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Worksheet on Simplification

Q: 2. Which operation should we do first?

Answer: Always start with brackets . Then solve orders , followed by division and multiplication , and finally addition and subtraction . For Example: (10 + 5) × 2 First solve the bracket → 15 × 2 = 30.

Q: 3. Do we solve division before multiplication?

Answer: Division and multiplication are done from left to right , not one before the other. For Example: 20 ÷ 5 × 2 First divide → 20 ÷ 5 = 4 Then multiply → 4 × 2 = 8.

Q: 4. What is the difference between BODMAS and PEMDAS?

Answer: Both mean the same thing. Some countries use BODMAS , while others use PEMDAS . The rule is the same.

Q: 5. How can I remember BODMAS easily?

Answer: Try this trick: 👉 “Big Owls Divide Many Apples Sweetly.”

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.

BODMAS is an important rule in mathematics that tells us the correct order to solve a mathematical expression. When we see a problem with many operations like addition, subtraction, multiplication, and division, we cannot solve it randomly. If we do, we may get the wrong answer.

So, we use BODMAS to solve problems step by step in the correct order.

BODMAS stands for:

👉 B – Brackets
👉 O – Orders (powers, roots)
👉 D – Division
👉 M – Multiplication
👉 A – Addition
👉 S – Subtraction

This rule helps students understand how to simplify expressions correctly and avoid confusion.

For Example of Simplification:

Simplify: 20 − (5 + 3 × 2)

Step I: Multiply → 3 × 2 = 6

Step II: Add → 5 + 6 = 11

Step III: Subtract → 20 − 11 = 9

BODMAS worksheet

What is Order of Operations?

The order of operations means the sequence in which mathematical operations should be performed. For example, in the expression:

👉 6 + 4 × 3

If we add first, we get the wrong answer.

According to BODMAS, we must multiply first and then add.

So,
4 × 3 = 12
6 + 12 = 18 ✔

This rule is also known worldwide as Order of Operations and in some countries it is called PEMDAS.

Printable Worksheet on Measurement

BODMAS Ladder

Operation	Meaning
Brackets	Solve first
Orders	Powers and roots
Division	Next step
Multiplication	After division
Addition	Then add
Subtraction	Last step

Simplification of Numerical Expressions

Simplification of Decimals

Fractions simplification

Simplification of Fractions

Free Worksheet on Simplification - #Answers

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.

1. What is BODMAS?

Answer:

BODMAS helps us solve mathematical expressions in the correct order:
B – Brackets, O – Orders, D – Division, M – Multiplication, A – Addition, S – Subtraction.

This rule is very useful in daily life when we calculate money, shopping bills, discounts, and measurements.

2. Which operation should we do first?

Answer:

Always start with brackets.
Then solve orders, followed by division and multiplication, and finally addition and subtraction.

For Example:

(10 + 5) × 2

First solve the bracket → 15 × 2 = 30.

3. Do we solve division before multiplication?

Answer:

Division and multiplication are done from left to right, not one before the other.

For Example:

20 ÷ 5 × 2