What’s 2/5 divided by 4 ( simplest form)
The Correct Answer and Explanation is :
To solve the problem ( \frac{2}{5} \div 4 ), we can follow a step-by-step approach to understand how to perform the division of a fraction by a whole number.
Step 1: Understand the Division of a Fraction by a Whole Number
When dividing a fraction by a whole number, we can rewrite the whole number as a fraction. The number 4 can be expressed as ( \frac{4}{1} ). Therefore, the expression becomes:
[
\frac{2}{5} \div \frac{4}{1}
]
Step 2: Apply the Rule of Dividing Fractions
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of ( \frac{4}{1} ) is ( \frac{1}{4} ). Thus, we can rewrite the division as a multiplication:
[
\frac{2}{5} \times \frac{1}{4}
]
Step 3: Multiply the Fractions
Next, we multiply the numerators and the denominators:
[
\frac{2 \times 1}{5 \times 4} = \frac{2}{20}
]
Step 4: Simplify the Result
The fraction ( \frac{2}{20} ) can be simplified. Both the numerator and the denominator can be divided by their greatest common divisor (GCD), which is 2:
[
\frac{2 \div 2}{20 \div 2} = \frac{1}{10}
]
Conclusion
Therefore, ( \frac{2}{5} \div 4 ) simplifies to ( \frac{1}{10} ).
This solution illustrates the process of converting division into multiplication by using the reciprocal, and then performing multiplication on the fractions. Simplifying the result is a crucial step to express the answer in its simplest form. Understanding these principles is essential for effectively working with fractions in various mathematical contexts.