Colin got 16 out of 80 correct in his test. what fraction of the marks did he get correct? give your answer in its simplest form.

 fraction collin correct.  

Solution:  

Collin correct 16 out of 80.  

It means total correct answer would be 16.  

Total number of question would be 80

We have to find the fraction of correct answer.  

Fraction =  

We get fraction,  

Now, we reduce the fraction if possible.  

We reduce fraction by divide numerator and denominator by same number .  

Here we divide numerator and denominator by 16 and we get ,  

Simplest fraction    

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