Enter any number and calculate its reciprocal.
A reciprocal is the "flip" of a number, meaning the number becomes the denominator, and 1 becomes the numerator. For a number \( a \), its reciprocal is: \( \text{Reciprocal of } a = \frac{1}{a} \) The key property of a reciprocal is that when a number is multiplied by its reciprocal, the result is always 1: \( a \times \frac{1}{a} = 1 \) Note: Zero does not have a reciprocal since division by zero is undefined.
Steps for Different Types of Numbers:
Solution:
\( \text{Reciprocal} = \frac{1}{40} = 0.025 \)
Result: The reciprocal of 40 is 0.025.
Solution:
Convert the decimal to a fraction:
\( 0.25 = \frac{1}{4} \)
Find the reciprocal:
\( \text{Reciprocal} = \frac{4}{1} = 4 \)
Result: The reciprocal of 0.25 is 4.
Solution:
\( \text{Reciprocal} = \frac{7}{5} \)
Result: The reciprocal of \( \frac{5}{7} \) is \( \frac{7}{5} \).
Solution:
Convert the mixed number to an improper fraction:
\( 4 \frac{3}{5} = \frac{23}{5} \)
Find the reciprocal:
\( \text{Reciprocal} = \frac{5}{23} \)
Result: The reciprocal of 4 3/5 is \( \frac{5}{23} \).