Question

initially, your waist measurement was forty - one and three - fourths inches. after one week, your waist is now forty - one and two - fifths inches. describe the difference between your waist measurements at the end of the first week. the waist measurement difference is negative one - fifth inch, a loss of one - fifth inch. the waist measurement difference is one - fifth inch, a loss of negative one - fifth inch. the waist measurement difference is negative seven - twentieths inch, a loss of seven - twentieths inch.

Explanation:

Step1: Convert mixed numbers to improper fractions

Initial waist: \( 41\frac{3}{4} = \frac{41\times4 + 3}{4}=\frac{167}{4} \)
Final waist: \( 41\frac{2}{5}=\frac{41\times5 + 2}{5}=\frac{207}{5} \)

Step2: Find the difference

Difference = Final - Initial = \( \frac{207}{5}-\frac{167}{4} \)
Find a common denominator (20): \( \frac{207\times4}{5\times4}-\frac{167\times5}{4\times5}=\frac{828}{20}-\frac{835}{20}=\frac{828 - 835}{20}=\frac{-7}{20} \)
\( \frac{-7}{20} \) is negative, meaning a loss of \( \frac{7}{20} \) inch.

Answer:

The waist measurement difference is negative seven - twentieths inch, a loss of seven - twentieths inch.