Question

Phoebe is slicing a quiche.

Slice 1 was equal to half of the quiche.
Slice 2 was equal to one-third of the remaining quiche.
Slice 3 was equal to one-quarter of the remaining quiche.
Slice 4 was equal to one-fifth of the remaining quiche.
And so on.

Slice 27 was equal to one out of 28 of the remainder quiche after slices 1,2,3,4...26 were cut.

So basically slice n was equal to 1/n+1 of the remaining quiche, after the previous slices were removed.

What fraction of the quiche remained after Slice 27 was removed?

Answer 1

Phoebe is slicing a quiche.

Slice 1 was equal to half of the quiche.

Slice 2 was equal to one-third of the remaining quiche.

Slice 3 was equal to one-quarter of the remaining quiche.

Slice 4 was equal to one-fifth of the remaining quiche.

And so on.

Slice 27 was equal to one out of 28 of the remainder quiche after slices 1,2,3,4...26 were cut.

So basically slice n was equal to 1/n+1 of the remaining quiche, after the previous slices were removed.

What fraction of the quiche remained after Slice 27 was removed?

Answer 2

Answer:

1/28 fraction

Step-by-step explanation:

Slice 1

• 1/2, remaining 1-1/2=1/2

Slice 2

• 1/2*1/3=1/6, remaining 1/2-1/6=2/6=1/3

Slice 3

• 1/3*1/4=1/12, remaining 1/3-1/12=3/12=1/4

Slice 4

• 1/4*1/5=1/20, remaining 1/4-1/20=4/20=1/5

...

Slice 27

• 1/27*1/28=1/756, remaining 1/27-1/27*28=1/28

• To sum up and generalize the observation above:
• Remaining fraction after slice n cut is:
• 1/n-1/n*1/(n+1)=(n+1-1)/n(n+1)=1/(n+1)

Answer: remaining part is 1/28