Instruction 1-4

Read and Write Whole Numbers in the Millions | Order and Compare Whole Numbers and Decimals | Order of Operations Using a Scientific Calculator | Order of Operations: the Manual Approach | Round off Whole Numbers

Student I approached the problem this way.		Student II approached the problem this way.

Which student is correct? Student II is correct because that student used the correct Order of Operations.

The Order of Operations tells us which operations to do and the order in which to do them. To remember the correct Order of Operations, some people remember the phrase:

Each letter of the phrase matches the first letter of the mathematical operation and helps show which order to do the mathematical operations.

Going back to the original problem:
 

Go through the list of operations
Are there any parentheses? NO
Are there any exponents? NO
Are there any multiplication or division problems? YES, so we do that operation first.
Are there any addition or subtraction problems? YES, so we do that operation second.

So we solve the problem by breaking it up in this way:

Let’s try this problem:

Go through the list of operations
Are there any parentheses? NO
Are there any exponents? YES, so we do that operation first.
Are there any multiplication or division problems? YES, so we do that operation second.
Are there any addition or subtraction problems? YES, so we do that operation third.

So we solve the problem by breaking it up in this way:

So the correct answer is 4.

Let’s try another problem:

Go through the list of operations
Are there any parentheses? YES, TWO PAIRS, so we do the parentheses with the inner most set first, then the second set.
Are there any exponents? NO
Are there any multiplication or division problems? YES, so we do that operation third.
Are there any addition or subtraction problems? NO

So we solve the problem by breaking it up in this way:

So the correct answer is 6.

Let’s try another problem:

Go through the list of operations
Are there any parentheses? NO
Are there any exponents? YES, so we do these from left to right
Are there any multiplication or division problems? NO
Are there any addition or subtraction problems? YES, BOTH Addition and Subtraction, so we do these problems from left to right.

So we solve the problem by breaking it up in this way:

So the correct answer is 3.

Let’s try really difficult problem involving all the steps:


Go through the list of operations
Are there any parentheses? YES, 2 PAIRS, so we work from the inner pair first, then do the outer pair
Are there any exponents? YES, 3 exponents, so we do these from left to right
Are there any multiplication or division problems? YES, BOTH, so we do these operations from left to right.
Are there any addition or subtraction problems? YES, BOTH, so we do these operations from left to right
REMEMBER THE ORDER OF OPERATIONS APPLIES INSIDE PARENTHESES AS WELL.

So we solve the problem by breaking it up in this way:

So the answer is 10.
 

Links for Students, Parents and Teachers

Now let's do Practice Exercise 1-4 (top).

Next Page:  Round off Whole Numbers (top)