Question

Ms. Shank ran 5 2/7 miles and Mr. Jones ran 4 3/4 miles. How much farther did Ms. Shank run than Mr. Jones?

Answer 1

Ms. Shank ran 5 2/7 miles.

Mr. Jones ran 4 3/4 miles.

To determine how much farther did Ms. Shank ran than Mr. Jones, you have to calculate the difference between both distances:

`5(2)/(7)-4(3)/(4)`

To calculate this difference, you can calculate the difference between the whole numbers and the difference between the fractions separately:

- Difference between whole numbers:

`5-4=1`

- Difference between fractions:

`(2)/(7)-(3)/(4)`

First, you have to express both fractions with the same denominator, the least common factor between "7" and "4" is 28, multiply the first fraction by 4 and the second by 7 to express both of them as their equivalent with denominator 28:

`(2\cdot4)/(7\cdot4)-(3\cdot7)/(4\cdot7)=(8)/(28)-(21)/(28)`

Now that both fractions have the same denominator you can calculate the difference between them:

`(8)/(28)-(21)/(28)=(8-21)/(28)=(-13)/(28)`

- The final step is to add the results of the difference between the whole numbers and the fractions:

`1+(-(13)/(28))=1-(13)/(28)`

Divide the whole number by 1 to express it as a fraction, then, multiply the fraction by 28. Once both fractions have the same denominator, you can calculate the difference

`\begin{gathered} 1-(13)/(28)=(1)/(1)-(13)/(28)=(1\cdot28)/(1\cdot28)-(13)/(28) \\ (28)/(28)-(13)/(28)=(28-13)/(28)=(15)/(28) \end{gathered}`

Ms. Shank ran 15/28 miles more than Mr. Jones.