$$ 3.8\left(23 \frac{1}{4}-100 \frac{1}{3}\right) \cdot \frac{7}{8} $$

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UpStudy AI · Accepted Answer

To evaluate the expression:

$$
3.8\left(23 \frac{1}{4} - 100 \frac{1}{3}\right) \cdot \frac{7}{8}
$$

let's break it down step by step.

### Step 1: Convert Mixed Numbers to Improper Fractions

1. **Convert $$23 \frac{1}{4}$$:**
   $$
   23 \frac{1}{4} = \frac{23 \times 4 + 1}{4} = \frac{92 + 1}{4} = \frac{93}{4}
   $$

2. **Convert $$100 \frac{1}{3}$$:**
   $$
   100 \frac{1}{3} = \frac{100 \times 3 + 1}{3} = \frac{300 + 1}{3} = \frac{301}{3}
   $$

### Step 2: Subtract the Fractions

$$
23 \frac{1}{4} - 100 \frac{1}{3} = \frac{93}{4} - \frac{301}{3}
$$

To subtract these, find a common denominator, which is 12:

$$
\frac{93}{4} = \frac{93 \times 3}{4 \times 3} = \frac{279}{12}
$$
$$
\frac{301}{3} = \frac{301 \times 4}{3 \times 4} = \frac{1204}{12}
$$
$$
\frac{279}{12} - \frac{1204}{12} = \frac{279 - 1204}{12} = \frac{-925}{12}
$$

### Step 3: Multiply by 3.8

First, express 3.8 as a fraction:

$$
3.8 = \frac{38}{10} = \frac{19}{5}
$$

Now multiply:

$$
\frac{19}{5} \times \frac{-925}{12} = \frac{19 \times (-925)}{5 \times 12} = \frac{-17,575}{60} = \frac{-3,515}{12} = -292 \frac{11}{12}
$$

### Step 4: Multiply by $$\frac{7}{8}$$

$$
-292 \frac{11}{12} \times \frac{7}{8} = \frac{-3515}{12} \times \frac{7}{8} = \frac{-24,605}{96}
$$

Simplify the fraction:

$$
\frac{-24,605}{96} = \frac{-24605}{96} \approx -256.3021
$$

### Final Answer

$$
3.8\left(23 \frac{1}{4} - 100 \frac{1}{3}\right) \cdot \frac{7}{8} \approx -256.3021
$$
The result of the expression $$ 3.8\left(23 \frac{1}{4} - 100 \frac{1}{3}\right) \cdot \frac{7}{8} $$ is approximately -256.3021.

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