Solve: (-10) + (-3) + 4 + (-12) - Adding Multiple Positive and Negative Numbers

Integer Addition with Mixed Signs

Solve the following problem:

(10)+(3)+4+(12)= (-10)+(-3)+4+(-12)=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:07 Let's start from point (-10) on the axis
00:11 The number is directed and negative
00:14 The negative direction on the axis is left, so we'll go 3 left
00:27 Now we'll continue from this point on the axis (-13)
00:31 The number is directed and positive
00:36 The positive direction on the axis is right, so we'll go 4 right
00:54 Now we'll continue from this point on the axis (9)
00:59 The number is directed and negative
01:03 The negative direction on the axis is left, so we'll go 12 left
01:19 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

Solve the following problem:

(10)+(3)+4+(12)= (-10)+(-3)+4+(-12)=

2

Step-by-step solution

Begin by observing the first exercise:

(10)+(3) (-10)+(-3)

We will locate the number minus 10 on the number line, and move three steps to the left, where each step represents one whole number:

-16-16-16-11-11-11-12-12-12-13-13-13-14-14-14-15-15-15-9-9-9-10-10-10

We reached the number minus 13.

Obtaining the following exercise:

(13)+4+(12)= (-13)+4+(-12)=

The next exercise is:

(13)+4 (-13)+4

Locate the number minus 13 on the number line, and move four steps to the right where each step represents one whole number:

-16-16-16-11-11-11-12-12-12-13-13-13-14-14-14-15-15-15-9-9-9-10-10-10

We reached the number minus 9.

Obtaining the following exercise:

(9)+(12)= (-9)+(-12)=

Locate the number minus 9 on the number line, and move twelve steps to the left where each step represents one whole number:

-16-16-16-11-11-11-12-12-12-13-13-13-14-14-14-15-15-15-9-9-9-10-10-10-21-21-21-20-20-20-19-19-19-18-18-18-17-17-17

We reached the number minus 21.

3

Final Answer

21 -21

Key Points to Remember

Essential concepts to master this topic
  • Addition Rule: Same signs add, different signs subtract and keep larger sign
  • Technique: Group negatives: (-10) + (-3) + (-12) = -25, then -25 + 4 = -21
  • Check: Count total negatives (-25) minus positives (4) equals -21 ✓

Common Mistakes

Avoid these frequent errors
  • Treating all numbers as positive
    Don't ignore negative signs and just add 10 + 3 + 4 + 12 = 29! This gives a positive result when the answer should be negative. Always pay attention to signs and group negative numbers first to see which sign dominates.

Practice Quiz

Test your knowledge with interactive questions

\( -5-(-2)= \)

-7-7-7-6-6-6-5-5-5-4-4-4-3-3-3-2-2-2-1-1-1000111222333444555666777

FAQ

Everything you need to know about this question

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

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You're probably ignoring the negative signs! Remember that (10) (-10) means negative 10, not positive. Count all your negatives first: -10, -3, and -12 total -25.

Should I work left to right or group similar signs?

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Both work, but grouping similar signs first is often easier! Add all negatives: (10)+(3)+(12)=25 (-10) + (-3) + (-12) = -25 , then add positives: 25+4=21 -25 + 4 = -21 .

How do I know if my final answer should be positive or negative?

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Look at which group is larger in absolute value. Here, the negatives total |-25| = 25, and positives total |4| = 4. Since 25 > 4, the answer takes the negative sign.

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

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There's no difference! Both represent negative three. The parentheses in (3) (-3) just make it clearer that the entire number is negative, especially in addition problems.

Can I use a number line to solve this?

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Absolutely! Start at 0, move left 10 spaces (for -10), left 3 more (for -3), right 4 spaces (for +4), then left 12 more (for -12). You'll end up at -21.

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