Addition and Subtraction of Directed Numbers: Complete the missing numbers

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

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:

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

$-125=\text{?}$

To know how much we need to add to the number 9 to get minus 1, we will count the number of steps between the numbers.

Also, we will pay attention to which direction we moved, if we moved right then the number is positive, if we moved left the number will be negative.

We will locate the number 9, and move left until we reach minus 1, where each step represents one whole number, as follows:

We discover that the number of steps is 10, and since we moved left, the number will be minus 10

To know how much we need to add to -6 to get 4, we'll count the number of steps between the numbers.

Also, we'll pay attention to which direction we moved, if we went right then the number is positive, if we went left the number will be negative.

We'll locate the number -6, and move right until we reach the number 4, where each step represents one whole number, as follows:

We'll discover that the number of steps is 10. Since we moved right, the number is positive

Remember the rule:

$-(-x)=+$

Write the exercise in the appropriate form:

$-8+?=16+2$

Solve:

$-8+?=18$

Add 8 to both sides in order to zero out the left side:

$-8+?+8=18+8$

$-8+8=0$

Therefore:

$0+?=26$

$?=26$

To find out how much we need to add to the number negative 3 in order to get 5, we will count the number of steps between the two numbers.

Also, we will pay attention to which direction we moved, if we moved to the right then the number is positive, if we moved to the left the number will be negative.

We will start from the number negative 3, and move to the right until we reach the number 5, with each step representing one whole number, as follows:

We discover that the number of steps is 8. Since we moved to the right, the number is positive

Let's locate the number 13 on the number line.

Since zero is greater than negative 2, we'll move two steps to the right from the number 13.

The number we've reached is 15:

Let's remember the law:

$-(-x)=+$

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

$?+13=-23$

We'll add minus 13 to both sides to zero out the left side:

$?+13-13=-23-13$

Now we get:

$?+0=-36$

$?=-36$

Let's remember the law:

$-(-x)=+$

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

$?+12=-40$

We'll add minus 12 to both sides to zero out the left side:

$?+12-12=-40-12$

Now we get:

$?+0=-52$

$?=-52$

Let's remember the law:

$-(-x)=+$

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

$?-2+4=-20$

$?-2=-20$

We'll move minus 2 to the right side and maintain the appropriate sign:

$?=-20-2$

Now we get:

$?=-22$

Let's remember the law:

$-(-x)=+$

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

$?+3+10=-40$

$?+13=-40$

We'll add minus 13 to both sides to zero out the left side:

$?+13-13=-40-13$

Now we get:

$?+0=-53$

$?=-53$

To know how much we need to add to the number 5 to get minus 6, we will count the number of steps between the numbers.

Also, we'll pay attention to which direction we moved, if we went right then the number is positive, if we went left the number will be negative.

We'll locate the number 5, and move left until we reach minus 6, where each step represents one whole number, as follows:

We'll discover that the number of steps is 11, since we went left, the number will be minus 11.

Let's count on the number line the steps between -12 and 30.

We can see that 42 steps are required: