mixed number to an improper fraction?

Converting $-3\frac{3}{4}$ to $-\frac{15}{4}$ makes subtraction much easier! It's hard to subtract mixed numbers directly, but fractions with the same denominator are simple to work with.

How do I remember the order of operations with negative signs?

Think PEMDAS! Exponents come before addition/subtraction. So in -2², do the exponent first (2² = 4), then apply the negative sign (-4). The negative isn't part of what gets squared.

What does subtracting a negative number really mean?

Subtracting a negative is the same as adding a positive! So $-(-\frac{15}{4})$ becomes $+\frac{15}{4}$ . Think "two negatives make a positive."

How do I add fractions with different denominators?

Convert both fractions to have the same denominator! Here, -4 becomes $-\frac{16}{4}$ , so you can add $-\frac{16}{4} + \frac{15}{4} = -\frac{1}{4}$ .

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