Question 832577
{{{(2/5+3/8)-3/20=(16/40+15/40)-6/40=16/40+15/40-6/40=(16+15-6)/40=25/40=highlight(5/8)}}}
To add or subtract fractions, you need to express them as equivalent fractions with the same denominator.
{{{2/5=2*8/(5*8)=16/40}}} , {{{3/8=3*5/(8*5)=15/40}}} and {{{3/20=3*2/(20*2)=6/40}}}
I chose {{{40}}} as a common denominator to add {{{2/5}}} and {{{3/8}}} because it is a multiple of both denominators {{{"( 5 and 8 )"}}} :
{{{5*8=40}}} .
The fact that {{{40}}} is also a multiple of {{{20}}} , the denominator of {{{3/20}}} was just a lucky coincidence.
Finally, when we get {{{15/40}}} as a result we realize that {{{15}}} and {{{40}}} are both multiples of {{{5}}}, and that
{{{5/8=5*5/(8*5)=25/40}}} .
Since {{{5/8=25/40}}} , we express the fraction in the simpler {{{5/8}}} way of writing it.
If {{{5}}} and {{{8}}} had any factor in common, I would simplify the fraction further, but {{{5}}} and {{{8}}} have no common factor.
 
NOTE ON EQUIVALENT FRACTIONS:
{{{2/5}}} of a pizza cut into 5 equal slices is 2 slices.
Each slice is {{{1/5}}} of the pizza.
You could mark your {{{2/5}}} portion of that pizza by sprinkling oregano on those 2 slices.
If each one of all 5 slices is split into 8 equal wedges, the pizza will be split into
{{{5*8=40}}} very thin pizza wedges, all the same size.
Each one of those 40 thin slivers of pizza is {{{1/40}}} of the pizza.
Your portion, which was {{{2/5}}} of the pizza, is now made up of
{{{2*8=16}}} of those thin slivers, so it is {{{16/40}}}.
It may be harder to eat that way, but {{{2/5=16/40}}} .
The denominator (the bottom number) got multiplied times 8, because each of the original slices was split into 8 equal slivers of pizza, and now there is a total of {{{5*8=40}}} such slivers to the whole pizza.
At the same time, the numerator (the top number, and the number of pieces in your portion was also multiplied times 8.
Multiplying numerator and denominator times the same number, you get an equivalent fraction. It has the same value. It is the same number, just written in a different way.