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 15 3 2 to an improper fraction: 15 3 2 = 3 47 .
Find the reciprocal of the improper fraction by swapping the numerator and denominator.
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 obtained by swapping the numerator and the denominator, which gives us 47 3 .
Final Answer Therefore, the reciprocal of 15 3 2 is 47 3 .
Examples
Imagine you are scaling a recipe that calls for 15 3 2 cups of flour, but you only want a fraction of the recipe. To find out what fraction of the original amount you are using, you need to find the reciprocal. In this case, the reciprocal of 15 3 2 is 47 3 , which tells you what fraction of the original recipe you are making. Understanding reciprocals helps in adjusting quantities and proportions in various real-life situations, such as cooking, mixing solutions, or calculating gear ratios.
