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\(\frac{23}{90}\)

If students have any queries regarding the questions given in the worksheet on simplification, please fill-up the bellow comment box so that we can help you.

However, suggestions for further improvement, from all quarters would be greatly appreciated.

● Numbers - Integers

Integers

Multiplication of Integers

Properties of Multiplication of Integers

Examples on Multiplication of Integers

Division of Integers

Absolute Value of an Integer

Comparison of Integers

Properties of Division of Integers

Examples on Division of Integers

Fundamental Operation

Examples on Fundamental Operations

Uses of Brackets

Removal of Brackets

Examples on Simplification

● Numbers - Worksheets

Worksheet on Multiplication of Integers

Worksheet on Division of Integers

Worksheet on Fundamental Operation

Worksheet on Simplification

7th Grade Math Problems

Math Homework Sheets 

From Worksheet on Simplification to HOME PAGE