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Welcome to this Mathscribe course! We hope you will find it fun and interesting.
We’ll start off with some arithmetic: addition, subtraction, multiplication, and division. This will help remind you of some mathematical concepts. It will also introduce the algebra grid to the left, which will play a major role in this course.
So this is how addition is illustrated on the grid: the total number of green squares is calculated by adding together the number in each smaller piece.
On the grid to the left, there is a rectangle of 8 squares, which are green except for 2 gray squares. So the number of green squares equals $8-2$.
This shows how to subtract a smaller number from a bigger number on the grid. First you draw a green area whose size is the bigger number, and then a gray area inside it whose size is the smaller number. The difference is then the remaining number of green squares.
We write multiplication using parentheses. So, when you see “$2(3)$,” think “2 copies of 3,” or “2 times 3.”
So to multiply two numbers on a grid, you think of a rectangle that’s as wide as one number and as tall as the other, and find its area by counting the number of squares inside it.
Division works differently on the grid than the other three operations. In each other case, your answer is the total number of green squares. For division, your answer is instead the length of some side of a rectangle.
In this course, we write division of two numbers in fractional form. When you see “$$6/2$$,” think “6 divided by 2.” You should interpret this either as “6 split into 2 groups” or as “the number of 2s in 6.”
We call this kind of division — where $$6/2$$ means “6 split into 2 groups” — “splitting up.”
So this is how “splitting up” division is illustrated on the grid. To divide one number by another, you draw a green rectangle for the first number which is as wide as the second number. Then their quotient — the answer to the division problem — is the height of the rectangle.
We call this kind of division — where $$6/2$$ means “the number of 2s in 6” — “counting out.”