Worksheet on Simplification

In worksheet on simplification, the questions are based in order to simplify expressions involving more than one bracket by using the steps of removal of brackets. This exercise sheet on simplifications has different types of questions that can be practiced by the students to get more ideas to simplify the expressions.

A. Simplify each of the following: 

1. 3 - (5 – 6 ÷ 3) 

2. – 25 + 14 ÷ (5 - 3) 

3. 25 – $\frac{1}{2}${5 + 4 - (3 + 2 – 1 + 3)} 

4. 27 - [38 - {46 - (15 - 13 - 2)}] 

5. 36 - [18 - {14 - (15 – 4 ÷ 2 x 2)}] 

6. 45 - [38 - {60 ÷ 3 – (6 - 9 ÷ 3) ÷ 3}]

7. 23 - [23 - {23 - (23 - 23 - 23)}] 

8. 2550 - [51 0 - {270 - (90 - 80 + 70)}] 

9. 4 + $\frac{1}{5}$ [{-10 x (25 - 13 - 3)} ÷ (-5)] 

10. 22 - $\frac{1}{4}$ {-5 - (- 48) ÷ (-16)} 

11. 63 - (-3) {-2 - 8 - 3} ÷ 3{5 + (-2) (-1)} 

12. [29 - (-2) {6 - (7 - 3)}] ÷ [3 x {5 + (-3) x (-2)}] 

B. Using brackets, write a mathematical expression for each of the following: 

1. Nine multiplied by the sum of two and five.

2. Twelve divided by the sum of one and three.

3. Twenty divided by the difference of seven and two.

4. Eight subtracted from the product of two and three.

5. Forty divided by one more than the sum of nine and ten.

6. Two multiplied by one less than the difference of nineteen and six.

C. Simplify the following fractions using BODMAS/PEMDAS Rules:

1. ($\frac{1}{9}$ + $\frac{1}{2}$) × 2$\frac{3}{8}$ + 5$\frac{1}{9}$

2. ($\frac{2}{5}$ + $\frac{3}{8}$) ÷ $\frac{2}{3}$ × 2 - 1$\frac{1}{9}$

3. 14 + [5 {4 + ($\frac{2}{7}$ of 63)}]

4. 49 [6 {5 (25 × $\frac{3}{5}$)}]

5. (8 × 6) ÷ 2 + 30 ÷ (5 × 2) - 3

6. $\frac{5}{6}$ + ($\frac{3}{4}$ × $\frac{5}{9}$) ÷ $\frac{1}{12}$ - $\frac{3}{4}$

7. (14 × 9) ÷ 3 + 12 ÷ (4 × 2) - 2

8. (25 × 6) × 2 - 16 ÷ (9 × 3) - 3

9. $\frac{5}{8}$ × of [8 + {4 (24 + $\overline{9 - 3}$)}] ÷ 4

10. $\frac{3}{5}$ × [$\frac{4}{3}$ + [6 (17 - $\overline{9 - 4}$)]

11. 9 + [7 {2 + ($\frac{3}{4}$ of 48)}] ÷ $\frac{2}{3}$

12. 4 [54 ÷ {4 + (12 - 10)}]

13. 50 ÷ [4 + {8 - (16 × $\frac{1}{4}$)}] + 8

14. 45 + [$\frac{1}{15}$ × {4 (25 ÷ $\frac{1}{5}$)}]

15. 4$\frac{4}{5}$ + ($\frac{4}{5}$ - $\overline{\frac{1}{4} - \frac{1}{5}}$) of 20

16. $\frac{2}{15}$ + {3 ($\frac{3}{4}$ of 8)} ÷ 3

17. 7$\frac{8}{9}$ - ($\frac{4}{9}$ - $\overline{\frac{1}{6} - \frac{1}{9}}$) of 2$\frac{1}{4}$

18. $\frac{3}{15}$ + ($\frac{7}{30}$ ÷ $\frac{1}{15}$) + 3(6 + 3)

19. $\frac{3}{16}$ + ($\frac{5}{8}$ ÷ $\frac{1}{4}$) + 3(6 - 4)

20. $\frac{2}{3}$ × of ($\frac{4}{9}$ - $\frac{1}{18}$) ÷ 3 $\frac{4}{27}$

21. $\frac{3}{4}$ × ($\frac{4}{9}$ - $\frac{1}{4}$) ÷ $\frac{5}{36}$

22. 4$\frac{1}{3}$ × 4$\frac{1}{2}$ ÷ (4$\frac{1}{2}$ + 2$\frac{1}{4}$)

23. $\frac{1}{3}$ of 2$\frac{13}{33}$ × 3$\frac{1}{4}$ ÷ ($\frac{1}{9}$ - $\frac{1}{18}$) + $\frac{2}{9}$

24. $\frac{2}{9}$ of 2$\frac{1}{3}$ × 3$\frac{1}{3}$ ÷ ($\frac{1}{9}$ + $\frac{2}{3}$)

25. 2$\frac{1}{3}$ + {4$\frac{3}{4}$ × (1$\frac{1}{3}$ - $\frac{2}{3}$)]

26. 24 + [9 - {2 + (2 × $\frac{3}{8}$)}]

27. 4$\frac{1}{7}$ + {3$\frac{3}{7}$ ÷ (2$\frac{4}{7}$ - $\frac{1}{7}$)}

28. 18 + [3 - {1 + (4 × $\frac{3}{16}$)}]

29. 95 - [4$\frac{1}{2}$ + {4 (7 + 5 - 3$\frac{1}{2}$)}]

30. 40 + [3 {2 (20 ÷ 3$\frac{1}{3}$)}]

31. $\frac{1}{3}$ + [3$\frac{1}{3}$ + {4 (18 - 9$\frac{1}{3}$)}]

32. 32$\frac{1}{2}$ + [4 {2 (11 × 9$\frac{1}{3}$)}]

33. 35 + [3$\frac{1}{4}$ of {6 - 3 (9 - $\overline{6 + 3}$)}]

34. 19 + [6 {3 + ($\frac{5}{16}$ of 64)}]

35. 18 + [5$\frac{1}{5}$ of {7 - 2(8 - $\overline{4 + 2}$)}]

36. 24 + [6 {4 + ($\frac{3}{8}$ × 56)}]

37. $\frac{4}{15}$ + {3 ($\frac{4}{5}$ of 25)} ÷ $\frac{20}{23}$

38. 1$\frac{1}{2}$ {3$\frac{9}{10}$ - (4$\frac{1}{2}$ + - $\overline{5\frac{1}{5} ÷ 2\frac{3}{5}}$)}

39. 3$\frac{3}{8}$ + {4 ($\frac{1}{8}$ of 32)} ÷ $\frac{1}{3}$

40. $\frac{3}{7}$ + {4 ($\frac{2}{5}$ × 25)} ÷ $\frac{1}{10}$

41. 1$\frac{1}{5}$ × (2$\frac{1}{12}$ ÷ $\frac{5}{12}$) + 3 ($\frac{1}{12}$ - $\frac{1}{15}$)

42. (3$\frac{2}{3}$ ÷ 1$\frac{2}{3}$) + ($\frac{1}{3}$ × $\frac{1}{6}$) + ($\overline{1\frac{1}{3} - \frac{1}{3}}$)

Students can check the answers of the worksheet on simplification given below to make sure that the answers are correct.

Worksheet on Simplification Answer:

A. 1. 0

2. -18

3. 24

4. 35

5. 21

6. 26

7. 46

8. 2370

9. 10

10. 24

11. 62

12. 1

B. 1. 9(2 + 5)

2. 12 ÷ (1 + 3)

3. 20 ÷ (7 - 2)

4. 2 x 3 - 8

5. 40 ÷ {1 + (9 + 10)}

6. 2 x {(19 - 6) - 1}

C. 1. 6($\frac{9}{16}$

2. 1($\frac{77}{360}$

3. 124

4. 22050

5. 24

6. 5$\frac{1}{12}$

7. 41$\frac{1}{2}$

8. 296$\frac{11}{27}$

9. 20

10. 44

11. 408

12. 36

13. 14$\frac{1}{4}$

14. 78$\frac{1}{3}$

15. 19$\frac{4}{5}$

16. 6$\frac{2}{15}$

17. 7$\frac{1}{72}$

18. 30$\frac{7}{10}$

19. 8$\frac{11}{16}$

20. $\frac{7}{28}$

21. 1$\frac{1}{20}$

22. 2$\frac{8}{9}$

23. 46$\frac{179}{198}$

24. 2$\frac{2}{9}$

25. 5$\frac{1}{2}$

26. 30$\frac{1}{4}$

27. 5$\frac{66}{119}$

28. 19$\frac{1}{4}$

29. 56$\frac{1}{2}$

30. 76

31. 38$\frac{1}{3}$

32. 853$\frac{5}{6}$

33. 54$\frac{1}{2}$

34. 157

35. 33$\frac{3}{5}$

36. 174

37. 69$\frac{4}{15}$

38. 2$\frac{1}{10}$

39. 51$\frac{3}{8}$

40. 400$\frac{3}{7}$

41. 6$\frac{1}{20}$

42. 3$\frac{23}{90}$

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