How to Use MDAS

How to Use MDAS Video

What is MDAS?

MDAS stands for Multiplication, Division, Addition, and Subtraction. It is part of the Order of Operations, a collection of rules that gives a sequence for simplifying mathematical operations. It is used when an expression or equation has more than one operation. According to the order of operations, all multiplication or division must occur before addition or subtraction. For example, the expression 6+4×5 involves addition and multiplication. According to MDAS, simplify the multiplication portion of the expression before adding. Since 4×5 equals 20, rewrite the expression as 6+20, which equals 26.

Why do we use this system?

Recall that multiplication is repeated addition, which means multiplication is more powerful than addition. And division is repeated subtraction, which means division is more powerful than subtraction. Mathematicians developed the Order of Operations to simplify multiple operations in the order of their relative power.

How to simplify expressions

Since multiplication and division are equally powerful, evaluate these two operations simultaneously, working from left to right. Once all multiplication and division operations are simplified, evaluate addition and subtraction. Since addition and subtraction are equally powerful, evaluate these two operations simultaneously, working from left to right.

Example 1

73+8×5

This expression involves subtraction, addition, and multiplication. According to MDAS, simplify all multiplication or division before adding or subtracting. Therefore, start by simplifying 8×5.

73+40

The two operations remaining in the expression are subtraction and addition. Since these operations are equal in power, read the expression from left to right and simplify the first operation, which is 73.

4+40

Next, solve 4+40.

44

This means that 73+8×5 can be simplified to 44.

Example 2

24÷4×3

This expression involves division and multiplication. Since both operations are equal in power, read the expression from left to right and simplify the first operation, which is 24÷4. Since 24÷4=6, rewrite the expression using 6.

6×3

Next, solve 6×3.

18

This means that 24÷4×3 can be simplified to 18.

Example 3

6+10×2÷4

This expression involves addition, multiplication, and division. According to MDAS, simplify all multiplication or division before adding or subtracting. Reading the expression from left to right, start by multiplying 10×2. Since 10×2=20, rewrite the expression using 20.

6+20÷4

The two operations remaining in the expression are addition and division. According to MDAS, simplify all multiplication or division before adding or subtracting. Therefore, simplify 20÷4.

6+5

Next, solve 6+5.

11

This means that 6+10×2÷4 can be simplified to 11.

Example 4

5+81÷9×37

This expression involves addition, division, multiplication, and subtraction. According to MDAS, simplify all multiplication or division before adding or subtracting. Reading the expression from left to right, start by simplifying 81÷9.

5+9×37

The three operations remaining in the expression are addition, multiplication, and subtraction. According to MDAS, simplify all multiplication or division before adding or subtracting. Therefore, simplify 9×3.

5+277

The two operations remaining in the expression are addition and subtraction. Since both operations are equal in power, read the expression from left to right and simplify the first operation, which is 5+27.

327

Next, solve 327.

25

This means that 5+81÷9×37 can be simplified to 25.

Hello! Today we are going to talk about MDAS. This acronym may look a little familiar because it is a part of the order of operations (PEMDAS).

PEMDAS stands for: parentheses, exponents, multiplication, division, addition, and subtraction. MDAS is just this final part right here. It tells you in what order to perform operations in an expression.

We want to complete all of the multiplication and division in order from left to right and then all of the addition and subtraction in order from left to right. It’s important that you group multiplication and division together and addition and subtraction together, because you can multiply and divide in any order, as long as it comes before addition and subtraction. And then the same thing with this—you can add and subtract in any order (typically you go from left to right).

So let’s try a few examples.

848÷2×3

 
First, look for any multiplication or division. Here we have both, so we need to simplify them from left to right. Start by dividing 8 by 2.

844×3

 
Then, multiply 4 and 3.

8412

 
Finally, perform any addition or subtraction. Subtract 12 from 84.

8412=72

 
So, this expression simplifies to 72.

Let’s try another one!

16+8×49÷3

 
Start by simplifying any multiplication or division in order from left to right. First, multiply 8 and 4.

16+329÷3

 
Then, divide 9 by 3.

16+323

 
From here, simplify addition and subtraction in order from left to right. Add 16 and 32.

483

 

Finally, subtract 3 from 48.

483=45

 

So, the answer is 45.

Let’s try one last problem together before we go.

18÷32+4×911

 
Start by simplifying any multiplication or division, in order from left to right. First, divide 18 by 3.

62+4×911

 
Then, multiply 4 and 9.

62+3611

 
From here, simplify addition and subtraction in order from left to right. Subtract 2 from 6.

4+3611

 
Then, add 4 and 36.

4011

 
Finally, subtract 11 from 40.

4011=29

 
And there you have it! I hope this video on MDAS was helpful. Thanks for watching, and happy studying!

MDAS Practice Questions

Question #1:

 
Simplify the following using MDAS:

4+3×1+61

10
11
12
13
Question #2:

 
Simplify the following using MDAS:

60×2+53+8×61

169
170
171
172
Question #3:

 
Simplify the following using MDAS:

16÷2÷4+4×216×4

46
54
46
81
Question #4:

 
Simplify the following using MDAS:

24÷6+1+8+3×(4)11

8
10
10
8
Question #5:

 
Simplify the following using MDAS:

7+32.5×(3)0.5+3

12.5
5.5
20
24
923061

 

by Mometrix Test Preparation | Last Updated: January 16, 2025