Final answer:
Rex ran 4/5 of a mile and swam 3/4 of a mile. The total distance he covered, expressed as a mixed number, is 1 11/20 miles.
Step-by-step explanation:
To find the total distance Rex covered, we need to add the distance he ran to the distance he swam.
Rex ran 4/5 of a mile, which is equal to 4/5 + 0/5 = 4/5 miles.
Rex swam 3/4 of a mile, which is equal to 3/4 + 0/4 = 3/4 miles.
To find the total distance, we add the distances together: 4/5 + 3/4. Since the denominators are different, we need to find a common denominator to add them. The least common denominator of 5 and 4 is 20. So, we rewrite 4/5 and 3/4 with the common denominator:
4/5 = 16/20
3/4 = 15/20
Now we can add the fractions: 16/20 + 15/20 = 31/20
The total distance Rex covered is 31/20 miles. To express it as a mixed number, we divide the numerator (31) by the denominator (20). The remainder becomes the numerator of the fraction part, and the quotient becomes the whole number part. Dividing 31 by 20, we get 1 remainder 11. So, the mixed number is 1 11/20 miles.