Cassie has a wood board that is 3/4 foot long. She wants to cut the board into pieces that are 1/8 foot long. Which expression will help Cassie find how many pieces she can cut?
The expression that will help Cassie find out how many pieces she can cut is
This question requires division. The expression used to find how many pieces Cassie can cut is:
This is not building the expression required but explains the principle behind it. It demonstrates the principle upon which the shortcut is built.
A fraction consists of two parts the top number and the bottom one.
Think of the top number as the count and the bottom as the size indicator. So you have:
Consider the action example of dividing 3 into 6.
We can do this division directly because their size indicators are the same. That is, we have:
So we need to see how many of
We can not do this directly in one operation as the size indicators are not the same.
Now that the size indicators (denominators) are the same we can just divide the counts (numerators)
I could explain more showing the connection between this and the shortcut method but what I have shown you will do for now.
If you wish further explanation leave me a message on https://socratic.org/users/abr-1