Question

The running back for the Bulldogs football team carried the ball 5 times for a total loss of 11 1/4 yards. Find the average change in field position on each run. Enter the average change as a simplified mixed number.

Answer 1

`\displaystyle 2\ (1)/(4)`

Explanation:

Fractions

They can be expressed as proper fractions, improper fractions or mixed numbers. Proper fractions are such that the numerator is less than the denominator, like 2/5, 7/11, -9/10. Improper fractions are those whose numerators are greater than the denominator, such as 5/3, 10/9, -21/8.

Mixed numbers are expressions made of whole numbers and a proper fraction, like 4 3/5, 1 1/2, -5 4/9. Mixed numbers can be transformed to improper fractions and vice-versa.

The question requires us to find the average change in field position on each run of the running back for the Bulldogs football team which carried the ball 5 times for a total loss of 11 1/4 yards.

The number 11 1/4 is mixed, to express it as an improper fraction, we add the numbers like

`\displaystyle 11+(1)/(4)=(45)/(4)`

This improper fraction will now be divided by 5 to find the average of 5 runs:

`\displaystyle ((45)/(4))/(5)=(9)/(4)`

We now need to separate the improper fraction to a mixed number, let's just divide 9 by 4 to get 2 as the quotient and 1 for the remainder, thus

`\boxed{\displaystyle (9)/(4)=2\ (1)/(4)}`