To solve the expression [tex]\(\frac{22}{7} \times\left[-\frac{7}{4}\right] \times\left[\frac{34}{4}\right] \times \frac{2}{1}\)[/tex], we can follow these steps:
### Step 1: Simplify the Expression
First, we can simplify each fraction individually and then multiply them together. Note that multiplication of fractions is straightforward: multiply the numerators together and the denominators together.
### Step 2: Combine the Numerators and Denominators
Write the numerators and denominators as follows:
Numerator: [tex]\(22 \times (-7) \times 34 \times 2\)[/tex]
Denominator: [tex]\(7 \times 4 \times 4 \times 1\)[/tex]
### Step 3: Calculate the Numerator
Now multiply the numerators together:
[tex]\[
22 \times (-7) = -154
\][/tex]
[tex]\[
-154 \times 34 = -5236
\][/tex]
[tex]\[
-5236 \times 2 = -10472
\][/tex]
So the final numerator is [tex]\(-10472\)[/tex].
### Step 4: Calculate the Denominator
Next, multiply the denominators together:
[tex]\[
7 \times 4 = 28
\][/tex]
[tex]\[
28 \times 4 = 112
\][/tex]
[tex]\[
112 \times 1 = 112
\][/tex]
So the final denominator is [tex]\(112\)[/tex].
### Step 5: Divide the Numerator by the Denominator
Finally, divide the numerator by the denominator to get the final result:
[tex]\[
\frac{-10472}{112} = -93.5
\][/tex]
### Conclusion
The detailed step-by-step solution to the expression [tex]\(\frac{22}{7} \times\left[-\frac{7}{4}\right] \times\left[\frac{34}{4}\right] \times \frac{2}{1}\)[/tex] is:
[tex]\[
\frac{-10472}{112} = -93.5
\][/tex]
### Summary
- Numerator: [tex]\(-10472\)[/tex]
- Denominator: [tex]\(112\)[/tex]
- Result: [tex]\(-93.5\)[/tex]
Thus, the answer is:
[tex]\[
\frac{22}{7} \times\left[-\frac{7}{4}\right] \times\left[\frac{34}{4}\right] \times \frac{2}{1} = -93.5
\][/tex]
