Solve -30 + 4 + (-8): Adding Multiple Negative Numbers

Integer Addition with Mixed Signs

Solve the following equation:

30+4+(8)= -30+4+(-8)=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's find the solution together.
00:13 First, imagine taking 4 steps to the right, on the positive side of the number line.
00:34 This will help us calculate the operation.
00:44 Next, let's take 8 steps to the left, towards the negative side of the number line.
01:04 And that's how we find the answer to the problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following equation:

30+4+(8)= -30+4+(-8)=

2

Step-by-step solution

Let's begin by locating negative 30 on the number line and moving 4 steps to the right (since 4 is greater than zero):

-27-27-27-28-28-28-29-29-29-30-30-30-31-31-31-32-32-32-33-33-33-34-34-34-35-35-35-36-36-36-37-37-37-38-38-38-39-39-39-40-40-40-26-26-26

We reach negative 26.

Resulting in the following exercise:

26+(8)= -26+(-8)=

Now let's locate negative 26 on the number line and move 8 steps to the left (since negative 8 is less than zero):

-27-27-27-28-28-28-29-29-29-30-30-30-31-31-31-32-32-32-33-33-33-34-34-34-35-35-35-36-36-36-37-37-37-38-38-38-39-39-39-40-40-40-26-26-26We reach negative 34

3

Final Answer

34 -34

Key Points to Remember

Essential concepts to master this topic
  • Order: Work from left to right when signs are mixed
  • Technique: First add -30 + 4 = -26, then add -26 + (-8)
  • Check: Starting at -30, move 4 right to -26, then 8 left to -34 ✓

Common Mistakes

Avoid these frequent errors
  • Adding absolute values and making result positive
    Don't add 30 + 4 + 8 = 42 and make it positive! This ignores the negative signs completely. Always keep track of signs: negative numbers stay negative, and adding a negative means moving further left on the number line.

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 don't I just add all the numbers and make the answer negative?

+

Because you have mixed signs! You must follow the rules: negative + positive means subtract, and negative + negative means add and keep negative. Don't ignore the individual signs of each number.

How do I know which direction to move on the number line?

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Positive numbers: move right. Negative numbers: move left. So +4 means 4 steps right, and +(-8) means 8 steps left from your current position.

Can I rearrange the numbers to make it easier?

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Yes! You can group negatives together: 30+(8)+4=38+4=34 -30 + (-8) + 4 = -38 + 4 = -34 . Addition is commutative, so order doesn't matter for the final answer.

What if I get confused about the signs?

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Use the number line method! Start at the first number and physically move step by step. Positive = right, negative = left. This visual approach prevents sign errors.

Is -34 really the right answer?

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Yes! Check it: 30+4=26 -30 + 4 = -26 , then 26+(8)=34 -26 + (-8) = -34 . You can also think: I owe 30,get30, get 4, so I owe 26,thenowe26, then owe 8 more = owe $34 total.

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