Which expression is equivalent to 1/5 divided by 1/2
The Correct Answer and Explanation is :
The expression ( \frac{1}{5} \div \frac{1}{2} ) can be simplified as follows:
Step 1: Understand division of fractions
Dividing fractions involves multiplying the first fraction by the reciprocal (the inverse) of the second fraction. The reciprocal of ( \frac{1}{2} ) is ( \frac{2}{1} ).
So, we rewrite the expression as:
[
\frac{1}{5} \div \frac{1}{2} = \frac{1}{5} \times \frac{2}{1}
]
Step 2: Multiply the fractions
To multiply two fractions, multiply the numerators (top numbers) and the denominators (bottom numbers):
[
\frac{1 \times 2}{5 \times 1} = \frac{2}{5}
]
Step 3: Simplified result
Thus, ( \frac{1}{5} \div \frac{1}{2} = \frac{2}{5} ).
Explanation
When dividing fractions, it’s essential to understand the concept of division in terms of multiplication. Dividing by a fraction is the same as multiplying by its reciprocal. The operation ( \frac{1}{5} \div \frac{1}{2} ) is asking, “How many ( \frac{1}{2} )’s fit into ( \frac{1}{5} )?” By multiplying by the reciprocal ( \frac{2}{1} ), we essentially flip the second fraction and multiply.
This concept is important in many real-world contexts, such as when converting measurements or dealing with ratios. In this case, ( \frac{1}{5} \div \frac{1}{2} ) shows how fractions can be manipulated through multiplication and division.
Final Answer:
The expression ( \frac{1}{5} \div \frac{1}{2} ) simplifies to ( \frac{2}{5} ).