Elena was running a course 7/8 of a mile long. She stopped 2/3 of the way through to drink some water. How far had she run at that point? Write the answer in simplest form.(1 point)
To find the distance Elena had run, we need to multiply the total distance of the course by the fraction of the way Elena had run before stopping.
The total distance of the course is 7/8 of a mile.
The fraction of the way Elena had run before stopping is 2/3.
To find the distance Elena had run, we multiply 7/8 by 2/3:
(7/8) * (2/3) = 14/24.
So, Elena had run 14/24 of a mile at that point. Simplifying the fraction, we get:
14/24 = 7/12.
Therefore, Elena had run 7/12 of a mile at that point in simplest form.
To find out how far Elena had run when she stopped, we need to calculate 2/3 of 7/8.
Step 1: Multiply the numerators: 2 * 7 = 14.
Step 2: Multiply the denominators: 3 * 8 = 24.
So, 2/3 of 7/8 is 14/24.
Now, we can simplify this fraction:
Step 3: Find the greatest common divisor (GCD) of 14 and 24, which is 2.
Step 4: Divide both the numerator and denominator by the GCD:
14 ÷ 2 = 7
24 ÷ 2 = 12
So, the simplified fraction is 7/12.
Therefore, Elena had run 7/12 of a mile at the point when she stopped.
To find how far Elena had run at the point she stopped, we need to multiply the length of the course by the fraction representing how far she had run before stopping.
The length of the course is 7/8 of a mile.
To find how far Elena had run before stopping, we multiply 7/8 by 2/3:
(7/8) * (2/3) = (7 * 2) / (8 * 3) = 14/24
The answer, in simplest form, is 14/24.