Addition and Subtraction of Directed Numbers: Solving the problem

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

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 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:

$13-8=5$

$5$

$(-10)-(+13)=$

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:

$-10-13=-23$

$-23$

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

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:

$-8-12=-20$

$-20$

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

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:

$-8+12=4$

$4$

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

Let's remember the rule:

$-(+x)=-x$

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

$-x-3x=$

We'll mark negative x on the number line, and go 3 steps to the left:

The solution is:

$-x-3x=-4x$

$-4x$

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

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:

$567\\+69\\636$

$636$

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

Let's remember the rule:

$+(-x)=-x$

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

$-x-5x=$

We'll mark negative x on the number line, and move 5 steps to the left:

The solution is:

$-x-5x=-6x$

$-6x$

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

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:

$x+3x=4x$

$4x$

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

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:

$x-4x=-3x$

$-3x$

$(-x)-(-6x)=$

Let's remember the rule:

$-(-x)=+x$

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

$-x+6x=$

We'll mark negative x on the number line, and move 6 steps to the right:

The solution is:

$-x+6x=5x$

$5x$

Solve the following exercise:

$(-\frac{1}{7})-(-\frac{7}{7})=$

Let's position minus $\frac{1}{7}$ on the number line and move one step to the right, since $\frac{7}{7}=\frac{1}{1}=1$

We should note that our result is a positive number:

Let's remember the rule:

$-(-x)=+x$

Now let's write the exercise in the appropriate form and solve it:

$-\frac{1}{7}+1=\frac{6}{7}$

$\frac{6}{7}$

$(+\frac{1}{4})+(2\frac{3}{4})=$

We will locate the number $\frac{1}{4}$ on the number line and move $2\frac{3}{4}$ steps to the right from it.

This means the resulting number will be positive:

Let's solve the exercise:

$\frac{1}{4}+2\frac{3}{4}=3$

3

$(+7)-(-6.7)=$

Let's remember the rule:

$-(-x)=+x$

Now let's write the exercise in the appropriate form and solve it:

$7+6.7=13.7$

$13.7$

$(-0.43)-(-0.87)=$

Let's remember the rule:

$-(-x)=+x$

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

$-0.43+0.87=$

We'll use the distributive property and solve the exercise step by step:

$0.87\\-0.43\\0.44$

$0.44$

$(+0.18)+(+0.88)=$

Let's remember the rule:

$+(+x)=+x$

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

$0.18+0.88=$

Since we are multiplying two positive numbers, the result will be positive.

Therefore:

$0.18\\+0.88\\1.06$

$1.06$

$(+0.76)-(+13.04)=$

Let's remember the rule:

$-(+x)=-x$

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

$0.76-13.04=$

We'll solve the exercise vertically, but keep in mind that the final result will be negative since we are subtracting a smaller number from a larger number:

$13.04\\-0.76\\12.28$

Remember that the answer is a negative number, which means:

$-\text{12}.28$

$-12.28$

$(-0.73)+(-13.07)=$

Let's remember the rule:

$+(-x)=-x$

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

$-0.73-13.07=$

Since we are subtracting a larger number from a smaller number, the result will be negative.

We'll combine the two numbers together vertically, but remember that the result will be negative:

$0.73\\+13.07\\13.80$

Therefore, the answer is:

$-0.73-13.07=-13.8$

$-13.8$