Solve 5(1/2) + 6(1/2) - 8(1/4)

Options

A. 2(3/4)
B. 3(3/4)
C. 2(1/4)
D. (1/2)

Answer

To solve the expression \( 5\frac{1}{2} + 6\frac{1}{2} - 8\frac{1}{4} \), we can follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we convert the mixed numbers into improper fractions.

- For \( 5\frac{1}{2} \):
\[ 5\frac{1}{2} = \frac{5 \times 2 + 1}{2} = \frac{10 + 1}{2} = \frac{11}{2} \]

- For \( 6\frac{1}{2} \):
\[ 6\frac{1}{2} = \frac{6 \times 2 + 1}{2} = \frac{12 + 1}{2} = \frac{13}{2} \]

- For \( 8\frac{1}{4} \):
\[ 8\frac{1}{4} = \frac{8 \times 4 + 1}{4} = \frac{32 + 1}{4} = \frac{33}{4} \]

### Step 2: Rewrite the Expression
Now we can rewrite the expression using the improper fractions:
\[ \frac{11}{2} + \frac{13}{2} - \frac{33}{4} \]

### Step 3: Find a Common Denominator
The common denominator for \( 2 \) and \( 4 \) is \( 4 \). We will convert the fractions:
- Convert \( \frac{11}{2} \) to have a denominator of \( 4 \):
\[ \frac{11}{2} = \frac{11 \times 2}{2 \times 2} = \frac{22}{4} \]

- Convert \( \frac{13}{2} \) to have a denominator of \( 4 \):
\[ \frac{13}{2} = \frac{13 \times 2}{2 \times 2} = \frac{26}{4} \]

### Step 4: Substitute Back into the Expression
Now substitute back into the expression:
\[ \frac{22}{4} + \frac{26}{4} - \frac{33}{4} \]

### Step 5: Combine the Fractions
Now we can combine the fractions:
\[ \frac{22 + 26 - 33}{4} = \frac{15}{4} \]

### Step 6: Convert Back to Mixed Number
Finally, we convert \( \frac{15}{4} \) back to a mixed number:
\[ \frac{15}{4} = 3\frac{3}{4} \]

Thus, the final answer is:
\[ 3\frac{3}{4} \]