Addition and Subtraction of Directed Numbers: Solving the problem

First, let's remember the rule:

$+(+x)=+x$

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

$-8+12=$

We'll draw a number line and place minus 8 on it, then move 12 steps to the right:

Therefore:

$-8+12=4$

Let's remember the rule:

$-(+x)=-x$

Now let's write the exercise in the appropriate form:

$6-11=$

We'll locate the number 6 on the number line and from there we'll move 11 steps to the left:

The answer is minus 5.

Let's add 8 to the number line and move 12 steps to the right.

Note that our result is a positive number:

.

Then simple solve the exercise:

$8+12=20$

Let's locate -10 on the number line and move 13 steps to the left.

Let's note that our result is a negative number:

Let's remember the rule:

$-(+x)=-x$

Now let's write the exercise in the appropriate form and solve it:

$-10-13=-23$

Let's locate -8 on the number line and move 12 steps to the left.

Let's note that our result is a negative number:

Let's remember the rule:

Now let's write the exercise in the appropriate form and solve it:

$-8-12=-20$

Let's remember the rule:

$-(-x)=+x$

Now let's write the exercise in the appropriate form:

$-8+13=$

We'll use the substitution law and solve:

$13-8=5$

First, let's remember the rule:

$+(-x)=-x$

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

$-x-5x=$

We'll add negative $x$ to the number line and move 5 steps to the left:

Therefore, the solution is:

$-x-5x=-6x$

First we need to locate the number 8 on the number line and move 4.5 steps to the left from it:

Remember the rule:

$+(-x)=-x$

Now let's rewrite the problem in the appropriate form and solve:

$8-4.5=3.5$

First we need to remember the rule:

$-(-x)=+x$

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

$-x+6x=$

Then, we will write -x on the number line and move 6 steps to the right:

Therefore, the solution is:

$-x+6x=5x$

First, let's remember the rule:

$-(+x)=-x$

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

$-x-3x=$

We'll add negative $x$ to the values on the number line and move 3 steps to the left:

Therefore, the solution is:

$-x-3x=-4x$

Let's position minus $\frac{1}{7}$ on the number line and move one step to the right, since $\frac{7}{7}=\frac{1}{1}=1$

We should note that our result is a positive number:

Let's remember the rule:

$-(-x)=+x$

Now let's write the exercise in the appropriate form and solve it:

$-\frac{1}{7}+1=\frac{6}{7}$

Let's remember the rule:

$-(-x)=+x$

Now let's write the exercise in the appropriate form:

$567+69=$

Let's solve the exercise vertically:

$567\\+69\\636$

First let's remember the rule:

$+(+x)=+x$

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

$x+3x=$

We'll can then add $x$ to the number line values and move 3 steps to the right:

Therefore, the solution is:

$x+3x=4x$

First, let's remember the rule:

$-(+x)=-x$

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

$x-4x=$

We'll add $x$ to the number line and go 4 steps to the left:

Therefore the solution is:

$x-4x=-3x$

Let's remember the rule:

$-(-x)=+x$

Now let's write the exercise in the appropriate form:

$-302+7.6=$

We'll locate -302 on the number line and go right 7.6 steps:

Note that our result will be negative.

Let's solve the exercise carefully by adding a decimal point to the number 302 to avoid confusion during the solution:

$302.0\\-7.6\\294.4$

Note that the final answer is negative, meaning:

$-294.4$

Let's mark minus $\frac{1}{5}$ on the number line and move $3\frac{4}{5}$ steps to the left, meaning our result will be a negative number:

Let's remember the rule:

$+(-x)=-x$

Now let's write the exercise in the appropriate form and solve it:

$-\frac{1}{5}-3\frac{4}{5}=-4$

First let's remember the rule:

$-(+x)=-x$

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

$100-1.01=$

We should note that we are subtracting between two positive numbers, meaning we will get a positive result.

Therefore:

$100\\-1.01\\98.99$

Let's remember the rule:

$+(+x)=+x$

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

$0.18+0.88=$

Since we are multiplying two positive numbers, the result will be positive.

Therefore:

$0.18\\+0.88\\1.06$

Using the following rule:

$+(-x)=-x$

Let's rewrite the exercise as seen below:

$-0.21-0.79=$

Since we are subtracting from a negative number, the result will be negative.

Therefore:

$-0.21\\-0.79\\-1 .00$

Let's first consider the rule:

$-(-x)=+x$

Now let's write the exercise in the appropriate form:

$-0.43+0.87=$

We'll use the distributive property and solve the exercise step by step:

$0.87\\-0.43\\0.44$