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:

$-8+12=4$

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:

$301-51=250$

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:

$8-4.5=3.5$

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

Note that our result is a positive number:

Now solve the following 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:

$567+69=$

Let's solve the exercise vertically:

$567\\+69\\636$

Let's remember the rule:

$-(+x)=-x$

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

$-8+13=$

We'll use the substitution law and solve:

$13-8=5$

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:

$2.25\\-0.85\\=1.40$

First, 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:

Finally, solve the exercise:

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

First we need to remember the rule:

$-(+x)=-x$

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

$0.76-13.04=$

Next we will solve the exercise vertically, keeping 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 must be a negative number, so we will add a minus sign to get:

$-\text{12}.28$

Given that we are adding two positive numbers together, the result will be positive.

Looking at the numbers, we know that the result must be greater than 12.

Then we can proceed to use simple addition to solve as follows:

$0.68\\+12.03\\12.71$

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:

$0.87\\-0.43\\0.44$

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 multiply the numerator and denominator of the fraction $\frac{2}{3}$ by 3 and the numerator and denominator of the fraction $\frac{1}{9}$ by 1 in order to find a common denominator:

$\frac{2\times3}{3\times3}=\frac{6}{9}$

$\frac{1\times1}{9\times1}=\frac{1}{9}$

Finally let's perform the addition operation to find our answer:

$\frac{1}{9}+\frac{6}{9}=\frac{7}{9}$

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 and solve it:

$7+6.7=13.7$

Let's remember the rule:

$-(+x)=-x$

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

$0.27-1.12=$

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

We'll use vertical subtraction and remember that the result is negative:

$1.12\\-0.27\\0.85$

The final result is:

$-0.85$

Let's remember the rule:

$+(-x)=-x$

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

$-0.73-13.07=$

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

We'll combine the two numbers together vertically, but remember that the result will be negative:

$0.73\\+13.07\\13.80$

Therefore, the answer is:

$-0.73-13.07=-13.8$