Solve Integer Expression: 4 + 3 + (-6) + (-9)

Integer Addition with Positive and Negative Numbers

4+3+(6)+(9)= 4+3+(-6)+(-9)=

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Step-by-step video solution

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00:00 Solve
00:03 The number is oriented and positive
00:07 The positive direction on the axis is to the right, so we'll take 4 to the right
00:13 The number is oriented and positive
00:16 The positive direction on the axis is to the right, so we'll take 3 to the right
00:22 The number is oriented and negative
00:25 The negative direction on the axis is to the left, so we'll take 6 to the left
00:36 The number is oriented and negative
00:39 The negative direction on the axis is to the left, so we'll take 9 to the left
00:51 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+3+(6)+(9)= 4+3+(-6)+(-9)=

2

Step-by-step solution

First, let's look at the first exercise:

4+3 4+3

We will locate the number 4 on the axis, and move right three steps, where each step represents a whole number in the following way:

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

We can see that we reached the number 7.

Now we get the exercise:

7+(6)+(9)= 7+(-6)+(-9)=

Let's look at the exercise:

7+(6)= 7+(-6)=

We will locate the number 7 on the axis, and move left six steps, where each step represents a whole number in the following way:

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

We can see that we reached the number 1.

Now we got the exercise:

1+(9)= 1+(-9)=

We will locate the number 1 on the axis, and move left nine steps, where each step represents a whole number in the following way:

-6-6-6-5-5-5-4-4-4-3-3-3-2-2-2-1-1-1000111222333-7-7-7-8-8-8-9-9-9

We can see that we reached the number minus 8.

3

Final Answer

8 -8

Key Points to Remember

Essential concepts to master this topic
  • Sign Rules: Adding a negative number is the same as subtracting
  • Method: 4+3=7 4 + 3 = 7 , then 7+(6)+(9)=715=8 7 + (-6) + (-9) = 7 - 15 = -8
  • Check: Count left/right moves on number line: 3 right, 15 left = 8 left from 0 ✓

Common Mistakes

Avoid these frequent errors
  • Treating all numbers as positive
    Don't ignore parentheses around negative numbers like (-6) and (-9) = 4 + 3 + 6 + 9 = 22! This treats subtraction as addition and gives the wrong sign. Always recognize that +(-n) means subtract n.

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 are some numbers in parentheses with negative signs?

+

The parentheses around (-6) and (-9) show these are negative numbers being added. Think of it as: "plus negative 6" which means the same as "minus 6".

How do I know whether to add or subtract each number?

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Look at the signs carefully! +4 +4 and +3 +3 are additions, while +(6) +(-6) and +(9) +(-9) are really subtractions.

Can I group the positive and negative numbers separately?

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Yes! Group positives: 4+3=7 4 + 3 = 7 . Group negatives: (6)+(9)=15 (-6) + (-9) = -15 . Then combine: 7+(15)=8 7 + (-15) = -8 .

How does the number line help me visualize this?

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Start at 0, move right for positive numbers (4, then 3 more), and move left for negative numbers (6 left, then 9 more left). You end up at -8!

What if I get confused about which direction to move?

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Remember: Positive = Right, Negative = Left. Adding a positive moves right, adding a negative moves left. The final position is your answer!

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