James and Luke took a three-day hike along the Appalachian Trail. The first day they hiked 4 1/6
miles, the second day they hiked 3 2/3
miles, and the third day they hiked 4 2/3
miles. What total distance did the boys hike? You must type your response as a simplified mixed number.
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(1 point)
miles
To find the total distance, we need to add the distances from each day.
4 1/6 + 3 2/3 + 4 2/3
To add these mixed numbers, we need to convert them to improper fractions.
4 1/6 = (6 * 4 + 1) / 6 = 25/6
3 2/3 = (3 * 3 + 2) / 3 = 11/3
4 2/3 = (3 * 4 + 2) / 3 = 14/3
Now we can add the fractions:
25/6 + 11/3 + 14/3
To add these fractions, we need a common denominator, which is 6.
25/6 + 11/3 + 14/3 = 25/6 + 22/6 + 14/3
Now we can add the numerators together:
25 + 22 + 14 = 61
Our answer is the numerator 61 over the denominator 6, and this fraction can be simplified.
61/6 = 10 1/6
Therefore, the total distance they hiked is 10 1/6 miles.
To find the total distance the boys hiked, we need to add up the distances from each day.
First day: 4 1/6 miles
Second day: 3 2/3 miles
Third day: 4 2/3 miles
To add these fractions, we'll first convert them to improper fractions:
4 1/6 = (6 * 4 + 1)/6 = 25/6
3 2/3 = (3 * 3 + 2)/3 = 11/3
4 2/3 = (3 * 4 + 2)/3 = 14/3
Now, let's add the fractions:
25/6 + 11/3 + 14/3
To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 6. Let's convert the fractions:
25/6 = (25 * 1)/6 = 25/6
11/3 = (11 * 2)/6 = 22/6
14/3 = (14 * 2)/6 = 28/6
Now, let's add the fractions:
25/6 + 22/6 + 28/6 = (25 + 22 + 28)/6 = 75/6
Finally, let's simplify the fraction:
75/6 = 12 3/6
The boys hiked a total distance of 12 3/6 miles on their three-day hike.
To find the total distance James and Luke hiked, you need to add up the distances they hiked each day.
First, let's add up the distances for each day:
- Day 1: 4 1/6 miles
- Day 2: 3 2/3 miles
- Day 3: 4 2/3 miles
To add mixed numbers, we need to convert them to improper fractions first.
- Day 1: 4 + 1/6 = (4 * 6 + 1) / 6 = 25/6
- Day 2: 3 + 2/3 = (3 * 3 + 2) / 3 = 11/3
- Day 3: 4 + 2/3 = (4 * 3 + 2) / 3 = 14/3
Now, let's add the converted fractions together:
25/6 + 11/3 + 14/3
To add fractions with different denominators, we need to find a common denominator.
The common denominator for 6, 3, and 3 is 6.
Now, let's rewrite the fractions with the common denominator:
25/6 + (11/3 * 2/2) + (14/3 * 2/2)
= 25/6 + 22/6 + 28/6
Now, add the numerators together while keeping the common denominator:
25/6 + 22/6 + 28/6 = (25 + 22 + 28) / 6 = 75/6
Now, we have an improper fraction. To convert it back to a mixed number, we divide the numerator by the denominator:
75 ÷ 6 = 12 with a remainder of 3
Therefore, the total distance James and Luke hiked is 12 3/6 miles. We can simplify this mixed number by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 3 in this case:
12 ÷ 3 / 6 ÷ 3 = 4/2
So, the simplified mixed number is 4 1/2 miles.