Find the product
`7(1)/(4)xx7/58xx1(11)/(21)`

Answer

To find the product of the fractions \( 7\frac{1}{4} \times \frac{7}{58} \times 1\frac{11}{21} \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
1. Convert \( 7\frac{1}{4} \) to an improper fraction:
\[ 7\frac{1}{4} = \frac{4 \times 7 + 1}{4} = \frac{28 + 1}{4} = \frac{29}{4} \]

2. Convert \( 1\frac{11}{21} \) to an improper fraction:
\[ 1\frac{11}{21} = \frac{21 \times 1 + 11}{21} = \frac{21 + 11}{21} = \frac{32}{21} \]

### Step 2: Write the Product of the Improper Fractions
Now we can rewrite the expression using the improper fractions:
\[ \frac{29}{4} \times \frac{7}{58} \times \frac{32}{21} \]

### Step 3: Multiply the Numerators and Denominators
Multiply the numerators together and the denominators together:
\[ \text{Numerator: } 29 \times 7 \times 32 \]
\[ \text{Denominator: } 4 \times 58 \times 21 \]

### Step 4: Simplify the Expression
1. Calculate the numerator:
\[ 29 \times 7 = 203 \]
\[ 203 \times 32 = 6496 \]
So, the numerator is \( 6496 \).

2. Calculate the denominator:
\[ 4 \times 58 = 232 \]
\[ 232 \times 21 = 4872 \]
So, the denominator is \( 4872 \).

### Step 5: Write the Resulting Fraction
Now we have:
\[ \frac{6496}{4872} \]

### Step 6: Simplify the Fraction
To simplify \( \frac{6496}{4872} \), we can divide both the numerator and denominator by their greatest common divisor (GCD).

Using the GCD, we find:
\[ \frac{6496 \div 1624}{4872 \div 1624} = \frac{4}{3} \]

### Final Answer
Thus, the product of \( 7\frac{1}{4} \times \frac{7}{58} \times 1\frac{11}{21} \) is:
\[ \frac{4}{3} \]

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