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

$-4+(-2)=$

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.

$-6$

$3+(-4)=$

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.

$-1$

$(+8)+(+12)=$

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:

$8+12=20$

$20$

$(-8)-(-13)=$

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:

$13-8=5$

$5$

$(+6)-(+11)=$

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.

$-5$

$(-8)+(+12)=$

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:

$-8+12=4$

$4$

$10+(-12)=$

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.

$-2$

$-12+5=$

We will locate the number negative 12 on the number line, and from there we will move 5 steps to the right (since 5 is greater than zero):

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

$-7$

$15-(-4)=$

Let's remember the following law:

$-(-x)=+$

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

$15+(4)=19$

$19$

$12-?=15$

We know that the distance between 12 and 15 is three steps.

In other words:

$12+3=15$

Now let's remember the rule:

$-(-x)=+$

We'll substitute x with the number 3 and get:

$12-(-3)=15$

Therefore, the answer is minus 3

$-3$

$-25-?=100$

We'll add ?+ to both sides to zero out the left side:

$-25-?+?=100+?$

$-?+?=0$

Therefore, we get:

$-25-0=100+\text{?}$

$-25=100+\text{?}$

We'll add minus 100 to both sides to zero out the right side:

$-25-100=100-100+\text{?}$

Now we get:

$-125=0+\text{?}$

$-125=\text{?}$

$-125$

$(+8)+(-4.5)=$

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:

$8-4.5=3.5$

$3.5$

$(+567)-(-69)=$

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:

$567\\+69\\636$

$636$

$(+x)-(+4x)=$

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:

$x-4x=-3x$

$-3x$

$(+x)+(+3x)=$

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:

$x+3x=4x$

$4x$