What is 5/8 divided by 1/4 ?
The Correct Answer and Explanation is :
The correct answer is: ( \frac{5}{2} ) or ( 2.5 )
To solve the division problem ( \frac{5}{8} \div \frac{1}{4} ), we can use the rule of dividing fractions, which involves multiplying by the reciprocal of the divisor. The reciprocal of ( \frac{1}{4} ) is ( \frac{4}{1} ) (or simply 4). Thus, we can rewrite the division as:
[
\frac{5}{8} \div \frac{1}{4} = \frac{5}{8} \times \frac{4}{1}
]
Next, we multiply the numerators together and the denominators together:
[
\frac{5 \times 4}{8 \times 1} = \frac{20}{8}
]
Now, we simplify ( \frac{20}{8} ). Both the numerator and the denominator can be divided by their greatest common divisor, which is 4:
[
\frac{20 \div 4}{8 \div 4} = \frac{5}{2}
]
So, the final answer to ( \frac{5}{8} \div \frac{1}{4} ) is ( \frac{5}{2} ) or ( 2.5 ).
Explanation:
Understanding how to divide fractions is essential in mathematics, especially in various applications like cooking, budgeting, and even nursing. The division of fractions can initially seem complex, but it follows a straightforward rule: instead of dividing, you multiply by the reciprocal.
The reciprocal of a fraction is simply what you get when you flip the numerator and denominator. For example, the reciprocal of ( \frac{1}{4} ) is ( \frac{4}{1} ). This concept is fundamental because it transforms the operation into a multiplication problem, which is often easier to manage.
In our example, after finding the reciprocal, we multiplied ( \frac{5}{8} ) by ( \frac{4}{1} ). This operation involved multiplying straight across for both the numerator and denominator. The resulting fraction ( \frac{20}{8} ) illustrates how multiplication can yield larger numbers that we can then simplify.
Lastly, reducing ( \frac{20}{8} ) to its simplest form shows the importance of simplifying answers for clarity and precision, especially in fields like healthcare where accurate measurements are critical. Thus, understanding how to divide fractions equips you with a valuable mathematical tool for everyday calculations.