Matt has 4 red balloons,3 green ones,2 yellow ones. what fraction of his balloons are red?

4/9

Step-by-step explanation:

There are

4+3+2 = 9 balloons

The fraction that are red = red balloons/ total balloons

fraction red = 4 red/9 total

4/9

9 x 8 divided by (5-3)=36

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4