Question

Jeremy and his friends ate $\dfrac{5}{8}$ of a pie. If the pie was cut into eight pieces, how much pie is left over?

Answer 1

Hint: We should remember that if we divide something into $n$ pieces, then the whole of that thing can be equated to $1=\dfrac{n}{n}.$ And if some part of it is utilized, then the remaining will be found out by subtracting the amount of utilized part from the whole. If $\dfrac{m}{n}$ part is utilized, then the amount of the remaining part is $\dfrac{n}{n}-\dfrac{m}{n}.$

Complete step by step solution:
When we consider the given problem, we can see that a pie is cut into $8$ pieces.
We know that if $\text{A}$ is cut into $n$ pieces, then the amount of the whole of $\text{A}$ can be equated to $\dfrac{n}{n}$ since it represents $1.$
Therefore, we can equate the amount of the whole of the pie that is cut into $8$ pieces to $1=\dfrac{8}{8}.$
Since the pie is cut into $8$ pieces, if we take one of the eight pieces, then we say that we have taken $\dfrac{1}{8}$ of the pie. So, there are eight times $\dfrac{1}{8}$ of the pie. That is, $8\times \dfrac{1}{8}=\dfrac{8}{8}.$
In the given problem, we can see that Jeremy and his friends ate $\dfrac{5}{8}$ of the pie. That is, five $\dfrac{1}{8}$ of the pie.
Now, to find the amount of pie that is left over, we will subtract the pieces of pie eaten by Jeremy and his friends by the whole of the pie.
Hence the amount of the pie that is left over is $\dfrac{8}{8}-\dfrac{5}{8}=\dfrac{3}{8}.$

Note: What we have done here, in simple words is, that we have subtracted the amount of pie Jeremy and his friend ate from the whole, that is $1,$ pie. That is $1-\dfrac{5}{8}.$ We have made the denominators the same by multiplying and dividing $1$ with $8.$ We get $\dfrac{8}{8}-\dfrac{5}{8}=\dfrac{3}{8}.$