Here we are going to learn about how Use order of operations to solve an equation.

You can often solve an equation by applying the rule called "PEMDAS"

What is PEMDAS rule ?

The rule or order that we us e to simplify expressions in math is called "PEMDAS" rule.

Very simply way to remember PEMDAS rule!

**P -----> Parentheses**

**E -----> Exponents **

**M ****-----> **Multiplication

**D -----> Division**

**A ****-----> **Addition

**S ****-----> **Subtraction

**Important notes : **

1. In a particular simplification, if you have both multiplication and division, do the operations one by one in the order from left to right.

2. Multiplication does not always come before division. We have to do one by one from left to right.

3. In a particular simplification, if you have both addition and subtraction, do the operations one by one in the order from left to right.

Let us look into some example problems to understand how to use order of operations to solve an equation.

**Example 1 : **

Solve the following equation

13 + 2(4) / 3(5 - 4) = q

In the numerator we have to multiply 2 and 4, in the denominator we have to subtract 4 from 5.

13 + 8 / 3(1) = q (Add the numerator)

21 / 3 = q (Divide 21 by 3)

7 = q

Hence the solution is 7.

**Example 2 :**

Solve the following equation

g = 15 ⋅ 6 / (16 - 7)

In the numerator, we have to do multiplication. In the denominator we have to perform subtraction.

g = 90 / 9 (Divide)

g = 10

Hence the solution is 10.

**Example 3 :**

Solve the following equation

d = [7(3) + 3 / 4 (3 - 1)] + 6

d = 21 + 3 / 4(2)] + 6

d = [24 / 8] + 6

d = 32 + 6

d = 38

Hence the solution is 38.

**Example 4 :**

Solve the following equation

p = (1/4)[7(2³) + 4(5²) - 6(2)]

p = (1/4)[7(8) + 4(25) - 6(2)]

p = (1/4)[56 + 100 - 12]

p = (1/4)[156 - 12]

p = (1/4)[144]

p = 36

Hence the solution is 36.

**Example 5 :**

Solve the following equation

a = [ 4 (14 - 1) / 3(6) - 5] + 7

a = [ 4 (13) / 18 - 5] + 7

a = [ 42 / 13] + 7

a = 4 + 7

a = 11

Hence the solution is 11.

**Example 6 :**

Solve the following equation

n = (1/8)[ 6 (3²) + 2 (4³) - 2(7) ]

n = (1/8)[ 6 (9) + 2 (64) - 14 ]

n = (1/8)[ 54 + 128 - 14 ]

n = (1/8)[ 182 - 14 ]

n = (1/8)[ 168 ]

n = 21

Hence the solution is 21.

After having gone through the stuff given above, we hope that the students would have understood "Use order of operations to solve an equation".

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