Onmatu- Pre-Algebra Article

Order of operations


At first, we will show one simple expression that contains subtraction (+) and multiplucation (×),
 
                           A = 2 + 3 × 4.

The first mistake that students make in this expression is to calculculate from the left to the right the value of expression A. That is, we teachers see as a result A = 5 × 4 = 20. This is completely WRONG!
What we need to do is to follow THE ORDER OF OPERATIONS!
In every expression that we need to calculate operation multiplication (×) and division (:) have a priority. That is we do multiplication and division before subtraction and addition.
Correctly, the value of our expression A is,

                       A = 2 + 12 = 14.

Let us calculate the value of one more expression tha contains operations subtraction and multiplication. We give an expression 
                        B = 3 - 4 × 2. 
Following the correct order of operations we get that our expression B has the value B = 3 - 8 = - 5. 
We remark that the operations addition and subtraction have the same order, that is it does not matter which operation we do first. 
The same case is with the operations multiplication and division. They too have the same order.

Let us calculate a value of the few following expressions for the better practice.

   3 + 4 : 2 - 5 + 2 × 3 = 3 + 2 - 5 + 6 = 6,

   4 - 10 : 5 - 16 : 4 + 2 = 6 - 2 - 4 = 0,

   80 : 10 - 4 × 3 - 2 = 8 - 12 - 2 = - 6.

Not so much difficult, right :).

In the end, we give some examples for your excersise. Wish you good luck!

                 45 : 5 - 7 × 2 + 3 =

                3 + 48 : 8 - 4 × 4 =

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