(3.6-1(1)/(8)div (3)/(4))cdot 15

To solve the expression \((3.6 - 1 \frac{1}{8} \div \frac{3}{4}) \cdot 15\), we need to follow the order of operations (PEMDAS/BODMAS):<br /><br />1. **Parentheses/Brackets**<br />2. **Exponents/Orders**<br />3. **Multiplication and Division (from left to right)**<br />4. **Addition and Subtraction (from left to right)**<br /><br />Let's break it down step by step:<br /><br />### Step 1: Convert the mixed number to an improper fraction<br />\[ 1 \frac{1}{8} = \frac{9}{8} \]<br /><br />### Step 2: Perform the division inside the parentheses<br />\[ \frac{9}{8} \div \frac{3}{4} \]<br /><br />To divide by a fraction, multiply by its reciprocal:<br />\[ \frac{9}{8} \times \frac{4}{3} = \frac{9 \times 4}{8 \times 3} = \frac{36}{24} = \frac{3}{2} \]<br /><br />### Step 3: Subtract the result from 3.6<br />\[ 3.6 - \frac{3}{2} \]<br /><br />Convert 3.6 to a fraction:<br />\[ 3.6 = \frac{36}{10} = \frac{18}{5} \]<br /><br />Now subtract:<br />\[ \frac{18}{5} - \frac{3}{2} \]<br /><br />Find a common denominator (which is 10):<br />\[ \frac{18}{5} = \frac{36}{10} \]<br />\[ \frac{3}{2} = \frac{15}{10} \]<br /><br />Subtract:<br />\[ \frac{36}{10} - \frac{15}{10} = \frac{21}{10} = 2.1 \]<br /><br />### Step 4: Multiply the result by 15<br />\[ 2.1 \times 15 = 31.5 \]<br /><br />So, the final answer is:<br />\[ (3.6 - 1 \frac{1}{8} \div \frac{3}{4}) \cdot 15 = 31.5 \]