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:

$567+69=$

Let's solve the exercise vertically:

$567\\+69\\636$

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.

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 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 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:

$13-8=5$

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 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:

$301-51=250$

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:

$-10-13=-23$

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:

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

To solve this problem, we will proceed as follows:

• Step 1: Identify the whole number and fractional parts of each mixed number.
• Step 2: Add the whole numbers separately.
• Step 3: Add the fractions by first finding a common denominator.
• Step 4: Combine the sums from Steps 2 and 3.

Now, let's work through the solution:

Step 1:
Extract the whole numbers and fractions:
$+12\frac{1}{3}$ has a whole number 12 and a fraction $\frac{1}{3}$.
$+8\frac{1}{4}$ has a whole number 8 and a fraction $\frac{1}{4}$.

Step 2:
Add the whole numbers:
12 + 8 = 20.

Step 3:
Add the fractions by finding a common denominator. The fractions are $\frac{1}{3}$ and $\frac{1}{4}$.
- The least common denominator of 3 and 4 is 12.
- Convert $\frac{1}{3}$ to $\frac{4}{12}$.
- Convert $\frac{1}{4}$ to $\frac{3}{12}$.

Add the fractions now:
$\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$.

Step 4:
Combine the sums from Steps 2 and 3:
The sum of the whole numbers is 20, and the sum of the fractions is $\frac{7}{12}$.
Thus, $+12\frac{1}{3} + +8\frac{1}{4} = 20\frac{7}{12}$.

Therefore, the solution to the problem is $20\frac{7}{12}$.

To solve this problem, we'll follow these steps:

• Step 1: Convert mixed numbers to improper fractions.
• Step 2: Find the least common denominator.
• Step 3: Perform the addition and convert back to a mixed number.

Let's work through each step:

Step 1: Convert mixed numbers to improper fractions.

$-13\frac{1}{4}$ = $-\left( 13 + \frac{1}{4} \right) = -\left( \frac{52}{4} + \frac{1}{4} \right) = -\frac{53}{4}$

$-9\frac{2}{7}$ = $-\left( 9 + \frac{2}{7} \right) = -\left( \frac{63}{7} + \frac{2}{7} \right) = -\frac{65}{7}$

Step 2: Determine a common denominator. The least common multiple of 4 and 7 is 28.

Convert the fractions:

$-\frac{53}{4} = -\frac{53 \times 7}{4 \times 7} = -\frac{371}{28}$

$-\frac{65}{7} = -\frac{65 \times 4}{7 \times 4} = -\frac{260}{28}$

Step 3: Add the fractions:

$-\frac{371}{28} + \left(-\frac{260}{28}\right) = -\frac{371 + 260}{28} = -\frac{631}{28}$

Converting $-\frac{631}{28}$ back to a mixed number:

Perform the division: $631 \div 28 \approx 22$ remainder 15.

This gives us a mixed number: $-22\frac{15}{28}$

Therefore, the solution to the problem is $-22\frac{15}{28}$.

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:

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

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:

$0.18\\+0.88\\1.06$

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:

$-0.73-13.07=-13.8$

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:

$0.87\\-0.43\\0.44$

First we need to remember the rule:

$-(+x)=-x$

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

$0.76-13.04=$

Next we will solve the exercise vertically, keeping 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 must be a negative number, so we will add a minus sign to get:

$-\text{12}.28$

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 solve the problem step-by-step:

• Step 1: Convert mixed numbers to improper fractions.

For $-12\frac{1}{4}$, convert to an improper fraction:

$-12\frac{1}{4} = -\left(12 + \frac{1}{4}\right) = -\left(\frac{48}{4} + \frac{1}{4}\right) = -\frac{49}{4}$

For $-8\frac{2}{7}$, convert to an improper fraction:

$-8\frac{2}{7} = -\left(8 + \frac{2}{7}\right) = -\left(\frac{56}{7} + \frac{2}{7}\right) = -\frac{58}{7}$

• Step 2: Subtract the second improper fraction from the first.

The operation becomes $-\frac{49}{4} - (-\frac{58}{7})$, which simplifies to $-\frac{49}{4} + \frac{58}{7}$.

Find a common denominator for $\frac{49}{4}$ and $\frac{58}{7}$. The least common denominator is 28.

Convert $-\frac{49}{4}$ and $\frac{58}{7}$ to equivalents with a denominator of 28:

$-\frac{49}{4} = -\frac{49 \times 7}{4 \times 7} = -\frac{343}{28}$

$\frac{58}{7} = \frac{58 \times 4}{7 \times 4} = \frac{232}{28}$

So, $-\frac{49}{4} + \frac{58}{7}$ becomes:

$-\frac{343}{28} + \frac{232}{28} = \frac{-343 + 232}{28} = \frac{-111}{28}$

• Step 3: Simplify the improper fraction $\frac{-111}{28}$ to a mixed number form.

Divide $-111$ by 28, which gives $-3$ and a remainder of 27. Thus:

$-3\frac{27}{28}$

Therefore, the solution to the problem is $-3\frac{27}{28}$.

To solve this problem, we'll follow these steps:

• Step 1: Convert the mixed numbers to improper fractions.
• Step 2: Find a common denominator and add the fractions.
• Step 3: Convert the resulting improper fraction back into a mixed number.

Let's begin by converting the mixed numbers into improper fractions:

The mixed number $-12\frac{1}{6}$ can be converted as follows:

$-12\frac{1}{6} = -\left(\frac{12 \times 6 + 1}{6}\right) = -\frac{73}{6}$

The mixed number $+10\frac{1}{3}$ can be converted as follows:

$10\frac{1}{3} = \frac{10 \times 3 + 1}{3} = \frac{31}{3}$

Next, we need a common denominator to add these fractions together. The denominators are 6 and 3, and the least common denominator is 6.

Convert $\frac{31}{3}$ to have the denominator of 6:

$\frac{31}{3} = \frac{31 \times 2}{3 \times 2} = \frac{62}{6}$

Now, we add the fractions:

$-\frac{73}{6} + \frac{62}{6} = \frac{-73 + 62}{6} = \frac{-11}{6}$

Convert $\frac{-11}{6}$ back into a mixed number:

$\frac{-11}{6} = -1\frac{5}{6}$ (since $11 \div 6 = 1$ with a remainder of 5)

Therefore, the solution to the problem is $-1\frac{5}{6}$.