Solve: (-3) + (-4) + (-7) ? -15 - Finding the Missing Operation

Integer Addition with Comparison Operations

Fill in the missing symbol (?):

(3)+(4)+(7)?15 (-3)+(-4)+(-7)\text{?}-15

❤️ 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
00:08 First, we need to choose the right sign.
00:12 Let's begin at point negative 3 on the number line.
00:16 Notice, this number is negative.
00:19 For negative direction, move 4 steps to the left.
00:26 Again, this is a negative number.
00:31 So, move 7 more steps to the left.
00:40 And you've solved for the left side!
00:47 Now, let's find the two solutions on the line.
00:51 On the left means going further from zero, making it smaller.
00:55 And that's how we solve the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Fill in the missing symbol (?):

(3)+(4)+(7)?15 (-3)+(-4)+(-7)\text{?}-15

2

Step-by-step solution

Let's solve the equation:

(3)+(4)+(7)= (-3)+(-4)+(-7)=

We'll first need to locate -3 on the number line and move four steps to the left (since minus 4 is less than zero):

-15-14-13-12-11-10-9-8-7-6-5-4-3

This will bring us to the number -7.

Now let's move seven steps to the left (since minus 7 is less than zero):

-15-14-13-12-11-10-9-8-7-6-5-4-3

This leaves us at the number -13..

The solution to the equation is:

(3)+(4)+(7)=14 (-3)+(-4)+(-7)=-14

Therefore, the missing sign must be:

14>15 -14>-15

3

Final Answer

> >

Key Points to Remember

Essential concepts to master this topic
  • Rule: When adding negative numbers, combine their absolute values
  • Technique: (-3) + (-4) + (-7) = -(3 + 4 + 7) = -14
  • Check: Compare -14 and -15 on number line: -14 > -15 ✓

Common Mistakes

Avoid these frequent errors
  • Confusing which negative number is greater
    Don't think -15 > -14 because 15 > 14 = wrong comparison! Negative numbers work opposite to positive numbers on the number line. Always remember that numbers closer to zero are greater than numbers farther from zero.

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 is -14 greater than -15 when 14 is less than 15?

+

On the number line, negative numbers get smaller as you move left. Since -14 is to the right of -15, we have -14 > -15. Think of it as being closer to zero!

How do I add multiple negative numbers quickly?

+

Add all the positive values first: 3 + 4 + 7 = 14. Then make the result negative: -14. This saves time and reduces errors!

What if I get confused about the comparison symbols?

+

Remember: the symbol always points to the smaller number. So -14 > -15 means -14 is greater, and the symbol points toward the smaller -15.

Can I use a number line to check my work?

+

Absolutely! Number lines are perfect for this. Plot both numbers and see which one is farther to the right - that's the greater number.

Why do we write negative numbers in parentheses?

+

Parentheses like (-3) help avoid confusion with subtraction. It clearly shows we mean negative three as a number, not subtracting three.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Signed Numbers (Positive and Negative) 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