Addition and Subtraction of Directed Numbers: Solving the problem

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

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

.

Let's solve the exercise:

$8+12=20$

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 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 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:

$13-8=5$

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

Let's remember the rule:

$+(-x)=-x$

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

$8-4.5=3.5$

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:

$567\\+69\\636$

Let's remember the rule:

$-(+x)=-x$

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

$x-4x=$

We'll mark x on the number line, and go 4 steps to the left:

The solution is:

$x-4x=-3x$

Let's remember the rule:

$+(+x)=+x$

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

$x+3x=$

We'll draw x on the number line, and move 3 steps to the right:

The solution is:

$x+3x=4x$

Let's remember the rule:

$+(-x)=-x$

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

$-x-5x=$

We'll mark negative x on the number line, and move 5 steps to the left:

The solution is:

$-x-5x=-6x$

Let's remember the rule:

$-(+x)=-x$

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

$-x-3x=$

We'll mark negative x on the number line, and go 3 steps to the left:

The solution is:

$-x-3x=-4x$

Let's remember the rule:

$-(-x)=+x$

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

$-x+6x=$

We'll mark negative x on the number line, and move 6 steps to the right:

The solution is:

$-x+6x=5x$

We will locate the number $\frac{1}{4}$ on the number line and move $2\frac{3}{4}$ steps to the right from it.

This means the resulting number will be positive:

Let's solve the exercise:

$\frac{1}{4}+2\frac{3}{4}=3$

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:

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

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:

$-294.4$

First, remember the rule:

$+(-x)=-x$

Place 301 on the number line and move 51 steps to the left:

Rewrite the exercise in the appropriate form and solve it:

$301-51=250$

Let's remember the rule:

$-(+x)=-x$

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

$0.76-13.04=$

We'll solve the exercise vertically, but keep in mind that the final result will be negative since we are subtracting a smaller number from a larger number:

$13.04\\-0.76\\12.28$

Remember that the answer is a negative number, which means:

$-\text{12}.28$

First, locate -0.85 on the number line and note that we are moving 2.25 steps to the right:

Then use the commutative property:

$2.25-0.85=$

Finally, solve vertically:

$2.25\\-0.85\\=1.40$