1.
rational numbers are numbers that can be written in form a/b where a and b are integers (-4,-3,-2,-1,0,1,2,3, etc) and b isn't 0
so for case [tex]\frac{a}{b}+\frac{c}{d}[/tex]
we need to make the denomenators the same
so for [tex]\frac{a}{b}+\frac{c}{d}[/tex], multiply left one by d/d and multiply right one by b/b to get
[tex]\frac{ad}{bd}+\frac{cb}{bd}=\frac{ad+cb}{bd}[/tex]
therefore [tex]\frac{a}{b}+\frac{c}{d}=\frac{ad+cb}{bd}[/tex][/tex] is the rule
2. do the same as previous but do minus
so for case [tex]\frac{a}{b}-\frac{c}{d}[/tex]
we need to make the denomenators the same
so for [tex]\frac{a}{b}-\frac{c}{d}[/tex], multiply left one by d/d and multiply right one by b/b to get
[tex]\frac{ad}{bd}-\frac{cb}{bd}=\frac{ad-cb}{bd}[/tex]
therefore [tex]\frac{a}{b}-\frac{c}{d}=\frac{ad-cb}{bd}[/tex][/tex] is the rule
3. not sure, I hope this is right
so for case [tex]\frac{a}{b}+\frac{c}{d}=0[/tex]
we need to make the denomenators the same
so for [tex]\frac{a}{b}+\frac{c}{d}[/tex], multiply left one by d/d and multiply right one by b/b to get
[tex]\frac{ad}{bd}+\frac{cb}{bd}=\frac{ad+cb}{bd}=0[/tex]
if we multiply both sides by bd we get
ad+cb=0
therefore, ad=-cb for the sum to always equal 0
4.
[tex](\frac{a}{b})(\frac{c}{d})=1[/tex]
[tex]\frac{ac}{bd}=1[/tex]
multiply both sides by bd
ac=bd for the product of the 2 fractions to equal 1
