Question 87579
<pre><font size = 3><b>
key works for radio wealth, last week the worked as fallows
monday 4 5/8 hrs
tuesday 7 1/6 hrs
wensday 9 3/4 hrs
thursday 8 1/2 hrs
friday 9 1/2 hrs
for how many hours did key worked last week?
show your sulotion

The original denominators 8,6,4,2,and 2 will all divide evenly into 24.
So 24 is their least common multiple, or the least common denominator.

   4 5/8 =   4 __/24
   7 1/6 =   7 __/24
   9 3/4 =   9 __/24 
   8 1/2 =   8 __/24
   9 1/2 =   9 __/24
          ----------

So the rule for fining each new numerator:

1. Divide each original denominator into the new denominator.
2. Take what you get and multiply it by the original numerator.
3. write that for the new numerator:

   4 5/8 =   4 __/24  <--- 8 divided into 24 gives  3;  3×5 = 15 
   7 1/6 =   7 __/24  <--- 6 divided into 24 gives  4;  4×1 =  4 
   9 3/4 =   9 __/24  <--- 4 divided into 24 gives  6;  6×3 = 18  
   8 1/2 =   8 __/24  <--- 2 divided into 24 gives 12; 12×1 = 12 
   9 1/2 =   9 __/24  <--- 2 divided into 24 gives 12; 12×1 = 12 
          ----------  

Now we fill in the blanks as above:

   4 5/8 =   4 <u>15</u>/24                                               
   7 1/6 =   7 <u> 4</u>/24   
   9 3/4 =   9 <u>18</u>/24                                              
   8 1/2 =   8 <u>12</u>/24 
   9 1/2 =   9 <u>12</u>/24                                              
          ----------

Add up the whole numbers, get 37.

   4 5/8 =   4 15/24                                               
   7 1/6 =   7  4/24   
   9 3/4 =   9 18/24                                              
   8 1/2 =   8 12/24 
   9 1/2 =   9 12/24                                              
          ---------- 
            37 

Add up the new numerators, getting 61 
and write it over the LCM 24

   4 5/8 =   4 15/24                                               
   7 1/6 =   7  4/24   
   9 3/4 =   9 18/24                                              
   8 1/2 =   8 12/24 
   9 1/2 =   9 12/24                                              
          ---------- 
            37 61/24

Divide 24 into 61

  __2_
24)61
   <u>48</u>
   13

Write the quotient 2 and put the remainder 13 over the divisor 24

That gives 2 13/24

Add the 37:

           2 13/24
         +37
         --------- 
          39 13/24

That's the answer.

Edwin</pre>