Solve: -5 + (-1/2) + 10 + (-3/4) | Mixed Number Operations

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 $\frac{15}{4}$.