What is the reciprocal of 3 1/5?
Understand the Problem
The question is asking for the reciprocal of the mixed number 3 1/5. To find the reciprocal, we first convert the mixed number into an improper fraction and then take the reciprocal of that fraction.
Answer
The reciprocal of \( 3 \frac{1}{5} \) is \( \frac{5}{16} \).
Answer for screen readers
The reciprocal of the mixed number ( 3 \frac{1}{5} ) is ( \frac{5}{16} ).
Steps to Solve
- Convert the mixed number to an improper fraction
To convert the mixed number ( 3 \frac{1}{5} ) to an improper fraction, we multiply the whole number by the denominator and add the numerator.
Calculation: $$ 3 \times 5 + 1 = 15 + 1 = 16 $$
So, the improper fraction is: $$ \frac{16}{5} $$
- Find the reciprocal of the improper fraction
The reciprocal of a fraction is obtained by swapping the numerator and the denominator.
Therefore, the reciprocal of ( \frac{16}{5} ) is: $$ \frac{5}{16} $$
The reciprocal of the mixed number ( 3 \frac{1}{5} ) is ( \frac{5}{16} ).
More Information
Finding the reciprocal is helpful in various mathematical operations, especially in division of fractions. The conversion from mixed number to improper fraction is a fundamental skill in fraction operations.
Tips
- Confusing the steps of converting mixed numbers with operations on fractions. Always make sure to follow through the conversion properly.
- Forgetting to take the reciprocal after converting to an improper fraction.
