Simplification and BODMAS Rule Practice Questions — State PSC Exam — Page 3

Calculate the exact numerical value of the given mathematical expression using the VBODMAS rule:

\frac{3}{5} \text{ of } 250 - \left[ 42 + \left\{ 24 \div \left( 7.5 - \overline{4.2 + 0.3} \right) \right\} \right]

Show answer & explanation

Answer: 100

Answer

100

Evaluating strictly according to VBODMAS order of operations yields 100: Vinculum gives 4.5, round brackets give 3, division in curly brackets gives 8, addition in square brackets gives 50, 'of' operation gives 150, and 150 - 50 = 100.

Step-by-Step Solution

1

Evaluate the expression under the vinculum (bar line)

4.2 + 0.3 = 4.5

According to the VBODMAS rule, the vinculum takes precedence over standard brackets and operations.

2

Simplify the innermost round brackets

7.5 - 4.5 = 3

Operations inside round parentheses ( ) are resolved next.

3

Evaluate the expression inside the curly brackets

24 / 3 = 8

Perform the division operation inside curly braces { }.

4

Evaluate the expression inside the square brackets

42 + 8 = 50

Perform addition within the outer square brackets [ ].

5

Calculate the 'of' operation

(3/5) * 250 = 150

The 'of' operation takes priority over standard addition and subtraction outside brackets.

6

Perform final subtraction

150 - 50 = 100

Subtract the total evaluated bracketed quantity from the 'of' calculation result.

Key Concept

Hierarchical priority of operations in VBODMAS involving vinculum, nested brackets, and fractional 'of' operations

Question 42Question →

What is the simplified numerical value of the following mathematical expression when evaluated strictly according to the VBODMAS rule?

40\% \text{ of } 150 - \left[ 16 + \left\{ 20 \div \left( 8.5 - \overline{3.1 + 1.4} \right) \right\} \right]

39

51

49

40

Show answer & explanation

Answer: 39

Answer

39

Evaluating strictly by VBODMAS priority: first the vinculum yields 4.5, then the round bracket gives 8.5 - 4.5 = 4, then division yields 20 ÷ 4 = 5, followed by square bracket addition 16 + 5 = 21. Finally, subtracting 21 from 40% of 150 (which is 60) gives 60 - 21 = 39.

Step-by-Step Solution

1

Evaluate the expression under the vinculum (bar)

\overline{3.1 + 1.4} = 4.5

The vinculum has the highest priority and must be evaluated first.

2

Evaluate the terms inside the round brackets

8.5 - 4.5 = 4

The next priority is resolving the innermost parentheses.

3

Perform division inside the curly brackets

20 \div 4 = 5

Inside curly brackets, division takes precedence over addition.

4

Evaluate the terms inside the square brackets

16 + 5 = 21

Resolve the outer square bracket by adding the terms.

5

Calculate the percentage term

40\% \text{ of } 150 = \frac{40}{100} \times 150 = 60

'Of' represents multiplication in percentage operations.

6

Perform final subtraction

60 - 21 = 39

Subtract the total bracket value from the percentage calculation.

Key Concept

VBODMAS Rule (Vinculum, Brackets, Orders, Division, Multiplication, Addition, Subtraction)

Question 43Question →

What is the simplified numerical value of the following mathematical expression when evaluated strictly using the BODMAS rule?

50 - \left[ 8 + \left\{ 16 \div \left( 8 - \overline{7 - 3} \right) \right\} \right]

38

44

50

46

Show answer & explanation

Answer: 38

Answer

The simplified numerical value of the expression is 38.

Evaluating step-by-step according to VBODMAS order gives: first vinculum 7 - 3 = 4, then round brackets 8 - 4 = 4, followed by curly bracket division 16 ÷ 4 = 4, then square bracket addition 8 + 4 = 12, and finally 50 - 12 = 38. The value 38 correctly demonstrates strict adherence to order of operations.

Step-by-Step Solution

1

Evaluate the expression under the vinculum bar

\overline{7 - 3} = 4

According to VBODMAS rules, operations under a vinculum bar have the highest priority.

2

Evaluate the expression inside the round brackets

8 - 4 = 4

Substitute the vinculum result into the round bracket.

3

Perform division inside the curly brackets

16 \div 4 = 4

Curly brackets are evaluated next after simplifying the inner round brackets.

4

Perform addition inside the square brackets

8 + 4 = 12

Resolve the remaining operations inside the outermost square brackets.

5

Perform final subtraction outside the brackets

50 - 12 = 38

Complete the evaluation by subtracting the bracket value from 50.

Key Concept

VBODMAS Rule (Vinculum, Brackets, Orders, Division, Multiplication, Addition, Subtraction)

Question 44Question →

What is the simplified value of the following mathematical expression when evaluated strictly using the VBODMAS rule?

15 + 2.5 \times \left[ 16 - \left\{ 10 \div \left( 3.5 - \overline{2.1 - 0.6} \right) \right\} \right]

42.5

192.5

23.75

50

Show answer & explanation

Answer: 42.5

Answer

The simplified value of the expression is 42.5.

Evaluating strictly according to VBODMAS rules, we first simplify the expression under the vinculum bar (2.1 - 0.6 = 1.5), then the round brackets (3.5 - 1.5 = 2), followed by the curly brackets (10 ÷ 2 = 5), and then the square brackets (16 - 5 = 11). Finally, executing multiplication before addition yields 15 + (2.5 × 11) = 15 + 27.5 = 42.5.

Step-by-Step Solution

1

Evaluate the expression under the vinculum (bar)

\overline{2.1 - 0.6} = 1.5

According to VBODMAS, the vinculum takes highest priority over standard brackets.

2

Evaluate the terms inside the innermost parentheses (round brackets)

3.5 - 1.5 = 2.0

Parentheses are evaluated next after resolving the vinculum.

3

Evaluate the expression inside the curly brackets

10 \div 2.0 = 5

Division within the curly brackets takes priority before moving outward.

4

Evaluate the expression inside the square brackets

16 - 5 = 11

Resolve the remaining operations within the square brackets.

5

Perform multiplication before addition

15 + (2.5 \times 11) = 15 + 27.5 = 42.5

Multiplication takes precedence over addition according to BODMAS rules.

Key Concept

Order of Operations (VBODMAS Rule)

Question 45Question →

What is the simplified value of the following mathematical expression?

45 \div 5 \times 3 + [18 - \{14 - (8 - 3)\}]

Show answer & explanation

Answer: 36

Answer

36

Following the BODMAS rule step by step:
1. Innermost parenthesis:

8 - 3 = 5

.
2. Curly braces:

14 - 5 = 9

.
3. Square brackets:

18 - 9 = 9

.
4. Left-to-right division and multiplication:

45 \div 5 \times 3 = 9 \times 3 = 27

.
5. Addition:

27 + 9 = 36

.

Step-by-Step Solution

1

Evaluate the innermost round brackets

8 - 3 = 5

According to the BODMAS rule, operations inside the innermost brackets must be solved first.

2

Evaluate the expression inside the curly braces

14 - 5 = 9

Substitute the result from the round brackets into the curly braces.

3

Evaluate the expression inside the square brackets

18 - 9 = 9

Substitute the result from the curly braces into the square brackets.

4

Perform Division and Multiplication from left to right

45 / 5 * 3 = 9 * 3 = 27

Division and multiplication have equal precedence and must be evaluated strictly from left to right.

5

Add the result of the bracket terms to the result of the arithmetic terms

27 + 9 = 36

Final addition yields the simplified result.

Key Concept

BODMAS Rule (Brackets, Orders, Division and Multiplication left-to-right, Addition and Subtraction left-to-right)

Question 46Question →

What is the value of the following mathematical expression?

25 - [18 - \{12 - (6 - \overline{4 - 1})\}]

16

18

22

12

Show answer & explanation

Answer: 16

Answer

16

Following the BODMAS priority (Vinculum

\rightarrow

Round Brackets

\rightarrow

Curly Braces

\rightarrow

Square Brackets

\rightarrow

Outermost Subtraction):
1. Vinculum:

\overline{4 - 1} = 3

2. Round brackets:

6 - 3 = 3

3. Curly braces:

12 - 3 = 9

4. Square brackets:

18 - 9 = 9

5. Outer subtraction:

25 - 9 = 16

.
Thus, 16 is the mathematically correct answer.

Step-by-Step Solution

1

Evaluate the expression under the vinculum bar

\overline{4 - 1} = 3

According to BODMAS, vinculum (bar bracket) has the highest priority.

2

Simplify the innermost round brackets

(6 - 3)

6 - 3 = 3

Evaluate terms inside round brackets next.

3

Simplify the curly braces

\{12 - 3\}

12 - 3 = 9

Evaluate terms inside curly braces next.

4

Simplify the square brackets

[18 - 9]

18 - 9 = 9

Evaluate terms inside square brackets next.

5

Perform final subtraction from 25

25 - 9 = 16

Complete the outermost operation.

Key Concept

BODMAS Rule with Vinculum (Bar Bracket)

Question 47Question →

What is the simplified value of the following mathematical expression?

\frac{7}{2} \div \left[ 1 \frac{1}{4} + \left\{ 2 \frac{1}{2} - \frac{1}{2} \times \left( 2.5 - \overline{\frac{1}{4} + \frac{1}{6}} \right) \right\} \right] \times \frac{5}{12}

\frac{7}{13}

\frac{35}{61}

\frac{1008}{325}

\frac{5}{13}

Show answer & explanation

Answer: $\frac{7}{13}$

Answer

The simplified value of the expression is

\frac{7}{13}

.

Following strict BODMAS precedence: First, simplify the bar term

\overline{\frac{1}{4} + \frac{1}{6}} = \frac{5}{12}

. Next, resolve the round bracket

\frac{5}{2} - \frac{5}{12} = \frac{25}{12}

. Multiplying by

\frac{1}{2}

gives

\frac{25}{24}

. The curly bracket simplifies to

\frac{5}{2} - \frac{25}{24} = \frac{35}{24}

. The square bracket yields

\frac{5}{4} + \frac{35}{24} = \frac{65}{24}

. Finally, evaluating left to right gives

\frac{7}{2} \times \frac{24}{65} \times \frac{5}{12} = \frac{7}{13}

.

Step-by-Step Solution

1

Evaluate the expression under the vinculum (bar bracket)

\overline{\frac{1}{4} + \frac{1}{6}} = \frac{3 + 2}{12} = \frac{5}{12}

According to BODMAS, the vinculum takes precedence over round brackets.

2

Evaluate the terms inside the round brackets

2.5 - \frac{5}{12} = \frac{5}{2} - \frac{5}{12} = \frac{30 - 5}{12} = \frac{25}{12}

Convert decimal

2.5

to fraction

\frac{5}{2}

and perform subtraction.

3

Perform multiplication inside the curly brackets

\frac{1}{2} \times \frac{25}{12} = \frac{25}{24}

Multiplication inside brackets precedes subtraction.

4

Evaluate the terms inside the curly brackets

2 \frac{1}{2} - \frac{25}{24} = \frac{5}{2} - \frac{25}{24} = \frac{60 - 25}{24} = \frac{35}{24}

Complete the subtraction inside the curly brackets.

5

Evaluate the terms inside the square brackets

1 \frac{1}{4} + \frac{35}{24} = \frac{5}{4} + \frac{35}{24} = \frac{30 + 35}{24} = \frac{65}{24}

Perform addition within the square brackets.

6

Perform division and multiplication from left to right

\frac{7}{2} \div \frac{65}{24} \times \frac{5}{12} = \frac{7}{2} \times \frac{24}{65} \times \frac{5}{12} = \frac{84}{65} \times \frac{5}{12} = \frac{7}{13}

Division and multiplication have equal precedence and are executed strictly from left to right.

Key Concept

BODMAS Rule with Vinculum and Nested Brackets

Question 48Question →

Calculate the exact numerical value of the following mathematical expression by applying the standard order of operations (BODMAS):

36.4 - \left[ 12.8 + \left\{ 6.5 \times \left( 4.4 - \overline{2.6 + 0.8} \right) \right\} \div 1.3 \right]

Show answer & explanation

Answer: 18.6

Answer

The simplified value of the mathematical expression is 18.6.

Strict application of BODMAS requires simplifying grouping symbols from the innermost vinculum outward, followed by resolving division prior to addition within brackets, yielding an exact answer of 18.6.

Step-by-Step Solution

1

Evaluate the expression underneath the vinculum (bar line)

\overline{2.6 + 0.8} = 3.4

The vinculum functions as an innermost bracket with highest evaluation priority.

2

Evaluate the terms inside the round brackets

4.4 - 3.4 = 1.0

Process operations inside round brackets next.

3

Perform multiplication within the curly braces

6.5 \times 1.0 = 6.5

Complete operations within the curly braces.

4

Execute division inside the square brackets

6.5 \div 1.3 = 5.0

Division takes precedence over addition according to BODMAS rules.

5

Perform addition within the square brackets

12.8 + 5.0 = 17.8

Finish evaluating all operations contained within the square brackets.

6

Perform final subtraction from left to right

36.4 - 17.8 = 18.6

Complete the outermost subtraction to arrive at the final simplified value.

Key Concept

BODMAS Rule with Vinculum and Decimals

Question 49Question →

Find the exact numerical value of the following mathematical expression evaluated strictly according to the VBODMAS rule:

75\% \text{ of } 160 - \left[ 3.5 \times 8 + \left\{ 48 \div \left( 14 - \overline{5 \times 2} \right) \right\} \right]

Show answer & explanation

Answer: 80

Answer

The simplified numerical value of the expression is

80

.

Evaluating the expression following strict VBODMAS hierarchy: bar expression

\overline{5 \times 2} = 10

, round brackets

14 - 10 = 4

, curly brackets

48 \div 4 = 12

, square brackets

3.5 \times 8 + 12 = 40

, and percentage 'of' term

75\% \text{ of } 160 = 120

. Finally,

120 - 40 = 80

.

Step-by-Step Solution

1

Evaluate the expression under the vinculum (bar)

\overline{5 \times 2} = 10

According to VBODMAS, operations grouped under a bar take highest priority.

2

Evaluate inside the innermost round brackets

(14 - 10)

14 - 10 = 4

Perform subtraction inside the parentheses.

3

Evaluate inside the curly brackets

\{48 \div 4\}

48 \div 4 = 12

Divide the number outside the round bracket by the result of the round bracket.

4

Evaluate inside the square brackets

[3.5 \times 8 + 12]

28 + 12 = 40

Perform multiplication (

3.5 \times 8 = 28

) before adding

12

.

5

Calculate the percentage term

75\% \text{ of } 160

\frac{75}{100} \times 160 = 120

Evaluate the 'of' operation before final subtraction.

6

Perform final subtraction

120 - 40

80

Subtract the total result of the bracketed expression from the percentage term.

Key Concept

Order of Operations (VBODMAS Rule)

Question 50Question →

Evaluate the following numerical expression strictly according to the VBODMAS rule:

2.5 \times 12 - \left[ 8 + \left\{ 15 \div \left( 4.5 - \overline{2.1 + 0.9} \right) \right\} \right]

What is the final calculated value?

Show answer & explanation

Answer: 12

Answer

12

Evaluating the expression following strict VBODMAS priority yields: Vinculum (2.1 + 0.9 = 3) -> Round brackets (4.5 - 3 = 1.5) -> Curly brackets (15 / 1.5 = 10) -> Square brackets (8 + 10 = 18) -> Multiplication (2.5 * 12 = 30) -> Subtraction (30 - 18 = 12).

Step-by-Step Solution

1

Evaluate the expression under the vinculum bar

2.1 + 0.9 = 3

According to the VBODMAS rule, operations under a vinculum take highest priority.

2

Evaluate the innermost round brackets

4.5 - 3 = 1.5

Perform subtraction inside the round brackets after resolving the vinculum.

3

Perform division within the curly brackets

15 / 1.5 = 10

Division inside curly brackets must be calculated before simplifying the outer bracket.

4

Perform addition within the square brackets

8 + 10 = 18

Complete the evaluation of the square bracket section.

5

Perform multiplication outside the brackets

2.5 * 12 = 30

Multiplication takes precedence over final subtraction.

6

Perform final subtraction

30 - 18 = 12

Complete the expression by subtracting the bracket result from the product.

Key Concept

VBODMAS Rule (Vinculum, Brackets, Orders, Division, Multiplication, Addition, Subtraction)

Simplification and BODMAS Rule

Answer

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