What is order of operations?

Question

I keep missing problems like this one on my math test:

(4 + 2) × 3 ÷ 2 - 1

Answer 1

The answer to this problem is 8.

The order of operations, which is used to obtain this correct answer, is the following:

P - Parentheses

E - Exponents

M - Multiplication

D - Division

A - Addition

S - Subtraction

The only catch to the above order of operations is the following:

Multiplication and Division are on the same level. They are performed in the order they appear from left to right.

The same goes for Addition and Subtraction. They are both on the same level also and are performed from left to right.

To help you remember the order of operations listed above you can think of the acronym for, “Please Excuse My Dear Aunt Sally.”

Some people also refer to the Order of Operations by the following acronym:

B - Brackets (or Parentheses)

O - Orders (Exponents or Roots)

D - Division

M - Multiplication

A - Addition

S - Subtraction

In the above order, Division is listed before Multiplication. As mentioned previously, this does not matter. They are (as are Addition and Subtraction) on the same level and thus are performed in the order they appear from left to right.

Now getting back to the type of problem that you frequently miss and how you can get the correct answer of 8:

(4 + 2) × 3 ÷ 2 - 1

Following the rules for the Order of Operations provided above (and I prefer PEMDAS) first calculate the sum inside the parentheses of 4+2= 6. There are no exponents in the expression, and next comes multiplication, division, and subtraction. So you would perform multiplication and division as they appear from left to right. This gives you 6*3 = 18. Then 18/2 = 9. The only operation left is subtraction (there is no remaining addition in the expression) so 9-1 = 8, your final answer.

Answer 2

The best way to remember the correct Order of Operations is using the acronym “Please Excuse My Dear Aunt Sally”:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

What that means for this expression

(4 + 2) x 3 / 2 – 1, is you would start with parentheses to get (4 + 2) = 6

=6 x 3 / 2 - 1       then Multiplication (6 x 3 = 18)

=18/2 – 1            then Division (18/2 = 9)

=9 – 1                 and finally Subtraction (9 - 1 = 8)

=8                   

So the end answer here would be 8 for this expression after simplifying it down :)

Answer 3

Here's a video explanation on how to solve any order of operations problem! If you have any further questions, feel free to reach out! Thanks!

Answer 4

(4+2) x3/2 -1

PEMDAS does M before D before A before S

Multiply then divide, then add, then subtract

= (4+2)x1.5 -1

= 6+3 -1

= 9 -1

= 8

but the Left to Right people are popular too

(4+2)x3/2 -1 = 6x3/2-1n=18/2-1 = 9-1 =8. which gives the same result

then there's the BODMAS order of operations with D before M

(4+2)x3/2 -1= same 8 again

that leaves the Right to Left view

(4+2)x3/2-1 = (4+2)x3/1 = (4+2)x3 = 4+6 = 10, but the parentheses still stop the Rightists from trying that.

Answer 5

🧠 What Is Order of Operations?

I will solve the problem below but first lets learn the rules.

✏️ Easy Way to Remember: PEMDAS ( Please Excuse My Dear Aunt Sally)

PEMDAS is a word that helps you remember the correct steps:

P – Parentheses

E – Exponents

M – Multiply

D – Divide

A – Add

S – Subtract

👉 But here’s a trick: Multiplication & Division are done left to right, whichever comes first.

Same with Addition & Subtraction — go left to right.

🔍 Solving the Example Problem (4 + 2) × 3 ÷ 2 - 1

1.  Parentheses first: (4 + 2) = 6
2.  → Now the problem is: 6 × 3 ÷ 2 - 1
3.  Multiply & Divide left to right:
4. 6 × 3 = 18
5. 18 ÷ 2 = 9
6.  Subtract:
7. 9 - 1 = 8

✅ Final Answer: 8

🧮 Another Example With Exponents 3² + 4

Step-by-step:

1.  Exponents: 3² means 3 × 3 = 9
2.  → Now the problem is: 9 + 4
3.  Addition: 9 + 4 = 13

✅ Final Answer: 13

⚠️ Common Mistake Alert!

Some students think they must multiply before dividing because in PEMDAS has the M first in the order.

That’s not true! Multiply and divide in the order they appear from left to right.

Let’s look at this:

Example: 20 ÷ 2 × 5

1. If you divide first: 20 ÷ 2 = 10 → then 10 × 5 = 50 ✅
2. ❌ Wrong Way: If you multiply first: 2 × 5 = 10 → then 20 ÷ 10 = 2 ❌

Big rule: Go left to right with multiply and divide.

The same applies for add and subtract.

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Answer 6

The order of operations is as follows: PEMDAS or BODMAS

P - Parentheses or B - Brackets

E - Exponents or O - Order

M - Multiplication

D - Division

A - Addition

S - Subtraction

You simply work out the expression in the order of either mnemonic device. For your example:

1) start with parentheses: (4 + 2) x 3 ÷ 2 - 1 = 6 x 3 ÷ 2 - 1

2) There are no exponents so you skip that step.

Note: For the rest you do multiplication and division as a pair, then addition and subtraction as a pair from left to right. This means if you have multiplication on the left and division on the right, you start with the multiplication.

3) Multiplication is on the left so you do that first: 6 x 3 ÷ 2 - 1 = 18 ÷ 2 - 1

4) Division next: 18 ÷ 2 - 1 = 9 - 1

5) Finally do subtraction: 9 - 1 = 8