Addition and Subtraction of Directed Numbers: Solving the problem

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 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 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:

$-10-13=-23$

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:

$567+69=$

Let's solve the exercise vertically:

$567\\+69\\636$

Let's add 8 to the number line and move 12 steps to the right.

Note that our result is a positive number:

Now solve the following exercise:

$8+12=20$

First, remember the rule:

$+(-x)=-x$

Place 301 on the number line and move 51 steps to the left:

Rewrite the exercise in the appropriate form and solve it:

$301-51=250$

First we need to locate the number 8 on the number line and move 4.5 steps to the left from it:

Remember the rule:

$+(-x)=-x$

Now let's rewrite the problem in the appropriate form and solve:

$8-4.5=3.5$

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:

$-8-12=-20$

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:

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

Note the following rule:

$-(+x)=-x$

Now let's rewrite the exercise as follows:

$100-1.01=$

We should note that we are subtracting between two positive numbers, meaning we will obtain a positive result.

Therefore:

$100\\-1.01\\98.99$

Let's remember the rule:

$-(-x)=+x$

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

$7+6.7=13.7$

Let's remember the rule:

$-(-x)=+x$

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

$-\frac{1}{6}+4\frac{2}{6}=$

We'll use the substitution law and solve:

$4\frac{2}{6}-\frac{1}{6}=4\frac{1}{6}$

Let's remember the rule:

$-(+x)=-x$

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

$-0.97-3.34=$

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

We'll connect the two numbers but won't forget that the final result is with a minus sign:

$0.97\\+3.34\\4.31$

In other words:

$-0.97-3.34=-4.31$

First, 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:

Finally, solve the exercise:

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

Note the following rule:

$-(-x)=+x$

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

$-302+7.6=$

We'll locate -302 on the number line and go right 7.6 steps:

Note that our result will be negative.

Let's solve the exercise carefully by adding a decimal point to the number 302 to avoid confusion during the solution:

$302.0\\-7.6\\294.4$

Note that the final answer is negative, meaning:

$-294.4$

Let's remember the rule:

$-(-x)=+x$

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

$2\frac{1}{5}+\frac{30}{50}=$

We'll reduce the fraction $\frac{30}{50}$ by 10$$

$2\frac{1}{5}+\frac{3}{5}=2\frac{4}{5}$

Let's first consider 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:

$0.87\\-0.43\\0.44$

Let's remember the rule:

$-(-x)=+x$

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

$-0.83+14.68=$

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

$14.68\\-0.83\\13.85$

Let's remember the rule:

$-(+x)=-x$

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

$0.27-1.12=$

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

We'll use vertical subtraction and remember that the result is negative:

$1.12\\-0.27\\0.85$

The final result is:

$-0.85$