As part of a 3-day workout plan to prepare for a triathlon, an athlete ran
7 and one eighth718
miles Monday,
11 and one third1113
miles Tuesday, and
14 and one sixth1416
miles Wednesday. How many miles did the athlete run in the 3-day period?
Please learn to write or type mixed numbers correctly.
7 1/8
11 1/3
14 1/6
Next change the fractions to equivalent fractions with a common denominator.
Then add the whole numbers and the numerators.
What do you get?
To find the total number of miles the athlete ran in the 3-day period, we need to add up the distances run on each day.
Let's start with Monday's distance: 7 and one eighth (7 1/8) miles. To add this to the total, convert the mixed number to an improper fraction. Multiplying the whole number, 7, by the denominator, 8, and adding the numerator, 1, we get 57/8.
Now let's move on to Tuesday's distance: 11 and one third (11 1/3) miles. Convert this to an improper fraction as well. Multiplying the whole number, 11, by the denominator, 3, and adding the numerator, 1, we get 34/3.
Finally, Wednesday's distance is 14 and one sixth (14 1/6) miles. Convert this to an improper fraction too. Multiplying the whole number, 14, by the denominator, 6, and adding the numerator, 1, we get 85/6.
Now, add up the three distances:
57/8 + 34/3 + 85/6
To add fractions with different denominators, we need to find a common denominator. In this case, the least common multiple of 8, 3, and 6 is 24.
Now, we can rewrite the fractions with a common denominator of 24:
(57/8) x (3/3) = 171/24
(34/3) x (8/8) = 272/24
(85/6) x (4/4) = 340/24
Add up the fractions:
171/24 + 272/24 + 340/24 = 783/24
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 3:
783/24 ÷ 3/3 = 261/8
Therefore, the athlete ran a total of 261/8 miles in the 3-day period.
To convert this improper fraction to a mixed number, divide the numerator (261) by the denominator (8):
261 ÷ 8 = 32 remainder 5
The whole number part is 32, and the fractional part is 5/8. Therefore, the athlete ran a total of 32 and 5/8 miles in the 3-day period.