Let’s take another look at this gift box
Each box contains 3 apples and 4 pears. Applying a bit of maths terminology we could write this as (3 apples + 4 pears ) with the brackets showing that they are boxed together.
There are 5 boxes in the gift box or 5 × (3 apples + 4 pears )
There is a total of 5 × 3 apples and 5 × 4 pears or
5 × (3 apples + 4 pears ) = 5 × 3 apples + 5 × 4 pears = 15apples + 20pears.
Now instead of replacing the apples and pears with known numbers use xs and ys.
In maths this is 5×(3x + 4y) or 5(3x + 4y)
In total there 5×3x s and 5×4y s
or 5(3x + 4y)=5×3x + 5×4y=15x + 20y
In the Game of Maths we use holders rather than boxes.
In cards the following hands give the same result whatever numbers are declared for x and y.
5(3x + 4y)
5×3x + 5×4y
Wherever there is a gap (or a change of card) above the long holder cut it into card sized holders