# How to Use MDAS

### 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 MDAS: 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. Examples:

1. $$7-3+8\times5$$
 $$7-3+\mathbf{8\times5}$$ This expression involves subtraction, addition, and multiplication. According to MDAS, simplify all multiplication or division before adding or subtracting. Therefore, start by simplifying $$8×5$$. $$\mathbf{7-3}+40$$ Since $$8×5=40$$, rewrite the expression using $$40$$. 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 $$7-3$$. $$\mathbf{4+40}$$ Since $$7-3=4$$, rewrite the expression using $$4$$. Next, solve $$4+40$$. $$44$$ $$4+40=44$$. Therefore, $$7-3+8×5$$ can be simplified to $$44$$.

1. $$24\div4\times3$$
 $$\mathbf{24\div4}\times3$$ 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 $$24÷4$$. $$\mathbf{6\times3}$$ Since $$24÷4=6$$, rewrite the expression using $$6$$. Next, solve $$6×3$$. $$\mathbf{18}$$ $$6×3=18$$. Therefore, $$24÷4×3$$ can be simplified to $$18$$.

1. $$6+10×2÷4$$
 $$6+\mathbf{10\times2}\div4$$ 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 $$10×2$$. $$6+\mathbf{20\div4}$$ Since $$10×2=20$$, rewrite the expression using $$20$$. 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 $$20÷4$$. $$\mathbf{6+5}$$ Since $$20÷4=5$$, rewrite the expression using $$5$$. Next, solve $$6+5$$. $$11$$ $$6+5=11$$. Therefore, $$6+10×2÷4$$ can be simplified to $$11$$.

1. $$5+81÷9×3-7$$
 $$5+\mathbf{81÷9}×3-7$$ 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 $$81÷9$$. $$5+\mathbf{9×3}-7$$ Since $$81÷9=9$$, rewrite the expression using $$9$$. 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 $$9×3$$. $$\mathbf{5+27} -7$$ Since $$9×3=27$$, rewrite the expression using $$27$$. 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 $$5+27$$. $$\mathbf{32-7}$$ Since $$5+27=32$$, rewrite the expression using $$32$$. Next, solve $$32-7$$. $$25$$ $$32-7=25$$. Therefore, $$5+81÷9×3-7$$ 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). So PEMDAS stands for: parentheses, exponents, multiplication, division, addition, and subtraction. So MDAS is just this final part right here. It tells you in what order to perform operations in an expression. So we first have M and D, and then we have A and S. addition and subtraction when you simplify an expression. So, 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.

$$84-8\div 2\times 3$$

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.

$$84-4\times 3$$

Then, multiply 4 and 3.

$$84-12$$

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

$$84-12=72$$

So, this expression simplifies to 72.

Let’s try another one!

$$16+8\times 4-9\div 3$$

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

$$16+32-9\div 3$$

Then, divide 9 by 3.

$$16+32-3$$

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

$$48-3$$

Finally, subtract 3 from 48.

$$48-3=45$$

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

$$18\div 3-2+4\times 9-11$$

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

$$6-2+4\times 9-11$$

Then, multiply 4 and 9.

$$6-2+36-11$$

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

$$4+36-11$$

$$40-11$$

Finally, subtract 11 from 40.

$$40-11=29$$

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

## Practice Questions

Question #1:

Simplify the following using MDAS:

$$4+3×1+6-1$$

$$10$$
$$11$$
$$12$$
$$13$$

MDAS is part of the Order of Operations (PEMDAS):

Parentheses
Exponents
Multiply
Divide
Subtract

Multiplication and division need to be completed before addition and subtraction. For this example, the first step is $$3×1$$.

$$4+3+6-1$$

From here, only addition and subtraction are left, so simply move from left to right. This simplifies to $$12$$.

Question #2:

Simplify the following using MDAS:

$$60×2+5-3+8×6-1$$

$$169$$
$$170$$
$$171$$
$$172$$

Multiplication and division need to be completed before addition and subtraction. For this example, the first step is $$60×2$$, then $$8×6$$. This leaves $$120+5-3+48-1$$. From here, only addition and subtraction are left, so work from left to right. This simplifies to $$169$$.

Question #3:

Simplify the following using MDAS:

$$16÷2÷4+4×2-16×4$$

$$46$$
$$-54$$
$$-46$$
$$81$$

Multiplication and division need to be completed before addition and subtraction. For this example, the first step is $$16÷2÷4$$. Working from left to right for this section, you are left with $$2$$. Now, simplify $$4×2$$ and $$16×4$$. Now, the multiplication and division step is complete.
$$2+8-64$$

From here, move on to addition and subtraction. Simplifying from left to right results in $$-54$$.

Question #4:

Simplify the following using MDAS:

$$24÷6+1+8+3×(-4)-11$$

$$8$$
$$-10$$
$$10$$
$$-8$$

Multiplication and division need to be completed before addition and subtraction. For this example, the first step is $$24÷6$$ and $$3×-4$$. Now we have $$4+1+8+(-12)-11$$, which simplifies to $$-10$$.

Question #5:

Simplify the following using MDAS:

$$7+3-2.5×(-3)-0.5+3$$

$$12.5$$
$$5.5$$
$$20$$
$$24$$
Multiplication and division need to be completed before addition and subtraction. For this example, the first step is to simplify $$2.5×(-3)$$, which is $$-7.5$$. Rewrite the expression as $$7+3+7.5-0.5+3$$, which simplifies to $$5$$.