what is the reciprocal of 8/5?
The Correct Answer and Explanation is :
The reciprocal of a fraction is obtained by swapping its numerator and denominator. Therefore, the reciprocal of ( \frac{8}{5} ) is ( \frac{5}{8} ).
Explanation
To understand the concept of reciprocals, let’s break it down further. A reciprocal is a value that, when multiplied by the original number, gives the product of 1. For any non-zero number ( x ), the reciprocal is represented as ( \frac{1}{x} ). When dealing with fractions, the reciprocal is specifically obtained by flipping the fraction.
For example, the fraction ( \frac{8}{5} ) consists of a numerator (the top part of the fraction) and a denominator (the bottom part). In this case, 8 is the numerator and 5 is the denominator. When we take the reciprocal of ( \frac{8}{5} ), we switch these two parts, leading us to ( \frac{5}{8} ).
Reciprocals are particularly useful in various mathematical operations, especially in division. Dividing by a fraction is equivalent to multiplying by its reciprocal. For instance, if you have a division problem such as ( \frac{a}{\frac{8}{5}} ), you can rewrite it as ( a \times \frac{5}{8} ). This simplification often makes calculations easier and more manageable.
Reciprocals also appear in different areas of mathematics, such as algebra, where they can help solve equations. For example, if you need to solve for ( x ) in an equation like ( \frac{8}{5}x = 10 ), you can multiply both sides by the reciprocal of ( \frac{8}{5} ), which is ( \frac{5}{8} ). This operation will isolate ( x ) and allow you to solve for it effectively.
In conclusion, the reciprocal of ( \frac{8}{5} ) is ( \frac{5}{8} ), and understanding how to find and use reciprocals is an essential skill in mathematics.