Please help us with this math problem

Question

 A machine Stamps 360 metal parts in 15 minutes. find the unit rate in parts per hour. 

 

Please show us steps and explain so my son can understand.

Answer 1

First, read and re-read the problem until you understand it and can put it into your own words.  Most word (story) problems are "made up" so they will be interesting.  In this problem the machine and metal parts are not important to the math.  Here's my re-worded question:  "What is 360 parts per 15 minutes expressed in parts per hour?"

 

Get formulas and notes.  To solve this problem, we will use the fact (not given) that there are 60 minutes per hour.  As a ratio, or fraction, this is (60 minutes)/(1 hour)=1.  The number 1 is called the multiplicative identity because we may multiply any value by 1 and not change the value, but we many change the units.  [extra note: do you know what the additive identity value is?]

 

O.K., we want to get to parts per hour, let's start with the ratio given in parts per 15 minutes:

   360 parts per 15 minutes

   (360 parts) / (15 minutes)

   ( (360 parts)/(15 minutes) ) * 1

   ( (360 parts)/(15 minutes) ) * ((60 minutes)/(1 hour))       

                    [written this was so minutes cancel out, leaving parts per hour]

    ((360)/(15)) * (60/1)) parts/hour

      1440 parts/hour    or  "1440 parts per hour"

    

           So, 360 parts per 15 minutes is 1440 parts per hour.  Now, you can talk about the machine and metal parts again (they have nothing to do with the math).  'the machine stamps 1440 metal parts per hour.

Answer 2

1 hour = 60 minutes

 

15 minutes goes into 1 hour four times, because 60/15=4

 

thus since 360 parts can be made in 15 min, 360x4 parts can be made in an hour and 360x4=1440 parts per hour