Solve: (-30) + (-2) + 30 + (-5) Step by Step

Integer Addition with Positive and Negative Numbers

(30)+(2)+30+(5)= (-30)+(-2)+30+(-5)=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:09 We'll use the commutative law to arrange the exercise in a way that's convenient to solve
00:18 Let's simplify what we can
00:35 The number is intentional, and negative
00:40 Let's start from point (-2) on the axis
00:42 The negative direction on the axis is to the left, so we'll take 5 to the left
01:00 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

(30)+(2)+30+(5)= (-30)+(-2)+30+(-5)=

2

Step-by-step solution

First, let's organize the exercise in a way that will make it easier and more convenient to solve.

Notice that the number 30 appears twice in the exercise, so let's start with it:

(30)+30+(2)+(5)= (-30)+30+(-2)+(-5)=

Let's look at the exercise:

30+30 -30+30

Since we move left from zero to minus 30, and then return right 30 steps, we will arrive at the same number we started from: 0

-30-30-30000+30

Now let's continue the exercise in the following way:

0+(2)+(5)= 0+(-2)+(-5)=

We'll locate the number minus 2 on the number line, and move left five steps where each step represents one whole number:

-5-5-5000-1-1-1-2-2-2-3-3-3-4-4-4222111-8-8-8-7-7-7-6-6-6

We can see that we arrived at minus 7.

3

Final Answer

7 -7

Key Points to Remember

Essential concepts to master this topic
  • Rule: Group opposites first to simplify calculations
  • Technique: (-30) + 30 = 0, then 0 + (-2) + (-5) = -7
  • Check: Count total: negative values (-30, -2, -5) minus positive (30) = -7 ✓

Common Mistakes

Avoid these frequent errors
  • Adding all numbers without considering signs
    Don't add 30 + 2 + 30 + 5 = 67 ignoring the negative signs! This treats all numbers as positive and gives completely wrong results. Always identify which numbers are negative first, then combine opposites like (-30) and (+30) to get 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 should I group (-30) and 30 together first?

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These are opposites that cancel each other out! When you add a number and its negative, you always get zero. This makes the problem much simpler: (30)+30=0 (-30) + 30 = 0 .

What does it mean to move left and right on a number line?

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Moving left means subtracting (going to smaller numbers), and moving right means adding (going to larger numbers). Negative numbers make you move left from your starting position.

How do I add multiple negative numbers together?

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When adding negatives, you're moving further left on the number line. So (2)+(5)=7 (-2) + (-5) = -7 because you move 2 steps left, then 5 more steps left.

Can I rearrange the numbers in any order?

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Yes! Addition is commutative, so you can rearrange terms to make calculations easier. Grouping opposites like (30)+30 (-30) + 30 first is a smart strategy.

What if I get confused by all the parentheses?

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The parentheses around negative numbers like (30) (-30) just show that the whole number is negative. You can think of it as "negative 30" instead of "subtract 30."

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