What is the reciprocal of 2 3/4?
Understand the Problem
The question is asking for the reciprocal of the mixed number 2 3/4. To find the reciprocal, we first need to convert the mixed number into an improper fraction and then take the reciprocal of that fraction.
Answer
The reciprocal of $2 \frac{3}{4}$ is $\frac{4}{11}$.
Answer for screen readers
The reciprocal of the mixed number $2 \frac{3}{4}$ is $\frac{4}{11}$.
Steps to Solve
- Convert the mixed number to an improper fraction
To convert the mixed number $2 \frac{3}{4}$ to an improper fraction, multiply the whole number by the denominator and add the numerator. Then, place that result over the original denominator.
$$ 2 \frac{3}{4} = \frac{(2 \times 4) + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4} $$
- Find the reciprocal of the improper fraction
The reciprocal of a fraction is obtained by swapping the numerator and the denominator. For the fraction $\frac{11}{4}$, the reciprocal will be:
$$ \text{Reciprocal} = \frac{4}{11} $$
The reciprocal of the mixed number $2 \frac{3}{4}$ is $\frac{4}{11}$.
More Information
The process of finding the reciprocal is useful in various mathematical operations, such as division of fractions. Knowing how to convert mixed numbers to improper fractions is also a key skill in fraction operations.
Tips
- Forgetting to convert the mixed number completely to an improper fraction before taking the reciprocal. Always ensure you perform this step accurately.
