2/5 divided by 1/4 as a fraction
The Correct Answer and Explanation is :
To divide two fractions, you multiply the first fraction by the reciprocal (or inverse) of the second fraction. Here’s the step-by-step process for dividing ( \frac{2}{5} ) by ( \frac{1}{4} ):
Step 1: Write the problem as a multiplication
When dividing by a fraction, we multiply by the reciprocal (invert the second fraction). So, the problem becomes:
[
\frac{2}{5} \div \frac{1}{4} = \frac{2}{5} \times \frac{4}{1}
]
Step 2: Multiply the fractions
To multiply fractions, multiply the numerators (top numbers) and the denominators (bottom numbers) separately:
[
\text{Numerator: } 2 \times 4 = 8
]
[
\text{Denominator: } 5 \times 1 = 5
]
So, the result of the multiplication is:
[
\frac{8}{5}
]
Step 3: Simplify if needed
In this case, ( \frac{8}{5} ) is already in its simplest form because 8 and 5 have no common factors other than 1.
Final Answer
The result of dividing ( \frac{2}{5} ) by ( \frac{1}{4} ) is:
[
\frac{8}{5}
]
Explanation:
The key to dividing fractions is understanding the reciprocal. Dividing by a fraction means asking how many times the denominator of the second fraction can fit into the numerator of the first. In this case, ( \frac{2}{5} ) divided by ( \frac{1}{4} ) asks how many times ( \frac{1}{4} ) fits into ( \frac{2}{5} ). By multiplying by the reciprocal of ( \frac{1}{4} ) (which is ( \frac{4}{1} )), we convert the division problem into a multiplication problem, making it easier to solve.
This method applies to all division of fractions and ensures that the operation is straightforward and efficient.