Solve 2/5 divided by 4 and reduce the answer
The Correct Answer and Explanation is:
To solve ( \frac{2}{5} \div 4 ), we need to follow these steps:
Step 1: Understand the operation
Dividing by a number is the same as multiplying by its reciprocal. The reciprocal of a number is simply 1 divided by that number. So, when we divide ( \frac{2}{5} ) by 4, we can rewrite the expression as:
[
\frac{2}{5} \div 4 = \frac{2}{5} \times \frac{1}{4}
]
Step 2: Multiply the fractions
When multiplying fractions, multiply the numerators together and the denominators together:
[
\frac{2}{5} \times \frac{1}{4} = \frac{2 \times 1}{5 \times 4} = \frac{2}{20}
]
Step 3: Simplify the fraction
Now, simplify ( \frac{2}{20} ). Both the numerator (2) and the denominator (20) share a common factor of 2. To simplify, divide both the numerator and the denominator by 2:
[
\frac{2}{20} = \frac{2 \div 2}{20 \div 2} = \frac{1}{10}
]
Final Answer:
[
\frac{2}{5} \div 4 = \frac{1}{10}
]
Explanation:
Dividing a fraction by a whole number involves multiplying the fraction by the reciprocal of the whole number. In this case, ( \frac{2}{5} \div 4 ) becomes ( \frac{2}{5} \times \frac{1}{4} ). Multiplying these fractions results in ( \frac{2}{20} ), which simplifies to ( \frac{1}{10} ).
This method is based on the rule that dividing by a number is equivalent to multiplying by its reciprocal. Reducing fractions is essential to express answers in their simplest form, making the final result easier to interpret. In this case, after simplifying ( \frac{2}{20} ), we get ( \frac{1}{10} ), which is the reduced form of the answer.
This process is useful for various mathematical operations involving fractions, as it provides a systematic approach to handle division and simplification.