How to solve a problem with a whole and one of its parts
In this problem, we work with a whole and one part of it.
We have the equation:
$1/6 Y$ means one sixth of Y. We can also write it as $1/6 × Y$. Y is some number, the whole that we are trying to find. We can draw it as one whole circle and divide it into 6 equal parts, so one part represents $1/6$ of the whole.
1. What we can already see in the equation
In the equation, we have:
On the left side, there is one sixth of the whole and also 10. Together, they make the whole Y.
That means the number 10 must represent the remaining part of the whole.
2. How large the missing part is
If we already have 1/6 Y of the whole Y, then $5/6$ of the whole Y is missing:
And according to the equation, this missing part is equal to 10.
3. How much one sixth is
If it is true that:
then we first find out how much 1/6 Y is. Five sixths has the value 10, so we find one sixth by dividing by five:
So $1/6$ of the whole Y is equal to 2.
4. How much the whole Y is
The whole has 6 sixths. If one sixth is 2, then the whole is:
Quick check
Substitute the value back into the equation:
That is correct, so the result is right.
