Ms. Keegan and Ms. Daniel took a two-day hike along the Appalachian Trail. The first day they hiked 4 ⅔ miles and the second day they hiked 2 ½ miles What total distance did they hike in simplest form?

Question

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7 1/6 miles
6 3/5 miles
7 3/5 miles
6 7/6 miles
Option 3

Answer 1

To find the total distance they hiked, we need to add the distances from the first day and the second day:

4 ⅔ miles + 2 ½ miles

To add these fractions, we need a common denominator. The smallest number that 3 and 6 both divide into evenly is 6.

Converting 4 ⅔ to an improper fraction: 4 ⅔ = (4 * 3 + 2) / 3 = 14/3

Converting 2 ½ to an improper fraction: 2 ½ = (2 * 2 + 1) / 2 = 5/2

Now, we can rewrite the expression:

14/3 miles + 5/2 miles

To add these fractions, we need to find a common denominator. The common denominator is 6.

Converting 14/3 to have a denominator of 6: (14/3) * (2/2) = 28/6

Converting 5/2 to have a denominator of 6: (5/2) * (3/3) = 15/6

Now, we can rewrite the expression with the common denominator:

28/6 miles + 15/6 miles

Adding these fractions gives us:

(28 + 15) / 6 = 43/6

So, in simplest form, the total distance they hiked is 6 7/6 miles.