find the sum of 1 1/2 and 3 5/8

There are steps taken to add mixed numbers with different denominators

First, rename both addends to fractions.  To do this take the
denominator x the integer  then add the numerator.  So:

1 1/2 = 2 (denominator) X 1 (integer) + 1 (numerator) = 3/2


3 5/8 =  8 (demoniator) x 3 (integer) + 5 (numerator) = 29/8

So our problem is now 3/2 + 29/8

We need to find the lowest common denominator.  First, find the
greatest common factor.  The GCF is the largest number that is a
common factor (or number) of both denominators.  In this case, the GCF
is 2.  We can either:

Multiply the denominators and divide by the GCF:
8 x 2 = 16  and 16 /2 = 8

OR

Divide one of the denominators by the GCF and then multiply that by
the other denominator:

2/2 = 1
1 x 8 = 8

Next we rename the fractions to use Least Common Denominator:

3/2 * 4/4 = 12/8

29/8 is already using the LCD


Now we have 12/8 + 29/8 = 41/8

Now we need to simpllfy the answer. Two ways to do this.  Determine
the largest whole number that is created by dividing 41 by 8, which is
5.

5 x 8= 40
41 - 40= 1

Therefore, we have 5 1/8

OR

Simply divide 41 by 8 and convert to a fraction and reduce.

41/8 = 5.125 or 5 125/1000

Reduce 125/1000 which reduces down to 1/8

Therefore:

1 1/2 + 3 5/8 = 5.125 or 5.125 or 5 1/8


-THV

That's a long, involved process for a simple problem:

1/2 = 4/8 therefore

    1 4/8
  + 3 5/8
  
  = 4 9/8

  = 5 1/8