Question

A park ranger hiked 3/4 mi to a lookout, another 5/7 mi to a bird's nest, and finally 5/14 mi to a campsite. How far did the park ranger hike?

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Answer 1

The park ranger hiked a total of 1 23/28 miles after converting each fraction to have a common denominator and adding them together.

Step-by-step explanation:

To find out how far the park ranger hiked in total, we need to add the three distances together:

• The distance from the starting point to the lookout: 3/4 mile
• The distance from the lookout to the bird's nest: 5/7 mile
• The distance from the bird's nest to the campsite: 5/14 mile

To add these fractions, they must first have a common denominator. The least common denominator (LCD) for 4, 7, and 14 is 28. Now, we convert each fraction to have the denominator of 28:

• 3/4 = 21/28 after multiplying by 7/7
• 5/7 = 20/28 after multiplying by 4/4
• 5/14 = 10/28 after multiplying by 2/2

Now we can add the fractions with the common denominator:

21/28 + 20/28 + 10/28 = 51/28

51/28 is equal to 1 23/28 miles since 51/28 is the same as 1 whole (28/28) plus 23/28.

Therefore, the park ranger hiked a total of 1 23/28 miles.

Answer 2

2 miles and 88 yards.

Step-by-step explanation:

4 has 2*2 as prime factors

5 is prime

10 has 2 and 5 as prime factors

Thus, the lowest common denominator will be 2*2*5

3/4=15/20

3/5=12/20

7/10=14/20

Now that we have three fractions with the same denominator, we can add the numerators

15+12+14=41

So 41/20ths

That’s 2 and 1/20th

So the final answer is 2 miles and 88 yards! :)