Addition and Subtraction of Directed Numbers: Number of terms

Let's apply the following rule in order to rewrite the equation:

$-(-x)=+$

$-30+2+(-8)+5=$

$-28+(-8)+5=$

Next we will locate negative 28 on the number line and proceed 8 steps to the left (since negative 8 is less than zero):

We reach negative 36.

Resulting in the following exercise:

$-36+5=$

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Next we locate negative 36 on the number line and proceed 5 steps to the right (since 5 is greater than zero):

We reach negative 31

Let's locate negative 30 on the number line and move 4 steps to the right (since 4 is greater than zero):

We reach negative 26.

Resulting in the following exercise:

$-26+(-8)=$

Now let's locate negative 26 on the number line and move 8 steps to the left (since negative 8 is less than zero):

We reach negative 34

Let's start with the leftmost exercise:

$(-4)+2$

We'll locate negative 4 on the axis and move two steps to the right, where each step represents one whole number:

We can see that we've reached negative 2.

Now we'll get the exercise:

$(-2)+(-3)+(-5)=$

Let's focus on the exercise:

$(-2)+(-3)$

We'll locate negative 2 on the axis and move three steps to the left, where each step represents one whole number:

We can see that we've reached negative 5.

Now we'll get the exercise:

$(-5)+(-5)=$

We'll locate negative 5 on the axis and move five steps to the left, where each step represents one whole number:

We can see that we've reached negative 10.

First, let's look at the first exercise:

$4+3$

We will locate the number 4 on the axis, and move right three steps, where each step represents a whole number in the following way:

We can see that we reached the number 7.

Now we get the exercise:

$7+(-6)+(-9)=$

Let's look at the exercise:

$7+(-6)=$

We will locate the number 7 on the axis, and move left six steps, where each step represents a whole number in the following way:

We can see that we reached the number 1.

Now we got the exercise:

$1+(-9)=$

We will locate the number 1 on the axis, and move left nine steps, where each step represents a whole number in the following way:

We can see that we reached the number minus 8.

First, let's organize the exercise in a way that will make it easier and more convenient to solve.

Notice that the number 30 appears twice in the exercise, so let's start with it:

$(-30)+30+(-2)+(-5)=$

Let's look at the exercise:

$-30+30$

Since we move left from zero to minus 30, and then return right 30 steps, we will arrive at the same number we started from: 0

Now let's continue the exercise in the following way:

$0+(-2)+(-5)=$

We'll locate the number minus 2 on the number line, and move left five steps where each step represents one whole number:

We can see that we arrived at minus 7.

Let's remember the rule:

$-(-x)=+x$

We'll write the exercise in the appropriate form:

$15+5+4+(-9)+8-4=$

Let's solve the exercise from left to right:

$15+5=20$

Now we'll get the exercise:

$20+4+(-9)+8-4=$

Let's solve the exercise from left to right:

$20+4=24$

Now we'll get the exercise:

$24+(-9)+8-4=$

Let's remember the rule:

$+(-x)=-x$

We'll write the exercise in the appropriate form:

$24-9+8-4=$

Let's solve the exercise from left to right:

$24-9=15$

$15+8=23$

$23-4=19$

Let's remember the rule:

$-(-x)=+x$

Let's write the exercise in the appropriate form:

$25+5+(-6)-4=$

Let's solve the exercise from left to right:

$25+5=30$

Now we get the exercise:

$30+(-6)-4=$

Let's remember the rule:

$+(-x)=-x$

Let's write the exercise in the appropriate form:

$30-6-4=$

Let's solve the exercise from left to right:

$30-6=24$

$24-4=20$

First, let's look at the first exercise:

$(-10)+(-3)$

We will locate the number minus 10 on the number line, and move left three steps, where each step represents one whole number:

We can see that we reached the number minus 13.

Now we got the exercise:

$(-13)+4+(-12)=$

The next exercise is:

$(-13)+4$

We will locate the number minus 13 on the number line, and move right four steps where each step represents one whole number:

We can see that we reached the number minus 9.

Now we got the exercise:

$(-9)+(-12)=$

We will locate the number minus 9 on the number line, and move left twelve steps where each step represents one whole number:

We can see that the number we reached is minus 21.

First, we solve the multiplication exercise, that is where there is a plus or minus sign before another sign.

$-27+7-6+2-11=$

Now we solve as a common exercise from left to right:

$-27+7=-20$

$-20-6=-26$

$-26+2=-24$

$-24-11=-35$

Let's begin by expanding the parentheses whilst paying attention to the minus and plus signs, which change accordingly:

$+(-9.5)=-9.5$

$+(-13)=-13$

We should obtain the following:

$7.5-9.5+5-13.5=$

Now let's solve the exercise from left to right:

$-2+5-13.5=$

$3-13.5=-10.5$