Final answer:
Jenna has 1/6 of a cake to share among 3 friends, which means each friend gets 1/18 of the cake after dividing the fraction by the number of friends, demonstrating the concept of multiplying by the reciprocal in fraction division.
Step-by-step explanation:
Understanding the Division of Fractions
Jenna has 1/6 of a cake and wishes to share it among her 3 friends equally. To divide the fraction of the cake she has by 3, you perform the following calculation: (1/6) ÷ 3. This is equivalent to (1/6) * (1/3), since dividing by a number is the same as multiplying by its reciprocal.
To find the reciprocal of 3, we write it as a fraction, which is 3/1. The reciprocal is then 1/3. So now we multiply the numerators (1 * 1) and the denominators (6 * 3), resulting in 1/18. Therefore, each of Jenna's friends would get 1/18 of the cake.
In conclusion, when faced with dividing a fraction by a whole number, the process involves multiplication by the reciprocal of that whole number. This concept is a fundamental part of fraction operations in mathematics.