Solve -4-((-14)+(-23)): Order of Operations with Negative Numbers

Order of Operations with Nested Parentheses

4((14)+(23))= -4-((-14)+(-23))=

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Always solve parentheses first
00:06 Note, positive times negative will always be negative
00:12 Let's solve the parentheses first
00:22 Note, negative times negative will always be positive
00:28 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

4((14)+(23))= -4-((-14)+(-23))=

2

Step-by-step solution

According to the order of operations, first we solve the exercise within parentheses:

Remember that the product of a positive and a negative results in a negative, therefore:

+(23)=23 +(-23)=-23

Now we obtain:

4(1423)= -4-(-14-23)=

We solve the exercise within parentheses:

4(37)= -4-(-37)=

Remember that the product of a negative and a negative results in a positive, therefore:

(37)=+37 -(-37)=+37

Now we obtain the exercise:

4+37=33 -4+37=33

3

Final Answer

33 33

Key Points to Remember

Essential concepts to master this topic
  • Rule: Solve innermost parentheses first, then work outward systematically
  • Technique: Convert (14)+(23) (-14)+(-23) to 37 -37 before subtracting
  • Check: Verify 4(37)=4+37=33 -4-(-37) = -4+37 = 33

Common Mistakes

Avoid these frequent errors
  • Ignoring parentheses and working left to right
    Don't solve -4-(-14)+(-23) = -4+14-23 = -13! This skips the parentheses rule and gives the wrong order. Always solve what's inside parentheses completely first, then apply the subtraction to that result.

Practice Quiz

Test your knowledge with interactive questions

\( 100-(5+55)= \)

FAQ

Everything you need to know about this question

Why do I solve the parentheses first when subtraction comes before them?

+

Parentheses always come first in order of operations (PEMDAS)! The subtraction sign outside waits until you've completely solved what's inside the parentheses.

How does subtracting a negative number work exactly?

+

Subtracting a negative is the same as adding a positive! Think: "minus a negative equals plus a positive". So 4(37)=4+37 -4-(-37) = -4+37 .

What if there are multiple sets of parentheses?

+

Work from the innermost parentheses outward, one set at a time. Solve each completely before moving to the next outer level.

Why is adding two negative numbers different from subtracting them?

+

When you add negatives like (14)+(23) (-14)+(-23) , you get more negative. When you subtract a negative, you change direction and add the positive value instead.

How can I remember the double negative rule?

+

Think of it like directions: "negative negative = positive". Two negatives cancel each other out, just like "don't not do it" means "do it"!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Commutative, Distributive and Associative Properties questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations