SIMPLIFYING COMPLEX FRACTIONS WORKSHEET

To simplify complex fractions, we have to be aware the concepts given below.

• How to add and subtract fractions
• Operation with mixed numbers
• How to multiply fractions
• How to divide fractions
• BODMAS Rule
• How to multiply integer and fraction.
  

Simplify the fractions in the numerator and the denominator separately, then divide the two fractions and simplify.

Simplify the following :

1) (2 - 1/4) / (2 + 1/4)               Solution

2) (1/2 + 1/5) / (3/4 - 1/2)            Solution

3)  (1 + 1/4 - 1/3) / (1 - 1/2 + 1/5)           Solution

4)  (1/3 + 1/4) / (1 - 1/5)                 Solution

5)  (22 + 11 ÷ 2) / (23 - 3 x 4)           Solution

6)  (15 - 33) / (17 - 7 x 3)          Solution

7)  (15 + 3 x 5²⁾ / (11 - 25 ÷ 2)              Solution

8)  (-4 - 11) / (12 - 9 ÷ 2)              Solution

9)  (1 - 3/4) / (2 + 1/4)              Solution

10)  (1/2 + 1/3 - 1/6) / (1/12 - 1/4)             Solution

11) (2   1/2 ÷ 3  3/4)      Solution

12)  (2/3 + 3/4) ÷ (1/2 - 1/3)     Solution

Simplifying Complex Fractions with Variables

1)  (1 + 1/x) /(1 - 1/x²)          Solution

2)  [4 + 12/(2x - 3)] / [5 + 15/(2x - 3)]         Solution

3)  [(2/x) - 5/(x + 3)] / [(3/x) + 3/(x+3)]            Solution

4)  [x/(x + 2) - x/(x - 2)] / [x/(x + 2) + x/(x - 2)]    Solution

5) [2a - (1/8a)] / [4 + (1/a)]     Solution

6)  [4/x² - 3/x] / [1/x² + 2/3x]     Solution

7) [5 - 1/a] / [1/a² - 25]    Solution

8) x - [(x + 2) / 3]      Solution

9)  2x/3 - [(2x + 1) / 6]     Solution

10) (x + 6)/2 - [(1 - 3x) / 7]     Solution

Evaluate the following.

Problem 1 :

[16 - (4 - 2)] ÷ [14 ÷ (3 + 4)]

Solution

Problem 2 :

21 / (6 - 9)

Solution

Problem 3 :

(18 ÷ 3) / (14 - 11)

Solution

Problem 4 :

[(8 x 7) - 5] / 17

Solution

Problem 5 :

(12 + 3 x 4) ÷ (5 + 7) 

Solution

Problem 6 :

[3 x (7 - 5)] ÷ 2

Solution

Problem 7 :

[2 x 8 - 1] ÷ [8 - 6 ÷ 2]

Solution

Problem 8 :

[4 + 8²] ÷ [11 - 35]

Solution

Problem 9 :

[25 - (16 - 11)] ÷ [12 ÷ 4 + 2]

Solution

Problem 10 :

[31 - 11] ÷ [12 ÷ 6]

Solution

Problem 11 :

[18 + 14 ÷ 2] ÷ [12 ÷ 4]

Solution

Problem 12 :

[22 + 11 ÷ 2] ÷ [23 - 3 x 4]

Solution

Problem 13 :

[-4 - 11] ÷ [12 - 9 ÷ 2]

Solution

Evaluate each expression.

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Problem 5 :

Solution

Problem 6 :

Solution

Problem 7 :

Solution

Problem 8 :

Solution

Problem 9 :

Solution

Problem 10 :

Solution

Problem 11 :

Solution

Problem 12 :

Solution