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 how far Elena had run at the point when she stopped, we need to multiply the length of the course by the fraction representing the portion she had run.
The length of the course is 7/8 of a mile.
The portion Elena had run can be calculated by multiplying 7/8 by 2/3.
(7/8) x (2/3) = (7 x 2)/(8 x 3) = 14/24.
So, Elena had run 14/24 of a mile when she stopped.
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2.
(14/2)/(24/2) = 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 that point, we can multiply the length of the course (7/8 mile) by the fraction of the course she had completed before stopping (2/3).
7/8 mile * 2/3 = (7*2)/(8*3) = 14/24 = 7/12
Therefore, Elena had run 7/12 of a mile at that point.
To find out how far Elena had run when she stopped to drink water, we need to multiply the total distance (7/8 mile) by the fraction of the course she ran before stopping (2/3).
To multiply fractions, we multiply the numerators (top numbers) together to get the new numerator, and we multiply the denominators (bottom numbers) together to get the new denominator.
So, multiplying 7/8 by 2/3, we get:
(7/8) * (2/3) = (7 * 2) / (8 * 3) = 14/24
Since 14/24 can be simplified further, we can divide both the numerator and denominator by their greatest common divisor, which is 2.
Dividing 14 by 2, we get 7, and dividing 24 by 2, we get 12.
So, the simplified form of 14/24 is 7/12.
Therefore, Elena had run 7/12 of a mile when she stopped to drink water.