Evaluate the Expression: 10-(-2)-3×4-(-4) Using Order of Operations

Q: Why does -(-2) become +2?

The rule is -(-x) = +x. Think of it as 'the opposite of negative 2 is positive 2'. Two negative signs cancel each other out!

Q: Do I handle multiplication before dealing with negative signs?

No! Handle negative signs first, then follow PEMDAS. So $ -(-2) $ becomes $ +2 $ before you do any multiplication.

Q: What if I get confused with all the negative signs?

Write it step by step! First, convert all -(-x) to +x. Then rewrite the expression clearly before following order of operations.

Q: How do I compare the final results?

Calculate each side completely first. Left side: $ 10+2-12 = 0 $. Right side: $ +4 = 4 $. Since 0 <.

Q: Why is 3×4 = 12 in this problem?

After converting negative signs, the left side becomes $ 10+2-3×4 $. Following order of operations, multiply first: $ 3×4 = 12 $, then work left to right.

Order of Operations with Negative Number Rules

$10-(-2)-3?4-(-4)$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the appropriate sign

00:03 Negative times negative is always positive

00:07 Let's open the parentheses

00:16 Let's calculate one operation

00:24 Let's find point (12) on the axis

00:27 Positive times negative is always negative

00:31 Let's take 3 jumps left (to the negative side) on the axis

00:41 This is the solution for the left side, now let's calculate the right side

00:45 Negative times negative is always positive

00:49 Let's open the parentheses

00:53 This is the solution for the right side

01:01 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

$10-(-2)-3?4-(-4)$

Step-by-step solution

First we need to remember the following laws:

$-(-x)=+x$

$+(-x)=-x$

We'll solve the left side first.

Let's rewrite the expression in the appropriate form:

$10+2-3=$

Next, we'll solve the exercise from left to right:

$10+2=12$

$12-3=9$

Now let's solve the right-hand side, using the laws we reminded ourselves of earlier.

We'll then rewrite the expression in the appropriate form and solve:

$4+4=8$

Since the left-hand side is larger, the appropriate sign will be:

$9 > 8$

Final Answer

$>$

Key Points to Remember

Essential concepts to master this topic

Rule: Apply negative signs before following PEMDAS order
Technique: Convert -(-2) to +2 and -(-4) to +4 first
Check: Left side: 10+2-3×4 = 0, Right side: -(-4) = +4, so 0 < 4 ✓

Common Mistakes

Avoid these frequent errors

Ignoring negative sign rules during calculations
Don't treat -(-2) as just -2 = wrong sign changes throughout! This creates errors in every step. Always remember that -(-x) = +x before applying order of operations.

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 -(-2) become +2?

The rule is -(-x) = +x. Think of it as 'the opposite of negative 2 is positive 2'. Two negative signs cancel each other out!

Do I handle multiplication before dealing with negative signs?

No! Handle negative signs first, then follow PEMDAS. So $-(-2)$ becomes $+2$ before you do any multiplication.

What if I get confused with all the negative signs?

Write it step by step! First, convert all -(-x) to +x. Then rewrite the expression clearly before following order of operations.

How do I compare the final results?

Calculate each side completely first. Left side: $10+2-12 = 0$ . Right side: $+4 = 4$ . Since 0 < 4, the answer is <.

Why is 3×4 = 12 in this problem?

After converting negative signs, the left side becomes $10+2-3×4$ . Following order of operations, multiply first: $3×4 = 12$ , then work left to right.

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Evaluate the Expression: 10-(-2)-3×4-(-4) Using Order of Operations

Order of Operations with Negative Number Rules

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why does -(-2) become +2?

Do I handle multiplication before dealing with negative signs?

What if I get confused with all the negative signs?

How do I compare the final results?

Why is 3×4 = 12 in this problem?

🌟 Unlock Your Math Potential

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