Simplify the following: 5/6÷1/2
Express your answer in simplest form.
The Correct Answer and Explanation is:
To simplify the expression ( \frac{5}{6} \div \frac{1}{2} ), we start by understanding how to divide fractions. The division of fractions can be transformed into multiplication by taking the reciprocal (or inverse) of the divisor. In this case, the divisor is ( \frac{1}{2} ).
Step 1: Identify the reciprocal
The reciprocal of ( \frac{1}{2} ) is ( \frac{2}{1} ) (or simply 2).
Step 2: Rewrite the division as multiplication
We can rewrite the original expression as follows:
[
\frac{5}{6} \div \frac{1}{2} = \frac{5}{6} \times \frac{2}{1}
]
Step 3: Perform the multiplication
Next, we multiply the numerators and denominators:
[
\frac{5 \times 2}{6 \times 1} = \frac{10}{6}
]
Step 4: Simplify the resulting fraction
Now we simplify ( \frac{10}{6} ). Both the numerator and the denominator can be divided by their greatest common divisor (GCD), which is 2:
[
\frac{10 \div 2}{6 \div 2} = \frac{5}{3}
]
Final Answer
Thus, the simplified form of ( \frac{5}{6} \div \frac{1}{2} ) is ( \frac{5}{3} ).
Conclusion
In summary, when dividing fractions, remember to multiply by the reciprocal of the divisor. This method helps us to simplify calculations efficiently. The expression ( \frac{5}{6} \div \frac{1}{2} ) transforms into ( \frac{5}{6} \times 2 ), allowing for straightforward multiplication and subsequent simplification. The resulting fraction ( \frac{10}{6} ) simplifies down to ( \frac{5}{3} ), which is in its simplest form. Understanding these steps will enhance your skills in fraction operations, a fundamental aspect of arithmetic that frequently appears in various mathematical contexts.