James and luke took a two-day hike along the Appalachian trial. the first day they hiked 4 1/6 and the second day they hiked 3 2/3. what total distance did the boys hike?
To find the total distance the boys hiked, we need to add the distances they hiked on each day.
First, let's convert the mixed numbers to improper fractions.
4 1/6 = (4 * 6 + 1) / 6 = 25/6
3 2/3 = (3 * 3 + 2) / 3 = 11/3
Next, add the two fractions:
25/6 + 11/3
To add these fractions, we need to find a common denominator. The least common multiple (LCM) of 6 and 3 is 6. Therefore, we multiply the numerators and denominators by the appropriate factors to obtain common denominators:
25/6 + 22/6
Combine the numerators:
(25 + 22) / 6 = 47/6
Now, we can express the improper fraction as a mixed number:
47/6 = 7 5/6
Therefore, the boys hiked a total distance of 7 5/6 on their two-day hike.
To find the total distance James and Luke hiked, we need to add the distance hiked on the first and second days.
First day: James and Luke hiked 4 1/6 miles.
Second day: James and Luke hiked 3 2/3 miles.
To add these fractions, we need to find a common denominator:
First day = 4 1/6 = (4 * 6 + 1) / 6 = 25/6
Second day = 3 2/3 = (3 * 3 + 2) / 3 = 11/3
Now let's add the fractions:
25/6 + 11/3
To add these fractions, we need them to have the same denominator. The least common multiple (LCM) of 6 and 3 is 6.
Multiply the numerator and denominator of the first fraction by 3:
(25/6) * (3/3) = 75/18
Multiply the numerator and denominator of the second fraction by 2:
(11/3) * (2/2) = 22/6
Now we can add the fractions:
75/18 + 22/6
To add these fractions, we need a common denominator. The LCM of 18 and 6 is 18.
Multiply the numerator and denominator of the first fraction by 1:
(75/18) * (1/1) = 75/18
Multiply the numerator and denominator of the second fraction by 3:
(22/6) * (3/3) = 66/18
Now we can add the fractions:
75/18 + 66/18 = (75 + 66) / 18 = 141/18
To simplify this fraction, we can divide the numerator and denominator by their greatest common divisor (GCD), which is 3:
141/18 = (141/3) / (18/3) = 47/6
Therefore, James and Luke hiked a total distance of 47/6 miles or approximately 7 5/6 miles.
To find the total distance that James and Luke hiked, we need to add the distances they covered on both days.
Let's start with the first day when they hiked 4 1/6 miles. To add this fraction to a whole number, we need to convert it to an improper fraction.
The whole number, 4, can also be expressed as 4/1.
Now let's convert the fraction, 1/6, to have the same denominator as 4/1. Multiply the numerator and denominator of 1/6 by 1, resulting in 1/6.
Now we can add the two fractions: 4/1 + 1/6. To do this, we need to find a common denominator, which in this case is 6.
To convert 4/1 to have the same denominator as 6, we multiply the numerator and denominator by 6, resulting in 24/6.
Now we can add the fractions: 24/6 + 1/6 = 25/6.
So, the distance covered on the first day is 25/6 miles.
Now let's move to the second day, where they hiked 3 2/3 miles. Again, we convert the mixed number to an improper fraction.
The whole number, 3, can be expressed as 3/1.
Now let's convert the fraction, 2/3, to have the same denominator as 3/1. Multiply the numerator and denominator of 2/3 by 1, resulting in 2/3.
Now we can add the two fractions: 3/1 + 2/3. To do this, we again need a common denominator, which is 3 in this case.
To convert 3/1 to have the same denominator as 3, we multiply the numerator and denominator by 3, resulting in 9/3.
Now we can add the fractions: 9/3 + 2/3 = 11/3.
So, the distance covered on the second day is 11/3 miles.
Finally, we can find the total distance covered by adding the distances from both days: 25/6 + 11/3.
To add these fractions, we need to convert them to have a common denominator. In this case, it is 6.
To convert 11/3 to have the same denominator as 6, we multiply the numerator and denominator by 2, resulting in 22/6.
Now we can add the fractions: 25/6 + 22/6 = 47/6.
Therefore, the total distance James and Luke hiked is 47/6 miles.