nikki loves to travel. he spent 4 5/6days in her first destination 3 2/3 days in her second destination 7 1/4 days in her third destination how many days longer was her last trip than the first two trips
Answer (1)
Answer:Calculate the total duration of the first two trips, then subtract this sum from the duration of the third trip. Step 1 . Convert mixed numbers to improper fractions. First trip: \(4\frac{5}{6}=\frac{(4\times 6)+5}{6}=\frac{29}{6}\) days. Second trip: \(3\frac{2}{3}=\frac{(3\times 3)+2}{3}=\frac{11}{3}\) days. Third trip: \(7\frac{1}{4}=\frac{(7\times 4)+1}{4}=\frac{29}{4}\) days. Step 2 . Calculate the total duration of the first two trips. Sum of first two trips: \(\frac{29}{6}+\frac{11}{3}\) Find a common denominator: \(\frac{29}{6}+\frac{11\times 2}{3\times 2}=\frac{29}{6}+\frac{22}{6}\) Total for first two trips: \(\frac{29+22}{6}=\frac{51}{6}\) days. Step 3 . Find the difference between the third trip and the sum of the first two trips. Difference: \(\frac{29}{4}-\frac{51}{6}\) Find a common denominator (least common multiple of \(4\) and \(6\) is \(12\)): \(\frac{29\times 3}{4\times 3}-\frac{51\times 2}{6\times 2}\) Difference: \(\frac{87}{12}-\frac{102}{12}=\frac{87-102}{12}=-\frac{15}{12}\) Simplify the fraction: \(-\frac{15}{12}=-\frac{5}{4}\) days. Solution The third trip was \(\frac{5}{4}\) days shorter than the first two trips combined.
