What is the reciprocal of $15 \frac{2}{3}$?
A. $15 \frac{3}{2}$
B. $3 \frac{2}{15}$
C. $\frac{45}{3}$
D. $\frac{3}{47}$
Answer (1)
Convert the mixed number to an improper fraction: 15 3 2 = 3 47 .
Find the reciprocal of the improper fraction by inverting it.
The reciprocal of 3 47 is 47 3 .
The final answer is 47 3 .
Explanation
Understanding the Problem We are asked to find the reciprocal of the mixed number 15 3 2 . The reciprocal of a number x is x 1 .
Converting to an Improper Fraction First, we need to convert the mixed number 15 3 2 to an improper fraction. To do this, we multiply the whole number part (15) by the denominator (3) and add the numerator (2). This gives us 15 ⋅ 3 + 2 = 45 + 2 = 47 . So, the improper fraction is 3 47 .
Finding the Reciprocal Now, we find the reciprocal of the improper fraction 3 47 . The reciprocal is found by inverting the fraction, which means swapping the numerator and the denominator.
Final Answer Therefore, the reciprocal of 3 47 is 47 3 .
Examples
Understanding reciprocals is useful in many real-life situations. For example, if you want to share a pizza equally among a group of friends, the reciprocal helps you determine each person's share. If you have 7 friends, each person gets 7 1 of the pizza. Another example is when converting units. If 1 inch is equal to 2.54 centimeters, then 1 centimeter is equal to 2.54 1 inches. Reciprocals are also used in calculating rates and proportions, making them a fundamental concept in everyday problem-solving.
