Order these integers on the number line below: -3, 0, -6, -10, 4, 5; Add these integers: -7 + 2; -13 + 7; 14 + 8.

Understand the Problem

The question involves two tasks: first, ordering a set of integers on a number line, and second, performing basic addition on two addition problems involving integers. The integers involved are negative and positive, indicating a need for an understanding of their placement on the number line and basic arithmetic operations.

Answer

The ordered integers are: $$ -10, -6, -3, 0, 4, 5, 6 $$; The sums are: $-5$, $-6$, $22$.

Steps to Solve

Order the integers on the number line To order the integers $-3, 0, -6, -10, 4, 5, 6$, we place them from the smallest to the largest:

The smallest number is $-10$.
Next is $-6$.
Then $-3$.
After that is $0$.
Next, we have $4$.
Followed by $5$.
Finally, the largest number is $6$.

So, the ordered sequence is: $$ -10, -6, -3, 0, 4, 5, 6 $$

Perform the first addition problem The first addition problem is $-7 + 2$. To solve it, we can think of $-7$ as moving left on the number line and $+2$ as moving right:

Start at $-7$ and move right $2$ units, so: $$ -7 + 2 = -5 $$

Perform the second addition problem The second addition problem is $-13 + 7$. Using the same approach:

Start at $-13$ and move right $7$ units: $$ -13 + 7 = -6 $$

Perform the third addition problem The last addition problem is $14 + 8$. This is straightforward as both numbers are positive: $$ 14 + 8 = 22 $$

The ordered integers are: $$ -10, -6, -3, 0, 4, 5, 6 $$

The results of the additions are:

$-7 + 2 = -5$
$-13 + 7 = -6$
$14 + 8 = 22$

More Information

In ordering integers, the number line helps visualize their placement, which is crucial for understanding negative and positive values. The addition of negative and positive integers requires recognizing how their signs affect the sum.

Tips

Confusing the direction of movement on the number line when adding negative numbers.
Failing to start from the correct number when performing multi-step additions.

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