Order of Operation (PEMDAS) Flashcards
PEMDAS is an acronym for
Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction
If there is more than one mathematical operation involved in your calculation, you must follow PEMDAS. The steps to perform PEMDAS are:
First, perform the operation inside the parenthesis or grouping symbol.
Simplify any number with exponents.
Perform multiplication or division from left to right.
Perform addition or subtraction from left to right.
Example 1: 9 + (3 x 2) – 4
The given problem has more than one operation involved. There is an addition, a multiplication, and a subtraction sign. There is also an operation inside the parenthesis. This means that we need to use PEMDAS.
Solution:
P – Perform the operation inside the parenthesis or grouping symbol.
The first thing we need to perform is the operation inside the parenthesis. In particular, we are going to solve 3 x 2 first.
pemdas 1
The operation inside the parenthesis is 3 x 2 which is equal to 6.
E – Simplify any number with exponents.
There are no exponents involved in the given problem. Thus, we will skip this step.
MD – Perform multiplication or division from left to right.
There is no more multiplication or division involved in 9 + 6 – 4. Therefore, we will skip this step.
AS – Perform addition or subtraction from left to right.
We perform addition first since it is the first one that appeared from the left. 9 + 6 = 15. Lastly, we perform subtraction: 15 – 4 = 11
pemdas 2
Let’s review what we have done:
9 + (3 x 2) – 4
9 + 6 – 4
15 – 4
11
Hence, using PEMDAS, 9 + (3 x 2) – 4 = 11
Example 2: (-17 – 2) x 3 – 9
P – Perform the operation inside the parenthesis.
The operation inside the parenthesis is – 17 – 2. By subtracting the given integers, we will obtain – 17 – 2 = – 19.
pemdas 3
E – Simplify any number with exponents.
The given problem doesn’t have any exponent. Thus, we will skip this step.
MD – Perform multiplication or division from left to right.
pemdas 4
AS – Perform addition or subtraction from left to right.
pemdas 5
Here’s a quick review of what we have done:
(-17 – 2) x 3 – 9
(-19) x 3 – 9
-57 – 9
– 66
Hence, using PEMDAS, (- 17 – 2) x 3 – 9 = -66
a number written on the upper right of another number which is called the base. This means that the base is raised to a certain power.
EXPONENT
Now, can you compute for 92?
Our exponent is 2 which means we need to use 9 two times in a multiplication Process:
92 = 9 x 9 = 81
Therefore, 92 = 81
Example 3: What is the value of 33 – (9 x 2) ÷ 6?
P – Perform the operation inside the parenthesis or grouping symbol.
pemdas 7
E – Simplify any number with exponents.
33 is a number with an exponent. Hence, we need to simplify it. Note that 33 = 3 x 3 x 3 = 27
pemdas 8
MD – Perform multiplication or division from left to right.
There is only division involved and there is no more multiplication sign left. Hence, we solve 18 ÷ 6
pemdas 9
AS – Perform addition or subtraction from left to right.
pemdas 10
A quick review of what we have done:
33 – (9 x 2) ÷ 6
33 – 18 ÷ 6
27 – 18 ÷ 6
27 – 3
24
Hence, using PEMDAS, 33 – (9 x 2) ÷ 6 = 24
Example 4: Compute for 81 ÷ (42 – 7) x 3
As usual, we start our computation with the operation inside the parenthesis. However, there are two things involved inside the parenthesis: An exponent and a subtraction sign. Note that it is easier to perform the exponent first before performing subtraction.
81 ÷ (42 – 7) x 3
81 ÷ (16 – 7) x 3
Now, we can perform subtraction which is inside the parenthesis:
81 ÷ (16 – 7) x 3
81 ÷ 9 x 3
We have already performed P of PEMDAS. Since there are no more exponents involved, we move to the next operations which are multiplication and division (MD). Let’s go back to the same problem:
81 ÷ 9 x 3
Since division appeared first from the left, we will perform it first.
81 ÷ 9 x 3
9 x 3
Lastly, we will perform multiplication
9 x 3 = 27
Example 5: Compute for 200 – 15² + (144 ÷ (-12) ) x (14 ÷ (-2))
Let us begin by performing the operations inside the parenthesis. There are two parentheses. Thus, we will perform the operations inside them simultaneously.
pemdas 11
We already did the P of PEMDAS so we are now on E which is exponents. We simplify the number with an exponent.
pemdas 12
We are now on the MD part of PEMDAS. There is only multiplication involved and there is no division sign left. Hence,
pemdas 13
Next is the AS part of PEMDAS. Since subtraction appeared first from the left, it is one that must be performed first.
pemdas 14
Finally, let us add the remaining numbers
pemdas 15
Here is a quick review of what we have done above:
200 – 152 + (144 ÷ (-12) ) x (14 ÷ (-2) )
200 – 152 + (- 12) x (- 7)
200 – 225 + 84
-25 + 84
59
Hence, using PEMDAS, 200 – 152 + (144 ÷ (-12) ) x (14 ÷ (-2) ) = 59
1) What is the value of 2
3 × (3 + 9) - 4
a) 101
b) 98
c) 94
d) 92
D
2) Calculate the following: (245 ÷ - 5) x 3 - (9 - 15)
a) 141
b) - 141
c) 11
d) - 11
B
3) Compute for 19 - (- 8 + 7) + 312
a) 332
b) - 332
c) 292
d) - 292
A
4) What is the answer to 8
3 4 x (- 3 - 12) + (5
2 ÷ x 2)
a) 270
b) - 270
c) 1870
d) - 1870
D
5) Compute for (5
3 x 2
2
) - (3
2 x 15)
a) 455
b) 405
c) 385
d) 365
D
