ORDER OF OPERATIONS WITH COMPLEX FRACTIONS

Evaluate the following.

Problem 1 :

[16 - (4 - 2)] ÷ [14 ÷ (3 + 4)]

Solution :

Step 1 :

We have to simplify the terms inside the brackets in both numerator and denominator.

Step 2 :

Dividing numerator by the denominator, we get

= 14/2

= 7

Problem 2 :

21 / (6 - 9)

Solution :

= 21 / (6 - 9)

Step 1 :

Simplifying the terms inside the bracket which is at the denominator.

= 21 / 3

Step 2 :

Dividing it, we get 7.

Problem 3 :

(18 ÷ 3) / (14 - 11)

Solution :

= (18 ÷ 3) / (14 - 11)

Step 1 :

Simplifying the numerator and denominator, we get

= 6 / 3

Step 2 :

Simplifying the numerator by denominator, we get

= 2

Problem 4 :

[(8 x 7) - 5] / 17

Solution :

[(8 x 7) - 5] / 17

Step 1 :

Simplifying the numerator, we get

= 56 - 5

= 51

Step 2 :

Dividing the numerator by the denominator, we get

= 51/17

= 3

Problem 5 :

(12 + 3 x 4) ÷ (5 + 7) 

Solution :

= (12 + 3 x 4)

Step 1 :

Simplfiying the numerator :

= (12 + 12)

= 24

Simplfiying the denominator  :

= (5 + 7)

= 12

Step 2 :

Dividing the numerator by the denominator, we get

= 24 / 12

= 2

Problem 6 :

[3 x (7 - 5)] ÷ 2

Solution :

= [3 x (7 - 5)] ÷ 2

Simplifying the numerator :

= 3 x (7 - 5)

According order of operation BODMAS, we simplify the terms inside the bracket first.

= 3 x 2

= 6

Now, dividing the numerator by the denominator, we get

= 6/2

= 3

Problem 7 :

[2 x 8 - 1] ÷ [8 - 6 ÷ 2]

Solution :

= [2 x 8 - 1] ÷ [8 - 6 ÷ 2]

Simplifying the numerator :

= [2 x 8 - 1]

= 16 - 1

= 15

Simplifying the denominator :

= [8 - 6 ÷ 2]

Do, division first and then subtraction.

= 8 - 3

= 5

Dividing the numerator by the denominator, we get

= 15/5

 = 3

Problem 8 :

[4 + 8²] ÷ [11 - 35]

Solution :

= [4 + 8²] ÷ [11 - 35]

Simplifying the numerator :

= [4 + 8²]

Expansion of 8² is 8 x 8, which is 64.

= 4 + 64

= 68

Simplifying the denominator :

= [11 - 35]

Subtracting these two and put the greater number sign for the result.

= -24

Now dividing the numerator by the denominator, we get

= 68/(-24)

= -17/6

Problem 9 :

[25 - (16 - 11)] ÷ [12 ÷ 4 + 2]

Solution :

= [25 - (16 - 11)] ÷ [12 ÷ 4 + 2]

Simplifying the numerator :

= [25 - (16 - 11)]

First simplify the terms which is inside the most interior bracket.

= 25 - 5

Subtracting it, we get

= 20

Simplifying the denominator :

= [12 ÷ 4 + 2]

First divide and then add.

= 3 + 2

= 5

Dividing the numerator by the denominator, we get

= 20/5

= 4

Problem 10 :

[31 - 11] ÷ [12 ÷ 6]

Solution :

= [31 - 11] ÷ [12 ÷ 6]

Simplifying the numerator :

= [31 - 11]

First simplify the terms which is inside the bracket.

= 31 - 11

= 20

Simplifying the denominator :

= [12 ÷ 6]

Dividing 12 by 6, we get

= 2

Now dividing the numerator by the denominator, we get

= 20/2

= 10

Problem 11 :

[18 + 14 ÷ 2] ÷ [12 ÷ 4]

Solution :

= [18 + 14 ÷ 2] ÷ [12 ÷ 4]

Simplifying the numerator :

= [18 + 14 ÷ 2]

First we have to divide.

= 18 + 7

By adding, we get

= 25

Simplifying the denominator :

= [12 ÷ 4]

= 3

Problem 12 :

[22 + 11 ÷ 2] ÷ [23 - 3 x 4]

Solution :

= [22 + 11 ÷ 2] ÷ [23 - 3 x 4]

Simplifying the numerator :

= [22 + 11 ÷ 2]

= 22 + 11/2

Since 11 is not divisible by 2,

= (44 + 11)/2

= 55/2

Simplifying the denominator :

= [23 - 3 x 4]

First do the multiplication and then subtraction should be done.

= 23 - 12

= 11

Now dividing the numerator by the denominator, we get

= (55/2) / 11

= 55/2 x (1/11)

= 5/2

Writing into mixed fraction, we get

= 2  1/2

Problem 13 :

[-4 - 11] ÷ [12 - 9 ÷ 2]

Solution :

= [-4 - 11] ÷ [12 - 9 ÷ 2]

Simplifying the numerator :

= [-4 - 11] 

Since we have same signs, we have to add and put the greater number sign for the result.

= -15

Simplifying the denominator :

= [12 - 9 ÷ 2]

= 12 - (9/2)

= (24 - 9) / 2

= 15 / 2

Now dividing the numerator by the denominator, we get

= -15 / (15/2)

= -15 x (2/15)

= -2