Questions: Calculate the value of 3/8 ÷ 13/12

Transcript text: Calculate the value of \[ \frac{3}{8} \div \frac{13}{12} \]

Solution

Solution Steps

To solve the division of two fractions, we can multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping its numerator and denominator.

Step 1: Define the Fractions

We start with the fractions \(\frac{3}{8}\) and \(\frac{13}{12}\).

Step 2: Find the Reciprocal of the Second Fraction

The reciprocal of \(\frac{13}{12}\) is \(\frac{12}{13}\).

Step 3: Multiply the First Fraction by the Reciprocal of the Second Fraction

\[ \frac{3}{8} \times \frac{12}{13} = \frac{3 \times 12}{8 \times 13} = \frac{36}{104} \]

Step 4: Simplify the Result

To simplify \(\frac{36}{104}\), we find the greatest common divisor (GCD) of 36 and 104, which is 4. Thus, \[ \frac{36 \div 4}{104 \div 4} = \frac{9}{26} \]

Step 5: Convert to Decimal Form

\[ \frac{9}{26} \approx 0.3462 \]

Final Answer

\(\boxed{\frac{9}{26}}\)

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