What is the reciprocal of 5/6?
The Correct Answer and Explanation is :
The reciprocal of ( \frac{5}{6} ) is ( \frac{6}{5} ).
Explanation:
The reciprocal of a fraction is found by swapping the numerator (top number) and the denominator (bottom number). In the case of ( \frac{5}{6} ), the numerator is 5, and the denominator is 6. To find the reciprocal, we simply switch their positions, resulting in ( \frac{6}{5} ).
In mathematical terms, the reciprocal of any nonzero fraction ( \frac{a}{b} ) is ( \frac{b}{a} ). This principle works for both proper fractions (where the numerator is smaller than the denominator) and improper fractions (where the numerator is larger than the denominator). The reciprocal operation also applies to whole numbers by expressing them as fractions. For example, the reciprocal of 5 (written as ( \frac{5}{1} )) would be ( \frac{1}{5} ).
Reciprocals are often used in various mathematical operations, especially in division. When you divide by a fraction, it is the same as multiplying by its reciprocal. For example, to divide by ( \frac{5}{6} ), you multiply by ( \frac{6}{5} ).
Example:
If you have the division problem ( \frac{1}{2} \div \frac{5}{6} ), you can convert it into multiplication by using the reciprocal of ( \frac{5}{6} ):
[
\frac{1}{2} \div \frac{5}{6} = \frac{1}{2} \times \frac{6}{5} = \frac{1 \times 6}{2 \times 5} = \frac{6}{10} = \frac{3}{5}.
]
This shows how reciprocals make division simpler by converting it into multiplication.
In conclusion, the reciprocal of ( \frac{5}{6} ) is ( \frac{6}{5} ), and understanding this concept is crucial for performing operations with fractions and solving equations involving fractions.