Divide these two fractions: [tex]$\frac{5}{6} \div \frac{6}{8}=?$[/tex]
Answer (1)
To divide fractions, multiply the first fraction by the reciprocal of the second.
The reciprocal of 8 6 is 6 8 , so the problem becomes 6 5 × 6 8 .
Multiply the numerators and denominators: 6 × 6 5 × 8 = 36 40 .
Simplify the fraction: 36 40 = 9 10 .
The final answer is 9 10 .
Explanation
Understanding the Problem We are asked to divide the fraction 6 5 by the fraction 8 6 . To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
Finding the Reciprocal The reciprocal of 8 6 is 6 8 . So, we need to calculate 6 5 × 6 8 .
Multiplying the Fractions To multiply fractions, we multiply the numerators together and the denominators together: 6 5 × 6 8 = 6 × 6 5 × 8 = 36 40 .
Simplifying the Fraction Now we simplify the fraction 36 40 by finding the greatest common divisor (GCD) of 40 and 36. The GCD of 40 and 36 is 4. We divide both the numerator and the denominator by 4: 36 40 = 36 ÷ 4 40 ÷ 4 = 9 10 .
Final Answer The simplified fraction is 9 10 . This can also be written as a mixed number: 1 9 1 . Therefore, the result of dividing 6 5 by 8 6 is 9 10 .
Examples
Dividing fractions is a fundamental skill with many real-world applications. For example, if you have 6 5 of a pizza and you want to share it equally among 8 6 of your friends, you would divide 6 5 by 8 6 to determine how much pizza each friend receives. This type of calculation is also useful in cooking, construction, and other fields where proportional relationships are important.
