Steven was beginning his training to run a half marathon. He ran 6 1/2 miles on Sunday, 5 1/4 miles on Tuesday, 7 miles on Wednesday, 8 3/4 miles on Thursday, 5 miles on Friday, and 12 1/2 miles on Saturday. How many miles per day did he average?
add 'em all up and divide by 6
To find out how many miles per day Steven averaged, we need to find the total number of miles he ran and then divide it by the number of days.
First, let's add up the total number of miles he ran:
6 1/2 miles + 5 1/4 miles + 7 miles + 8 3/4 miles + 5 miles + 12 1/2 miles
To add the fractions, we need to get a common denominator, which is 4
6 1/2 miles = 6 + 1/2 = 6 2/4 miles
5 1/4 miles = 5 + 1/4 = 5 1/4 miles
8 3/4 miles = 8 + 3/4 = 8 3/4 miles
12 1/2 miles = 12 + 1/2 = 12 2/4 miles
Now we can add them together:
6 2/4 miles + 5 1/4 miles + 7 miles + 8 3/4 miles + 5 miles + 12 2/4 miles = 44 3/4 miles
So, Steven ran a total of 44 3/4 miles.
Now let's figure out how many days he trained.
He ran on Sunday, Tuesday, Wednesday, Thursday, Friday, and Saturday. So he trained for 6 days.
To find the average, we divide the total number of miles by the number of days:
44 3/4 miles ÷ 6 days
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
44 3/4 miles × 1/(6 days)
To perform the calculation, we first convert the mixed number to an improper fraction:
44 3/4 miles = (4 × 44 + 3)/(4) miles = 179/4 miles
Now we can calculate the average:
(179/4 miles) × (1/(6 days))
To multiply fractions, we simply multiply the numerators and the denominators:
(179 × 1)/(4 × 6) miles/days
179/24 miles/days
Therefore, Steven averaged approximately 7 11/24 miles per day during his training.
To find the average number of miles Steven ran per day, we need to add up the total number of miles he ran and then divide it by the number of days.
Let's calculate it step-by-step:
1. Convert the mixed numbers to improper fractions:
6 1/2 = 6 + 1/2 = (6 * 2 + 1) / 2 = 13/2
5 1/4 = 5 + 1/4 = (5 * 4 + 1) / 4 = 21/4
8 3/4 = 8 + 3/4 = (8 * 4 + 3) / 4 = 35/4
12 1/2 = 12 + 1/2 = (12 * 2 + 1) / 2 = 25/2
2. Add up all the distances:
13/2 + 21/4 + 7 + 35/4 + 5 + 25/2
To add fractions, we first need to make sure they have a common denominator:
13/2 + 21/4 + 7 + 35/4 + 5 + 25/2
= 26/4 + 21/4 + 7 + 35/4 + 5 + 25/2
Now, add the numerators together and keep the common denominator:
26/4 + 21/4 + 7 + 35/4 + 5 + 25/2
= (26 + 21 + 7 + 35) / 4 + 5 + 25/2
= 89 / 4 + 5 + 25/2
3. Combine the mixed numbers and fractions:
89 / 4 + 5 + 25/2
= (89 + 20 + 50) / 4 + 5
= 159 / 4 + 5
4. Convert the number 5 to a fraction with a denominator of 4:
5 = 5/1 = 20/4
Now, we have:
159 / 4 + 20/4
= (159 + 20) / 4
= 179 / 4
5. Finally, divide the total distance by the number of days:
179 / 4 = 44.75
Therefore, Steven averaged approximately 44.75 miles per day during his training for the half marathon.