SECTION 1-WHOLE NUMBER ARITHMETIC

THE ORDER OF OPERATIONS

Sometimes you have an expression like "5 + 4 x 3 - 6 / 3." Expressions like this have several operations, but they do not contain any parenthesis telling you what operation to do first. What should you do when you come across such a hideous expression?

Well there is a rule known as the MDAS rule. This rule is also nicknamed the "My Dear Aunt Sally" rule since the first letters of this phrase spell iut MDAS. This rule applies to expression with more than one operation, and no parenthesis.

The rule tells us to first perform any multiplication.
Our second step is to perform any division.
Our third step is to perform any addition.
And finally perform any subtraction.

With this in mind let's take another look at the expression "5 + 4 x 3 - 6 / 3".

Step 1: multiplication.
Buried in this expression is "4 x 3."
4 x 3 = 12
Therefore 5 + 4 x 3 - 6 / 3 = 5 + (4 x 3) - 6 / 3 = 5 + 12 - 6 / 3
Step 2: division
Buried in the expression is "5 + 12 - 6 / 3" is the division problem "6 / 3."
6 / 3 = 2
Therefore 5 + 12 - 6 / 3 = 5 + 12 - (6 / 3) = 5 + 12 - 2
Step 3: addition
Buried in the expression is "5 + 12 - 2" is the division problem "5 + 12"
5 + 12 = 17
Therefore 5 + 12 - 2 = (5 + 12) - 2 = 17 - 2
Step 4: subtraction
17 - 2 = 15

Conclusion
5 + 4 x 3 - 6 / 3 = 15

***** I'll show you this process three more times *****

Example 2: 15 x 4 - 10 / 5

Step 1: multiplication.
Buried in this expression is "15 x 4 ."
15 x 4 = 60
Therefore 15 x 4 - 10 / 5 = (15 x 4) - 10 / 5 = 60 - 10 / 5
Step 2: division
Buried in the expression is "60 - 10 / 5" is the division problem "10 / 5."
10 / 5 = 2
Therefore 60 - 10 / 5 = 60 - (10 / 5) = 60 - 2
Step 3: addition
There is no addition component in this expression so proceed on to the next step.
Step 4: subtraction
60 - 2 = 58

Conclusion
15 x 4 - 10 / 5 = 58

*****

Example 3: 25 + 12 x 11 - 10 / 2

Step 1: multiplication.
Buried in this expression is "12 x 11 ."
12 x 11 = 132
25 + 12 x 11 - 10 / 2 = 25 + (12 x 11) - 10 / 2 = 25 + 132 - 10 / 2
Step 2: division
Buried in the expression is "25 + 132 - 10 / 2" is the division problem "10 / 2."
10 / 2 = 5
25 + 132 - 10 / 2 = 25 + 132 - (10 / 2) = 25 + 132 - 5
Step 3: addition
Buried in the expression "25 + 132 - 5" is the addition problem "25 + 132"
25 + 132 = 157
25 + 132 - 5 = (25 + 132) - 5 = 157 -5
Step 4: subtraction
157 - 5 = 152

Conclusion
25 + 12 x 11 - 10 / 2 = 152

*****

Example 4: 70 + 60 / 12 - 32

Step 1: multiplication.
There is no multiplication component so go on to the next step
Step 2: division
Buried in the expression is "70 + 60 / 12 - 32" is the division problem "60 / 12."
60 / 12 = 5
70 + 60 / 12 - 32 = 70 + (60 / 12) - 32 = 70 + 5 - 32
Step 3: addition
Buried in the expression "70 + 5 - 32" is the addition problem "70 + 5"
70 + 5 = 75
70 + 5 - 32 = (70 + 5) - 32 = 75 - 32
Step 4: subtraction
75 - 32 = 43

Conclusion
70 + 60 / 12 - 32 = 43

There is no problem section for this topic.

All text, images, and source code c2003 Martin Selditch.