Question 204272
The first piece is 2{{{1/2}}}
The 2nd is 1{{{3/4}}}


Let's add those by first changing your two MIXED fractions to IMPROPER fractions.  


Take 2 {{{1/2}}} and multiply the 2 in the denominator times the 2 in the fraction.  Now add 1 from the numerator.  (2 * 2) + 1 = 5

Put the 5 in the numerator and keep the 2 in the denominator and you get:  {{{5/2}}}


Therefore:   2 {{{1/2}}} =  {{{5/2}}}


Let's now take 1 {{{3/4}}} and change it to an improper fraction by multiplying the 4 in the denominator times the 1.  Now add 3 from the numerator.  (4 * 1) + 3 = 7.

Put the 7 in the numerator and keep the 4 in the denominator and you get: {{{7/4}}}


Therefore:  1 {{{3/4}}} = {{{7/4}}}



These two fractions represent the TOTAL AMOUNT of what is taken from the WHOLE 5 inch loaf so far.  What is the TOTAL amount?  Let's add the two fractions....


{{{5/2}}} + {{{7/4}}}   We have to find a common denominator.  How about 4?

What does a denominator of 4 do to the first fraction?  WELL, for {{{5/2}}} you ask yourself: "How many times does 2 go into 4?  The answer is 2.  
SO you multiply 2 times 5 in the numerator and you get:

{{{10/4}}}


Now let's add --- both fractions have a common denominator:


{{{10/4 + 7/4}}} = {{{17/4}}}


Therefore, the TWO pieces added together add up to be {{{17/4}}}.  How much of the bread is left?  Let's just subtract the 2 pieces (which was this fraction:{{{17/4}}}) from the whole 5 inch loaf.  


{{{5/1}}} - {{{17/4}}}.  Once again, how about if we make our common denominator 4?   How many times does 1 go into 4?   The answer is 4, so let's multiply 4 times 5 in the numerator and we get:  {{{20/4}}}



SO now that we have two common denominators, we can subtract:


{{{20/4}}} - {{{17/4}}} = {{{3/4}}}


Therefore, the third piece of the bread is {{{3/4}}} inch long.


I hope this helps. :-)