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

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:

$-(-x)=+$

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 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.

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.

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.

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.

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 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 -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:

$-8-12=-20$

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:

$-8+13=$

We'll use the substitution law and solve:

$13-8=5$

Let's locate negative 10 on the number line.

Now let's look at the operation in the exercise, since the operation is $+3$

And since the number 3 is greater than 0, we will move three steps to the right from negative 10, where each step represents one whole number as follows:

We can see that the number we reached is negative 7.

Let's locate the number 14 on the number line.

Now let's look at the operation in the exercise, since the operation is $+(-19)$

And since minus 19 is less than 0, we will move nineteen steps to the left from the number 14, where each step represents one whole number as follows:

We can see that the number we reached is minus 5.