Question

Mark is training to run a half marathon,

which is 13.1 miles. Last week, he ran 6 3/5 miles on Monday,
6 2/3 on Wednesday, and 6 7/10 on Friday. On Tuesday,
he jogged 9 3/10 miles, and on Sunday, he loped along for 9 1/3
Compare each day, which day did mark run the farthest?
Which day did he run the least?
Did mark run farther on Tuesday or Sunday?

Answer 1

1.Sunday is the day when Mark ran the farthest.

2. Monday is the day when Mark ran the least.

3.Mark ran farther on Sunday compared to Tuesday.

Explanation:

To determine whether Mark ran farther on Tuesday or Sunday, we need to compare the distances he ran on each day.

On Tuesday, Mark jogged 9 3/10 miles.

On Sunday, Mark loped along for 9 1/3 miles.

Let's convert the fractions to a common denominator to make the comparison easier.

9 3/10 = 9 + 3/10 = 9 + 3/10 = 90/10 + 3/10 = 93/10

9 1/3 = 9 + 1/3 = 9 + 1/3 = 27/3 + 1/3 = 28/3

Now we can compare the distances:

- Tuesday: 93/10 miles

- Sunday: 28/3 miles

To compare fractions, we need to find a common denominator. In this case, the common denominator is 30.

- Tuesday: (93/10) * (3/3) = 279/30

- Sunday: (28/3) * (10/10) = 280/30

From the comparison, we can see that Mark ran slightly farther on Sunday with a distance of 280/30 miles, which simplifies to 9 1/3 miles.

Therefore, Mark ran farther on Sunday compared to Tuesday.

Answer 2

A)

Mark ran the following distances on Monday, Wednesday, and Friday:

• Monday,
  `6(3)/(5)`
• Wednesday,
  `6(2)/(3)`
• Friday,
  `6(7)/(10)`

To compare these, we can give them all a common denominator. We can do this by finding the least common multiple (LCM) of 5, 3, and 10, which is 30, then multiplying each fraction's numerator and denominator by a number that is a factor pair of 30 with the fraction's denominator.

Monday Wednesday Friday

`(3)/(5)* (6)/(6) = \frac{\bold{18}}{30}`
`(2)/(3)* (10)/(10) = \frac{\bold{20}}{30}`
`(7)/(10)* (3)/(3) = \frac{\bold{21}}{30}`

`\implies 18 < 20 < 21`

Therefore, Mark ran the farthest on Friday, and he ran the least on Monday.

Notice that we can compare the fractional (non-whole) part of each mixed number because the base for each one is the same: 6.

B)

Mark ran the following distances on Tuesday and Sunday:

• Tuesday,
  `9(3)/(10)` miles
• Sunday,
  `9(1)/(9)` miles

We can intuitively say that
`(3)/(10)` is larger than
`(1)/(9)`, so Mark ran the farthest on Tuesday.

However, if we want to find this analytically, we can multiply the numerator and denominator of each fraction by the denominator of the other fraction to get a common denominator, then compare the numerators of the resulting fractions:

Tuesday Sunday

`(3)/(10) * (9)/(9) = {\frac{\bold{18}}{90}}`
`(1)/(9) * (10)/(10) = {\frac{\bold{10}}{90}}`

`\implies 18 > 10`

C)

We can do this easily using our answers to the previous problems:

Monday, Wednesday, Friday, Sunday, Tuesday