Jon ran around the track that was 1/8 of a mile long. he ran around the track 24times. how many miles did jon run?

Question

It's to help my son with his homework because my way is not the right way the teacher saying please help

Answer 1

To change the units without changing the value, we use the Multiplicative Identity (that is, 1).  We may multiply anything by 1 and it stays the same.

 

Let's call once around tract a "lap".  That means that a lap = 1/8 mile.  Or,

      1 = (8 laps)/(1 mile) = (1 mile)/(8 laps)      [we may choose the one to use]

 

So, Jon ran:

          24 laps

          (24 laps)*1

          (24 laps) * ((1 mile)/(8 laps))

          (24)*(1/8) miles           [note: laps cancel out, leaving miles]

          3 miles

 

Now, most teachers and tutors have done this so very many times that they forget how important the units are to someone who is learning.  So, your son may see:

       24/8 = 3

     or 24*(1/8) = 3

     or  (1/8)*24 = 3

  and then have to re-attach the units.  It's better to get them correct from the start.

 

In words,

   24 times around the track is 3 miles.       (8 laps + 8 laps + 8 laps)