Basic Definitions: Omitting parentheses

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

• Calculate the absolute values of the numbers: $|+71| = 71$ and $|-18| = 18$.
• Subtract the smaller absolute value from the larger one: $71 - 18 = 53$.
• Determine the sign of the result by using the sign of the number with the larger absolute value. Here, $71$ is larger and positive, so the result is positive.

Now, let's go through the calculations:
Step 1: Calculate the absolute difference $71 - 18 = 53$.
Step 2: The number with the larger absolute value is $71$, which is positive. Thus, the result is also positive.

Therefore, the solution to the problem is $53$.

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

• Step 1: Identify the given numbers.
• Step 2: Apply the subtraction operation.
• Step 3: Calculate the result.

Now, let's work through each step:
Step 1: The given numbers are $+43$ and $+15$.
Step 2: We need to subtract $+15$ from $+43$.
Step 3: Performing this calculation gives us $43 - 15 = 28$.

Therefore, the solution to the problem is $28$.

To solve this problem, we will follow these steps:

• Simplify the given expression $(+\frac{18}{6})$.
• Recognize that subtracting a negative fraction, $(-(-\frac{1}{4}))$, is equivalent to adding its positive counterpart.
• Perform the addition to find the final result.

Now, let's work through each step:

Step 1: Simplify the expression $\frac{18}{6}$.

Divide 18 by 6:

$\frac{18}{6} = 3$

Step 2: Recognize the operation with the negative fraction:

Subtracting a negative is equivalent to adding a positive:

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

Step 3: Perform the addition:

Convert 3 to a fraction with a common denominator of 4:

$3 = \frac{12}{4}$

Add the fractions:

$\frac{12}{4} + \frac{1}{4} = \frac{13}{4}$

Step 4: Convert the fraction $\frac{13}{4}$ to a decimal:

$\frac{13}{4} = 3.25$

Therefore, the solution to the problem is $\mathbf{3.25}$.

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

• Simplify the fraction $-\frac{2}{4}$.
• Perform the subtraction with the positive number.

Step 1: Simplify $-\frac{2}{4}$.
- The fraction $-\frac{2}{4}$ simplifies to $-\frac{1}{2}$ because both the numerator and the denominator can be divided by 2.

Step 2: Perform the subtraction.
- Now, calculate $-\frac{1}{2} - 3.5$.

To subtract the numbers, transform $-\frac{1}{2}$ into a decimal: $-0.5$.

Thus, the expression becomes:

$-0.5 - 3.5 = -4.0$.

Therefore, the solution to the problem is $-4$.

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

• Step 1: Simplify $(-2^2)$.
• Step 2: Convert $-3\frac{3}{4}$ to an improper fraction.
• Step 3: Subtract the results from Step 1 and Step 2.

Now, let's work through each step:
Step 1: $-2^2$ means square the 2 first and then apply the negative: $-2^2 = -(2^2) = -4$.

Step 2: Convert $-3\frac{3}{4}$ into an improper fraction:
A mixed fraction $-3\frac{3}{4}$ can be represented as $-\left(3 + \frac{3}{4}\right) = -\left(\frac{12}{4} + \frac{3}{4}\right) = -\frac{15}{4}$.

Step 3: Subtract the results:
Subtract $-(-\frac{15}{4})$ from $-4$:
This is equivalent to $-4 + \frac{15}{4}$. To add these, convert $-4$ to a fraction with the same denominator: $-4 = -\frac{16}{4}$.
Now, $-\frac{16}{4} + \frac{15}{4} = -\frac{16 - 15}{4} = -\frac{1}{4}$.

Therefore, the solution to the problem is $-\frac{1}{4}$.

The given mathematical expression is $(+0.5) + (+\frac{1}{2})$. Let us solve this step by step:

• Step 1: Recognize equivalency: $\frac{1}{2}$ in decimal form is $0.5$.
• Step 2: Rewriting the expression: $(+0.5) + (+0.5)$.
• Step 3: Direct addition: $0.5 + 0.5 = 1$.

Both terms are positive, and hence they add directly without altering each other's sign, resulting in a total of $1$. Therefore, the solution is $1$.

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

• Step 1: Convert the mixed number
• Step 2: Add the numbers
• Step 3: Determine the sign and calculate the result

Now, let's work through each step:

Step 1: Convert $-4\frac{1}{16}$ to a decimal.
The fraction $\frac{1}{16}$ is equivalent to $0.0625$ as a decimal. Therefore, the mixed number $-4\frac{1}{16}$ converts to $-4.0625$.

Step 2: Add $+2.16$ to $-4.0625$.
The expression becomes $2.16 + (-4.0625)$, which is equivalent to $2.16 - 4.0625$.

Step 3: Perform the subtraction operation.
Subtract $4.0625$ from $2.16$:

$2.16 - 4.0625 = -1.90625$

Therefore, the solution to the problem is $-1.90625$.

To solve this problem, we'll convert both numbers to fractions and then perform the addition:

Step 1: Convert $-3\frac{2}{6}$ to an improper fraction.
First, simplify $\frac{2}{6}$ to $\frac{1}{3}$:
$-3\frac{2}{6} = -3\frac{1}{3} = -\left(\frac{3 \times 3 + 1}{3}\right) = -\frac{10}{3}$.

Step 2: Convert $-2.75$ to a fraction.
$-2.75 = -2\frac{75}{100}$. Simplify $\frac{75}{100}$ to $\frac{3}{4}$:
$-2\frac{3}{4} = -\left(\frac{2 \times 4 + 3}{4}\right) = -\frac{11}{4}$.

Step 3: Find a common denominator and add the fractions.
The common denominator for 3 and 4 is 12.
Convert $-\frac{10}{3}$ to $-\frac{40}{12}$ and $-\frac{11}{4}$ to $-\frac{33}{12}$.

Step 4: Add the fractions:
$-\frac{40}{12} + -\frac{33}{12} = -\frac{73}{12}$.

Step 5: Convert $-\frac{73}{12}$ back to a mixed number.
$-\frac{73}{12} = -6\frac{1}{12}$.

Therefore, the solution to the problem is $-6\frac{1}{12}$.