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Find the product 1/10xx91xx5(11)/(13...

Find the product
`1/10xx91xx5(11)/(13`

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To find the product of the expression \( \frac{1}{10} \times 91 \times 5 \frac{11}{13} \), we can follow these steps: ### Step 1: Convert the mixed fraction to an improper fraction The mixed fraction \( 5 \frac{11}{13} \) can be converted to an improper fraction. To do this, we multiply the whole number (5) by the denominator (13) and add the numerator (11): \[ 5 \frac{11}{13} = \frac{(5 \times 13) + 11}{13} = \frac{65 + 11}{13} = \frac{76}{13} \] ### Step 2: Rewrite the expression Now we can rewrite the original expression using the improper fraction: \[ \frac{1}{10} \times 91 \times \frac{76}{13} \] ### Step 3: Simplify the expression We can simplify the multiplication. First, we can express 91 as \( \frac{91}{1} \): \[ \frac{1}{10} \times \frac{91}{1} \times \frac{76}{13} \] Now we can multiply the fractions: \[ = \frac{1 \times 91 \times 76}{10 \times 1 \times 13} = \frac{91 \times 76}{130} \] ### Step 4: Calculate \( 91 \times 76 \) Now we calculate \( 91 \times 76 \): \[ 91 \times 76 = 6916 \] So, we have: \[ \frac{6916}{130} \] ### Step 5: Simplify the fraction Next, we can simplify \( \frac{6916}{130} \). We can divide both the numerator and the denominator by 2 (since both are even): \[ \frac{6916 \div 2}{130 \div 2} = \frac{3458}{65} \] ### Step 6: Divide to find the mixed number Now we can divide \( 3458 \) by \( 65 \): \[ 3458 \div 65 = 53 \quad \text{(whole number)} \] Now, we find the remainder: \[ 3458 - (53 \times 65) = 3458 - 3445 = 13 \] So, we can express this as a mixed number: \[ 53 \frac{13}{65} \] ### Final Answer Thus, the final answer is: \[ 53 \frac{13}{65} \]
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