Addition and Subtraction of Directed Numbers - Examples, Exercises and Solutions

Let's remember the rule:

$-(-x)=+x$

Therefore, the exercise we received is:

$-5+2=$

We'll locate minus 5 on the number line and move two steps to the right (since 2 is greater than zero):

We can see that we've arrived at the number minus 3.

We'll locate minus 4 on the number line and move two steps to the left (since minus 2 is less than zero):

We can see that we've arrived at the number minus 6.

We will locate the number 3 on the number line, then move 4 steps to the left from it (since minus 4 is less than zero):

We can see that we have reached the number minus 1.

Let's remember the rule:

$-(-x)=+$

We'll write the exercise in the appropriate form:

$3+(2)=$

We'll locate the number 3 on the number line, from which we'll move 2 steps to the right (since 2 is greater than zero):

We can see that we've reached the number 5.

Let's remember the rule:

$-(-x)=+$

We'll write the exercise in the appropriate form:

$14+(3)=$

We'll locate the number 14 on the number line, from which we'll move 3 steps to the right (since 3 is greater than zero):

We can see that we've reached the number 17.

Let's locate negative 2 on the number line.

Since negative 2 is less than 0, we'll move two steps left from zero, where each step represents one whole number as follows:

Now let's look at the operation in the exercise.

Since the operation is $+3$

And since 3 is greater than 0, we'll move three steps right from negative 2, where each step represents one whole number as follows:

We can see that we arrived at the number 1.

Let's locate the number 5 on the number line.

Since the number 5 is greater than 0, we will move five steps to the right from zero, where each step represents one whole number as follows:

Now let's look at the operation in the exercise.

Since the operation is $+(-2)$

And the number minus 2 is less than 0, we will move two steps to the left from number 5, where each step represents one whole number as follows:

We can see that the number we reached is 3.

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:

$-8+12=4$

We will locate the number 10 on the number line, then move 12 steps to the left from it (since minus 12 is less than zero):

We can see that we have reached the number minus 2.

Let's remember the rule:

$-(-x)=+$

We'll write the exercise in the appropriate form:

$-3+(4)=$

We'll locate the number negative 3 on the number line, from which we'll move 4 steps to the right (since 4 is greater than zero):

We can see that we've reached the number 1.