Suppose two fractions are both less than 1. Can their sum be greater than 1? Can the sum be greater than 2? Explain.

Question

Suppose two fractions are both less than 1. Can their sum be greater than 1? Can the sum be  greater than 2? Explain.

anonymous · Answer

if our 2 fractions are both 9/10, is that more than 1 when you add them together?

anonymous · Answer

yes

anonymous · Answer

if our fractions are as close to one as possible, but not going over, (999/1000 or 9999/10000) can their sum be greater than 2?

anonymous · Answer

No

anonymous · Answer

this answers your question, but i don't know exactly how to put it in words

anonymous · Answer

ok

anonymous · Answer

explain

anonymous · Answer

hmmm...maybe we could use an inequality...
lets assume 2 fractions, X and Y must be greater than 2 when added together
for simplicity sake (and to make this work), lets assume X=Y
so, X+Y>2 is what we are trying to prove
since X=Y, lets substitute X in for Y into our original equation
X+X>2
2x>2
X>1
but since X cant be greater than 1, there is no way for 2X>2 and thus no way for X+Y>2