1/5 divided by 15/4
The Correct answer and Explanation is :
The correct answer is: ( \frac{4}{75} )
To divide fractions, you can follow a straightforward process: multiply the first fraction by the reciprocal of the second fraction. Here’s how you can solve ( \frac{1}{5} \div \frac{15}{4} ):
- Identify the fractions: You have ( \frac{1}{5} ) and ( \frac{15}{4} ).
- Find the reciprocal of the second fraction: The reciprocal of ( \frac{15}{4} ) is ( \frac{4}{15} ).
- Rewrite the division as multiplication: [
\frac{1}{5} \div \frac{15}{4} = \frac{1}{5} \times \frac{4}{15}
] - Multiply the fractions: To multiply fractions, multiply the numerators together and the denominators together: [
\frac{1 \times 4}{5 \times 15} = \frac{4}{75}
] - Final Result: The result of ( \frac{1}{5} \div \frac{15}{4} ) is ( \frac{4}{75} ).
Explanation
When dividing fractions, the process of multiplying by the reciprocal simplifies the calculation. This is based on the property that dividing by a number is equivalent to multiplying by its reciprocal. The reciprocal of a fraction ( \frac{a}{b} ) is ( \frac{b}{a} ).
In this case, we begin with ( \frac{1}{5} ), which is a simple fraction representing one part out of five equal parts. When we divide this by ( \frac{15}{4} ), we are essentially asking how many times ( \frac{15}{4} ) fits into ( \frac{1}{5} ). By flipping ( \frac{15}{4} ) to its reciprocal ( \frac{4}{15} ) and performing multiplication, we can directly find the solution without complex division.
This method is not only efficient but also eliminates potential errors that can arise from dividing fractions directly. Multiplying the numerators and denominators yields a product that can often be simplified further, although in this case ( \frac{4}{75} ) is already in its simplest form. Thus, the final answer is ( \frac{4}{75} ).