`[2-(1)/(3)]-[5-(1)/(4)]+(2(1)/(3))xx[1.5]`

Options

A. 5/8
B. 5/12
C. 6/13
D. 9/13

Answer

To solve the expression `[2 - (1/3)] - [5 - (1/4)] + (2(1/3)) * [1.5]`, we will break it down step by step.

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we convert the mixed numbers into improper fractions where necessary:
- \( 2 - \frac{1}{3} = \frac{6}{3} - \frac{1}{3} = \frac{5}{3} \)
- \( 5 - \frac{1}{4} = \frac{20}{4} - \frac{1}{4} = \frac{19}{4} \)
- \( 2 \frac{1}{3} = \frac{7}{3} \)

So, we can rewrite the expression as:
\[ \frac{5}{3} - \frac{19}{4} + \frac{7}{3} \times 1.5 \]

### Step 2: Calculate \( \frac{7}{3} \times 1.5 \)
Next, we calculate \( \frac{7}{3} \times 1.5 \):
- \( 1.5 = \frac{3}{2} \)
- Therefore, \( \frac{7}{3} \times \frac{3}{2} = \frac{7 \times 3}{3 \times 2} = \frac{7}{2} \)

Now, our expression looks like:
\[ \frac{5}{3} - \frac{19}{4} + \frac{7}{2} \]

### Step 3: Find a Common Denominator
To combine the fractions, we need a common denominator. The least common multiple of 3, 4, and 2 is 12.

Now we convert each fraction:
- \( \frac{5}{3} = \frac{5 \times 4}{3 \times 4} = \frac{20}{12} \)
- \( \frac{19}{4} = \frac{19 \times 3}{4 \times 3} = \frac{57}{12} \)
- \( \frac{7}{2} = \frac{7 \times 6}{2 \times 6} = \frac{42}{12} \)

### Step 4: Combine the Fractions
Now we can combine the fractions:
\[ \frac{20}{12} - \frac{57}{12} + \frac{42}{12} \]

Combine them:
\[ \frac{20 - 57 + 42}{12} = \frac{5}{12} \]

### Final Answer
The final answer is:
\[ \frac{5}{12} \]