Addition of Fractions: Multiplication of signed numbers

To solve the problem $-\frac{3}{8}-(-\frac{5}{8})-(-\frac{1}{2})$, we will follow these steps:

• Step 1: Address the negative signs. Note that subtracting a negative is the same as adding its positive counterpart:
• $-\frac{3}{8}$ remains the same.
• $-(-\frac{5}{8})$ becomes $+\frac{5}{8}$.
• $-(-\frac{1}{2})$ becomes $+\frac{1}{2}$.
• Step 2: Write the expression with the adjusted signs: $-\frac{3}{8} + \frac{5}{8} + \frac{1}{2}$.
• Step 3: Find a common denominator for the fractions. The denominators are 8 and 2. The least common denominator is 8.
• Step 4: Convert all fractions to have this common denominator:
• $-\frac{3}{8}$ is already with a denominator of 8.
• $\frac{5}{8}$ is already with a denominator of 8.
• $\frac{1}{2} = \frac{4}{8}$.
• Step 5: Perform the arithmetic operations on the numerators while retaining the common denominator:
$-\frac{3}{8} + \frac{5}{8} + \frac{4}{8} = \frac{-3+5+4}{8}$.
• Step 6: Compute the result: Calculate $-3 + 5 + 4 = 6$, therefore the fraction becomes $\frac{6}{8}$.
• Step 7: Simplify the fraction $\frac{6}{8}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
$\frac{6}{8} = \frac{3}{4}$.

Therefore, the solution to the problem is $\frac{3}{4}$.

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

• Step 1: Simplify $-\frac{14}{7}$.
• Step 2: Perform arithmetic operations in sequence, converting all parts as necessary.
• Step 3: Combine the fractions into a single fraction and simplify.

Now, let's work through each step:
Step 1: Simplify $-\frac{14}{7}$. Since $14 \div 7 = 2$, $-\frac{14}{7} = -2$.

Step 2: We rewrite the expression properly:
$-2 + (-3) - \frac{1}{2} - (-\frac{1}{4})$.

Simplify and operate on each part:
Convert $-3$ to a fraction with a denominator of 1: $-\frac{3}{1}$.
Evaluate the subtraction of a negative: $-(-\frac{1}{4}) = \frac{1}{4}$.

Rewrite the expression using fractions:
$-\frac{2}{1} + (-\frac{3}{1}) - \frac{1}{2} + \frac{1}{4}$.

Step 3: Add and subtract the fractions using a common denominator. The least common denominator for 1, 2, and 4 is 4.
$-\frac{2}{1} = -\frac{8}{4}$,
$-\frac{3}{1} = -\frac{12}{4}$,
$-\frac{1}{2} = -\frac{2}{4}$.

Combining these, we get:
$-\frac{8}{4} - \frac{12}{4} - \frac{2}{4} + \frac{1}{4} = \frac{-8 - 12 - 2 + 1}{4}$.

Simplify the numerator: $-8 - 12 - 2 + 1 = -21$.
Thus, we have:
$\frac{-21}{4}$.

Therefore, the solution to the problem is $-\frac{21}{4}$, which corresponds to choice 3.

To solve the problem, we will follow these steps:

• Simplify each fraction where possible.
• Find a common denominator for all fractions.
• Convert each fraction to have this common denominator.
• Perform the required operations: subtraction and addition.

Let's begin solving the problem:

Step 1: Simplify each fraction.
- $-\frac{4}{16}$ simplifies to $-\frac{1}{4}$ since both numerator and denominator can be divided by 4.
- The fractions $-(-\frac{3}{8})$, $\frac{2}{8}$, and $-\frac{1}{4}$ are already in their simplest forms.

Step 2: Find the common denominator.
The denominators are 4 and 8. The least common denominator (LCD) is 8.

Step 3: Convert each fraction to an equivalent fraction with this common denominator:
- $-\frac{1}{4}$ becomes $-\frac{2}{8}$ because $\frac{1}{4} \times \frac{2}{2} = \frac{2}{8}$.
- $-(-\frac{3}{8})$ simplifies to $\frac{3}{8}$ (due to subtracting a negative, which makes it positive).
- $\frac{2}{8}$ remains unchanged, as it already has the common denominator.
- $-\frac{1}{4}$ becomes $-\frac{2}{8}$ for the same reason as above.

Step 4: Perform the operations:
$-\frac{2}{8} + \frac{3}{8} + \frac{2}{8} - \frac{2}{8}$.

Adding and subtracting these fractions with a common denominator:
- Combine them as $(-2 + 3 + 2 - 2)/8 = 1/8$.

Therefore, the solution to the problem is $\frac{1}{8}$.

To solve the given problem of adding $-3 + (-\frac{1}{2}) + \frac{3}{8} + \frac{5}{8}$, we will use the following steps:

• Step 1: Calculate $\frac{3}{8} + \frac{5}{8}$
• Step 2: Subtract $-\frac{1}{2}$ from the result of step 1
• Step 3: Add the final result to $-3$

Now, let us work through each step:

Step 1: Calculate $\frac{3}{8} + \frac{5}{8}$. Since these fractions have the same denominator, we simply add their numerators: $\frac{3 + 5}{8} = \frac{8}{8} = 1$.

Step 2: Now we subtract $-\frac{1}{2}$ from 1. We can rewrite $1$ as $\frac{8}{8}$ and $-\frac{1}{2}$ as $-\frac{4}{8}$ (since their least common denominator is 8). So: $1 - \left(-\frac{1}{2}\right) = \frac{8}{8} - \left(-\frac{4}{8}\right) = \frac{8 + 4}{8} = \frac{12}{8} = \frac{3}{2}.$

Step 3: Finally, we add this result to $-3$. $-3$ can be expressed as $-\frac{6}{2}$ and $\frac{3}{2}$ remains the same: $-3 + \frac{3}{2} = -\frac{6}{2} + \frac{3}{2} = \frac{-6 + 3}{2} = \frac{-3}{2} = -\frac{5}{2}.$

Hence, the solution to the problem is $-\frac{5}{2}$.

To solve this problem, we must simplify the expression $-\frac{1}{2} + \frac{3}{4} + (-\frac{1}{5}) + (-\frac{4}{5})$.

First, we need to find the least common denominator (LCD) for the fractions 2, 4, and 5. The LCD is 20.

Next, we convert each fraction to an equivalent fraction with the common denominator of 20:

• $-\frac{1}{2}$ becomes $-\frac{10}{20}$
• $\frac{3}{4}$ becomes $\frac{15}{20}$
• $-\frac{1}{5}$ becomes $-\frac{4}{20}$
• $-\frac{4}{5}$ becomes $-\frac{16}{20}$

Now we perform the addition and subtraction:

$-\frac{10}{20} + \frac{15}{20} - \frac{4}{20} - \frac{16}{20}$

Combine the numerators:

$-10 + 15 - 4 - 16 = -15$

Thus, the resulting fraction is:

$-\frac{15}{20}$

We simplify $-\frac{15}{20}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 5:

$-\frac{15}{20} = -\frac{3}{4}$

Therefore, the solution to the problem is $-\frac{3}{4}$, which corresponds to choice 2.

To solve this problem, we'll perform operations involving both fractions and whole numbers:

• Step 1: Combine the fractional parts $-\frac{4}{9}$ and $\frac{5}{9}$.

• Step 2: Add the remaining whole numbers $5$ and $-2$.

• Step 3: Sum the results from Step 1 and Step 2.

Let's start:
Step 1: Work with the fractions together. - We have $-\frac{4}{9}$ and $\frac{5}{9}$, both have the same denominator, thus can be directly added: $-\frac{4}{9} + \frac{5}{9} = \frac{-4+5}{9} = \frac{1}{9}$

Step 2: Add the integer components $5$ and $-2$: $5 + (-2) = 5 - 2 = 3.$

Step 3: Combine results from Step 1 and Step 2: $3+\frac{1}{9}=\frac{27}{9}+\frac{1}{9}=\frac{28}{9}$.

Therefore, the final result of the expression is $\frac{28}{9}$.

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

• Step 1: Simplify the integers using addition.
• Step 2: Simplify the fractions, ensuring a common denominator before adding.
• Step 3: Combine results from integers and fractions for the final answer.

Let's work through each step:

Step 1: Combine the integers $-5$ and $10$.

$-5 + 10 = 5$

Step 2: Simplify and add the fractions $-\frac{1}{2}$ and $-\frac{3}{4}$.

To add the fractions, we need a common denominator. The denominators are 2 and 4. The least common denominator is 4.

Convert $-\frac{1}{2}$ to an equivalent fraction with a denominator of 4:

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

Now add $-\frac{2}{4}$ and $-\frac{3}{4}$:

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

Step 3: Combine the result of the integer addition and the fraction addition.

The integer result is 5 and the fraction result is $-\frac{5}{4}$. Convert 5 to a fraction with the same denominator:

$5 = \frac{20}{4}$

Combine the fractions:

$\frac{20}{4} + -\frac{5}{4} = \frac{20 - 5}{4} = \frac{15}{4}$

Therefore, the solution to the problem is $\frac{15}{4}$.