Question

4/5 of the birthday cake was eaten on your birthday the next day you ate 1/2 of what was left. You got to finish the cake, how much was left? Hint: Leave your answer as a fraction

Answer 1

Convert the fraction 4/5 to a fraction that is more flexible to work with:

(1-4/5)=(5/5)-(4/5)
(5/5)-(4/5)=1/5

Eating half of one fifth:
Again, convert the fraction into something that is more flexible to work with. Here, the best thing to do is to make the numerator even. You are able to multiply a fractions numerator and denominator by any integer because the same number over itself is simply equal to 1. So, in essence, you are multiplying the fraction by one.

So we have:

(1/5)*(2/2)= 2/10
^
Equal to 1

So we have 2/10 left. You eat half of 2/10, so you simply divide this fraction by 2. Keep in mind that dividing is the same thing as multiplying by the reciprocal:

(2/10)/2
or
(2/10)*(1/2)= (1/10)

So, what is left is (1/10) of the cake.