Solve (-4)+2+(-3)+(-5): Adding Multiple Negative Numbers

Integer Addition with Multiple Negative Terms

(4)+2+(3)+(5)= (-4)+2+(-3)+(-5)=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 The number is intended, and negative
00:07 The negative direction on the axis is left, so we'll take 4 to the left
00:13 The number is intended, and positive
00:17 The positive direction on the axis is right, so we'll take 2 to the right
00:24 The number is intended, and negative
00:30 The negative direction on the axis is left, so we'll take 3 to the left
00:37 The number is intended, and negative
00:42 The negative direction on the axis is left, so we'll take 5 to the left
00:47 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)+2+(3)+(5)= (-4)+2+(-3)+(-5)=

2

Step-by-step solution

Let's start with the leftmost exercise:

(4)+2 (-4)+2

We'll locate negative 4 on the axis and move two steps to the right, where each step represents one whole number:

-6-6-6-5-5-5-4-4-4-3-3-3-2-2-2-1-1-1000111222333

We can see that we've reached negative 2.

Now we'll get the exercise:

(2)+(3)+(5)= (-2)+(-3)+(-5)=

Let's focus on the exercise:

(2)+(3) (-2)+(-3)

We'll locate negative 2 on the axis and move three steps to the left, where each step represents one whole number:

-6-6-6-5-5-5-4-4-4-3-3-3-2-2-2-1-1-1000111222333

We can see that we've reached negative 5.

Now we'll get the exercise:

(5)+(5)= (-5)+(-5)=

We'll locate negative 5 on the axis and move five steps to the left, where each step represents one whole number:

-6-6-6-5-5-5-4-4-4-3-3-3-2-2-2-1-1-1000111-7-7-7-8-8-8-9-9-9-10-10-10

We can see that we've reached negative 10.

3

Final Answer

10 -10

Key Points to Remember

Essential concepts to master this topic
  • Direction Rule: Adding negatives means moving left on number line
  • Technique: (4)+2=2 (-4) + 2 = -2 , then continue with remaining terms
  • Check: Count total negative and positive values: -12 + 2 = -10 ✓

Common Mistakes

Avoid these frequent errors
  • Treating negative signs as subtraction
    Don't change (-4) + 2 + (-3) + (-5) into 4 - 2 - 3 - 5 = wrong signs! This ignores the actual values and their signs. Always keep negative numbers as negative and follow left-to-right addition rules.

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 do I keep getting positive answers when the result should be negative?

+

You might be ignoring the negative signs or treating them as subtraction. Remember: (4) (-4) means negative four, not subtract four!

Should I add all the negatives first, then the positives?

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You can group them for easier calculation! Add negatives: (4)+(3)+(5)=12 (-4) + (-3) + (-5) = -12 , then add the positive: 12+2=10 -12 + 2 = -10 .

How do I visualize this on a number line?

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Start at -4, move right 2 steps to get -2, then move left 3 steps to get -5, finally move left 5 steps to reach -10.

What's the difference between +(-3) and just -3?

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There's no difference! Both mean adding negative three. The parentheses just make it clearer that we're adding a negative number.

Can I change the order of the numbers?

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Yes! Addition is commutative, so (4)+2+(3)+(5) (-4) + 2 + (-3) + (-5) equals 2+(4)+(5)+(3) 2 + (-4) + (-5) + (-3) . The result is always -10.

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