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Simplification and BODMAS Rule

50 questions

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Question 21Question →
What is the simplified value of the following expression?
25% of 160−[12÷{315+(1.8−0.6+0.4‾)}]×525\% \text{ of } 160 - \left[ 12 \div \left\{ 3\frac{1}{5} + \left( 1.8 - \overline{0.6 + 0.4} \right) \right\} \right] \times 5
Show answer & explanation

Answer: 25

Answer

25
Evaluating the expression following the standard BODMAS priority (Vinculum →\rightarrow Brackets →\rightarrow Orders/Percentage →\rightarrow Division →\rightarrow Multiplication →\rightarrow Subtraction):
1. Vinculum: 0.6+0.4‾=1\overline{0.6 + 0.4} = 1
2. Round brackets: 1.8−1=0.81.8 - 1 = 0.8
3. Curly brackets: 315+0.8=3.2+0.8=43\frac{1}{5} + 0.8 = 3.2 + 0.8 = 4
4. Square brackets: 12÷4=312 \div 4 = 3
5. Percentage: 25% of 160=4025\% \text{ of } 160 = 40
6. Final calculation: 40−(3×5)=40−15=2540 - (3 \times 5) = 40 - 15 = 25.
Hence, the correct value is 25.

Step-by-Step Solution

1
Evaluate the expression under the vinculum bar 0.6+0.4‾\overline{0.6 + 0.4}
0.6+0.4=1.00.6 + 0.4 = 1.0
The vinculum (bar bracket) takes the highest priority in the hierarchy of brackets.
2
Evaluate the innermost round brackets (1.8−1.0)(1.8 - 1.0)
1.8−1.0=0.81.8 - 1.0 = 0.8
Round brackets must be resolved next after the vinculum.
3
Convert mixed fraction 3153\frac{1}{5} to decimal and evaluate the curly brackets {3.2+0.8}\left\{ 3.2 + 0.8 \right\}
315=3.23\frac{1}{5} = 3.2, so 3.2+0.8=4.03.2 + 0.8 = 4.0
Curly brackets are evaluated after resolving all inner terms.
4
Evaluate the square brackets [12÷4.0]\left[ 12 \div 4.0 \right]
12÷4=312 \div 4 = 3
Square brackets enclose the remaining multi-bracket expression.
5
Evaluate the 'of' percentage operation 25% of 16025\% \text{ of } 160
25100×160=40\frac{25}{100} \times 160 = 40
'Of' / percentage operations take precedence over standard multiplication and subtraction.
6
Perform multiplication before subtraction in 40−3×540 - 3 \times 5
3×5=153 \times 5 = 15, then 40−15=2540 - 15 = 25
According to BODMAS, multiplication precedes subtraction.

Key Concept

Hierarchy of Brackets and BODMAS Rule
Estimated Time:2m 0s
Question 22Question →
Evaluate the following mathematical expression by applying the standard order of operations (BODMAS):
18÷[412−{214+34×(4.8−2.4+0.4‾)}]+5.518 \div \left[ 4 \frac{1}{2} - \left\{ 2 \frac{1}{4} + \frac{3}{4} \times \left( 4.8 - \overline{2.4 + 0.4} \right) \right\} \right] + 5.5
What is the final numerical value of the simplified expression?
Show answer & explanation

Answer: 29.5

Answer

The simplified numerical value of the given expression is 29.5.
Following the BODMAS rule systematically, we first resolve the vinculum to get 2.8, then evaluate the round brackets (4.8 - 2.8 = 2.0). Next, inside the curly brackets, multiplication yields 1.5 and addition yields 3.75. Evaluating the square brackets yields 4.5 - 3.75 = 0.75. Dividing 18 by 0.75 gives 24, and adding 5.5 gives the final correct answer of 29.5.

Step-by-Step Solution

1
Evaluate the expression under the vinculum bar
\overline{2.4 + 0.4} = 2.8
The vinculum (bar) takes highest priority over standard parentheses and operations.
2
Simplify the innermost round brackets
4.8 - 2.8 = 2.0
Perform subtraction inside the round brackets next.
3
Perform multiplication inside the curly brackets
34×2.0=1.5\frac{3}{4} \times 2.0 = 1.5
Multiplication precedes addition within the curly brackets according to BODMAS.
4
Complete evaluation inside the curly brackets
2 \frac{1}{4} + 1.5 = 2.25 + 1.5 = 3.75
Convert the mixed fraction 2 1/4 to decimal 2.25 and add 1.5.
5
Evaluate the terms inside the square brackets
4 \frac{1}{2} - 3.75 = 4.5 - 3.75 = 0.75
Convert mixed fraction 4 1/2 to decimal 4.5 and subtract 3.75.
6
Perform division before final addition
18÷0.75=2418 \div 0.75 = 24
Division takes precedence over the final addition operation.
7
Add the final constant
24 + 5.5 = 29.5
Complete the evaluation by adding 5.5 to 24.

Key Concept

Hierarchy of operations in BODMAS including vinculum bar, nested brackets, and precedence of operations.
Estimated Time:1m 30s
Question 23Question →
Calculate the numerical value of the following mathematical expression:
75% of 240−[42÷{214+(3.5−1.8−0.8‾)×1.5}]75\% \text{ of } 240 - \left[ 42 \div \left\{ 2\frac{1}{4} + \left( 3.5 - \overline{1.8 - 0.8} \right) \times 1.5 \right\} \right]
Show answer & explanation

Answer: 173

Answer

The simplified numerical value of the expression is 173.
Applying the VBODMAS rule sequentially (vinculum, round brackets, multiplication, addition within curly brackets, square bracket division, percentage evaluation, and final subtraction) yields 173.

Step-by-Step Solution

1
Evaluate the vinculum bar expression
1.8−0.8‾=1.0\overline{1.8 - 0.8} = 1.0
Under VBODMAS rules, the vinculum (bar) grouping has the highest priority and must be evaluated first.
2
Evaluate the subtraction inside the round brackets
3.5−1.0=2.53.5 - 1.0 = 2.5
Evaluate the parentheses next using the result from the vinculum evaluation.
3
Perform multiplication inside the curly brackets
2.5×1.5=3.752.5 \times 1.5 = 3.75
Within the curly brackets, multiplication precedes addition according to BODMAS.
4
Perform addition inside the curly brackets
214+3.75=2.25+3.75=6.02\frac{1}{4} + 3.75 = 2.25 + 3.75 = 6.0
Convert the mixed fraction 2142\frac{1}{4} to decimal 2.252.25 and add to 3.753.75.
5
Perform division inside the square brackets
42÷6.0=742 \div 6.0 = 7
Resolve the square brackets by dividing 42 by the value of the curly bracket expression.
6
Evaluate the percentage 'of' expression
75% of 240=0.75×240=18075\% \text{ of } 240 = 0.75 \times 240 = 180
The 'of' operator indicates multiplication applied to percentage.
7
Subtract the square bracket result from the percentage value
180−7=173180 - 7 = 173
Perform final subtraction to complete the calculation.

Key Concept

Hierarchical priority of operations in VBODMAS (Vinculum -> Brackets -> Of -> Division -> Multiplication -> Addition -> Subtraction)
Question 24Question →
What is the simplified numerical value of the following mathematical expression when evaluated using the standard BODMAS rule?
60% of 350−[514+{36÷(4.5−2.1+0.9‾)}]×460\% \text{ of } 350 - \left[ 5 \frac{1}{4} + \left\{ 36 \div \left( 4.5 - \overline{2.1 + 0.9} \right) \right\} \right] \times 4
Show answer & explanation

Answer: 93

Answer

The simplified numerical value of the given expression is 93.
Following the BODMAS rule: first evaluate the vinculum \(\overline{2.1 + 0.9} = 3\), then the round bracket \(4.5 - 3 = 1.5\), then the curly bracket \(36 \div 1.5 = 24\), then the square bracket \(5.25 + 24 = 29.25\). Next, evaluate the percentage term \(60\% \text{ of } 350 = 210\) and the product \(29.25 \times 4 = 117\). Finally, subtracting 117 from 210 gives 93.

Step-by-Step Solution

1
Evaluate the expression under the vinculum bar
\overline{2.1 + 0.9} = 3.0
The vinculum (bar) has the highest priority inside nested grouping symbols.
2
Evaluate the terms inside the round brackets
4.5 - 3.0 = 1.5
Subtract the result of the vinculum from 4.5 inside the round brackets.
3
Evaluate the division inside the curly brackets
36÷1.5=2436 \div 1.5 = 24
Perform division within the curly braces.
4
Evaluate the addition inside the square brackets
5 \frac{1}{4} + 24 = 5.25 + 24 = 29.25
Convert the mixed fraction to decimal (5.25) and add to 24.
5
Calculate the percentage term and multiplication term
60\% \text{ of } 350 = \frac{60}{100} \times 350 = 210 \quad \text{and} \quad 29.25 \times 4 = 117
According to BODMAS, percentage/off and multiplication must be computed before final subtraction.
6
Perform the final subtraction
210 - 117 = 93
Subtract the multiplied bracket result from the percentage value.

Key Concept

Order of Operations (BODMAS/PEMDAS) with Vinculum and Nested Brackets
Question 25Question →

Determine the exact result of the given mathematical expression after applying the standard order of operations (BODMAS):

32.4−45×[45÷{2.5×4−(7.6−4.1−1.5‾)}]32.4 - \frac{4}{5} \times \left[ 45 \div \left\{ 2.5 \times 4 - \left( 7.6 - \overline{4.1 - 1.5} \right) \right\} \right]
Show answer & explanation

Answer: 25.2

Answer

The simplified numerical value of the expression is 25.2.
Following the standard BODMAS priority order: evaluate the vinculum (4.1 - 1.5 = 2.6), round brackets (7.6 - 2.6 = 5), curly brackets (2.5 * 4 - 5 = 5), square brackets (45 / 5 = 9), multiplication ((4/5) * 9 = 7.2), and finally subtraction (32.4 - 7.2 = 25.2).

Step-by-Step Solution

1
Evaluate the sub-expression under the vinculum bar
\overline{4.1 - 1.5} = 2.6
The vinculum acts as the innermost grouping symbol and takes highest priority.
2
Simplify the expression inside the round brackets
(7.6 - 2.6) = 5.0
Parentheses (round brackets) are evaluated next.
3
Evaluate operations inside the curly brackets using operator precedence
\{2.5 \times 4 - 5.0\} = \{10 - 5.0\} = 5
Multiplication precedes subtraction inside the curly brackets.
4
Evaluate the division inside the square brackets
[45÷5]=9[45 \div 5] = 9
Square brackets are solved after resolving inner curly brackets.
5
Perform multiplication outside the bracket
\frac{4}{5} \times 9 = 0.8 \times 9 = 7.2
Multiplication takes precedence over final addition/subtraction.
6
Perform the final subtraction
32.4 - 7.2 = 25.2
Subtraction is the final step in the BODMAS order of operations.

Key Concept

BODMAS Rule with Vinculum and Nested Brackets
Estimated Time:1m 30s
Question 26Question →

What value is obtained upon simplifying the mathematical expression given below using the correct order of operations (BODMAS)?

87.5% of 120−[225×{24.5−(4.5÷2.4−0.9‾×1.6+115)}]87.5\% \text{ of } 120 - \left[ 2 \frac{2}{5} \times \left\{ 24.5 - \left( 4.5 \div \overline{2.4 - 0.9} \times 1.6 + 1 \frac{1}{5} \right) \right\} \right]
Show answer & explanation

Answer: 60.660.6

Answer

60.660.6
The correct result 60.660.6 is achieved by systematically resolving operations from the innermost group outward: first the bar/vinculum, followed by division and multiplication inside the parentheses, subtraction in the curly brackets, multiplication in the square brackets, and finally subtracting this total from 87.5%87.5\% of 120120.

Step-by-Step Solution

1
Evaluate the expression under the vinculum (bar)
2.4−0.9‾=1.5\overline{2.4 - 0.9} = 1.5
The vinculum has the highest priority among grouping symbols.
2
Evaluate the terms inside the parentheses (...)(...) using BODMAS
4.5÷1.5×1.6+115=3×1.6+1.2=4.8+1.2=6.04.5 \div 1.5 \times 1.6 + 1 \frac{1}{5} = 3 \times 1.6 + 1.2 = 4.8 + 1.2 = 6.0
Perform division first (4.5÷1.5=34.5 \div 1.5 = 3), then multiplication (3×1.6=4.83 \times 1.6 = 4.8), and finally addition (4.8+1.2=6.04.8 + 1.2 = 6.0).
3
Simplify the expression inside the curly brackets {...}\{...\}
24.5−6.0=18.524.5 - 6.0 = 18.5
Subtract the result of the parentheses from 24.524.5.
4
Simplify the expression inside the square brackets [...][...]
225×18.5=2.4×18.5=44.42 \frac{2}{5} \times 18.5 = 2.4 \times 18.5 = 44.4
Convert the mixed fraction 2252 \frac{2}{5} to decimal 2.42.4 and multiply by 18.518.5.
5
Calculate the percentage value
87.5% of 120=78×120=10587.5\% \text{ of } 120 = \frac{7}{8} \times 120 = 105
Convert 87.5%87.5\% to the equivalent fraction 78\frac{7}{8} and multiply by 120120.
6
Perform the final subtraction
105−44.4=60.6105 - 44.4 = 60.6
Subtract the value of the square brackets from the percentage result.

Key Concept

Strict evaluation of nested brackets (vinculum, round, curly, square) and mixed operators (percentage, fraction, division, multiplication) using the BODMAS rule.
Question 27Question →

What is the final numerical value of the following expression evaluated using the standard BODMAS rule?

50−[18÷3×(4+2)]50 - [18 \div 3 \times (4 + 2)]
Show answer & explanation

Answer: 14

Answer

The final simplified value of the expression is 14.
Following the BODMAS order of operations: first simplify the inner bracket (4+2)=6(4 + 2) = 6. Next, evaluate inside the square bracket from left to right: 18÷3=618 \div 3 = 6, and then 6×6=366 \times 6 = 36. Finally, subtract from 50 to get 50−36=1450 - 36 = 14.

Step-by-Step Solution

1
Evaluate the innermost round brackets
4+2=64 + 2 = 6
According to BODMAS, operations inside brackets must be performed first.
2
Perform division inside the square brackets
18÷3=618 \div 3 = 6
Division and multiplication have equal priority and are performed from left to right.
3
Perform multiplication inside the square brackets
6×6=366 \times 6 = 36
Multiply the quotient obtained from division by the bracketed sum.
4
Subtract the result inside brackets from 50
50−36=1450 - 36 = 14
Perform subtraction as the final operation.

Key Concept

BODMAS / Order of Operations
Question 28Question →
What exact numerical result is obtained when simplifying the following multi-bracket expression according to the BODMAS order of operations?
75% of 240−[38.5+{1512−(6.8×2.5−4.2+3.8‾)÷0.5}]75\% \text{ of } 240 - \left[ 38.5 + \left\{ 15\frac{1}{2} - \left( 6.8 \times 2.5 - \overline{4.2 + 3.8} \right) \div 0.5 \right\} \right]
Show answer & explanation

Answer: 144

Answer

The final simplified numerical value of the given expression is 144.
Following the BODMAS rule strictly: first evaluate the vinculum 4.2+3.8‾=8\overline{4.2 + 3.8} = 8; then resolve round brackets (6.8×2.5−8=9)(6.8 \times 2.5 - 8 = 9); next resolve curly brackets (15.5−9÷0.5=−2.5)(15.5 - 9 \div 0.5 = -2.5); then square brackets (38.5−2.5=36)(38.5 - 2.5 = 36); and finally compute 75% of 240=18075\% \text{ of } 240 = 180. Subtracting 3636 from 180180 gives the correct result of 144.

Step-by-Step Solution

1
Evaluate the vinculum (bar) operator first
\overline{4.2 + 3.8} = 8
According to BODMAS, the vinculum takes precedence over round brackets.
2
Simplify the terms inside the round brackets (parentheses)
6.8 \times 2.5 - 8 = 17 - 8 = 9
Multiplication precedes subtraction inside the innermost round brackets.
3
Simplify the terms inside the curly brackets (braces)
15.5 - (9 \div 0.5) = 15.5 - 18 = -2.5
Division (9÷0.5=189 \div 0.5 = 18) is performed before subtracting from 15.515.5 (151215\frac{1}{2}).
4
Simplify the terms inside the square brackets
38.5 + (-2.5) = 36
Adding the negative result from the curly brackets to 38.538.5 yields 3636.
5
Calculate the percentage 'Of' operation and perform final subtraction
75\% \text{ of } 240 - 36 = 180 - 36 = 144
'Of' operation (75%×240=18075\% \times 240 = 180) is calculated before subtracting the bracketed total.

Key Concept

BODMAS Rule with Vinculum and Nested Brackets
Estimated Time:2m 0s
Question 29Question →
What is the result when the mathematical expression 45−[12+(8÷2×3)]45 - [12 + (8 \div 2 \times 3)] is simplified strictly adhering to the standard BODMAS order of operations?
Show answer & explanation

Answer: 21

Answer

21
Following the BODMAS rule, operations inside the innermost parentheses are solved first from left to right: 8÷2=48 \div 2 = 4, then 4×3=124 \times 3 = 12. Next, addition inside the square brackets gives 12+12=2412 + 12 = 24. Finally, subtracting 24 from 45 yields 21.

Step-by-Step Solution

1
Evaluate division inside the parentheses
8 ÷ 2 = 4
Division and multiplication have equal priority and are evaluated from left to right inside parentheses.
2
Evaluate multiplication inside the parentheses
4 × 3 = 12
Completing the operations within the parentheses.
3
Add the values inside the square brackets
12 + 12 = 24
Evaluating the bracketed addition.
4
Subtract from the outer term
45 - 24 = 21
Performing final subtraction outside the brackets.

Key Concept

BODMAS Rule (Order of Operations)
Estimated Time:45s
Question 30Question →

What is the simplified value of the following mathematical expression evaluated using the standard BODMAS rule?

24+16÷4×2−(7−5−2‾)24 + 16 \div 4 \times 2 - (7 - \overline{5 - 2})
Show answer & explanation

Answer: 28

Answer

28
Following the standard order of operations (BODMAS), we first simplify the expression under the vinculum bar: 5−2=35 - 2 = 3. Next, we complete the subtraction inside the parentheses: 7−3=47 - 3 = 4. Then, we resolve division and multiplication from left to right: 16÷4=416 \div 4 = 4, and 4×2=84 \times 2 = 8. Finally, combining addition and subtraction gives 24+8−4=2824 + 8 - 4 = 28.

Step-by-Step Solution

1
Evaluate the expression under the vinculum (bar)
\overline{5 - 2} = 3
The vinculum takes the highest priority in bracket operations.
2
Evaluate the round brackets
(7 - 3) = 4
Operations within brackets must be solved next.
3
Perform Division and Multiplication from left to right
16 \div 4 = 4; \quad 4 \times 2 = 8
Division and multiplication share equal precedence and are performed in order from left to right.
4
Perform Addition and Subtraction from left to right
24 + 8 - 4 = 28
Final addition and subtraction operations are executed left-to-right.

Key Concept

BODMAS Rule with Vinculum (Order of Operations)
Question 31Question →
What is the simplified numerical value of the following mathematical expression when evaluated strictly according to the BODMAS rule?
45−[3×{12÷(1.5+2.7−1.2‾)}+2.5]×245 - \left[ 3 \times \left\{ 12 \div \left( 1.5 + \overline{2.7 - 1.2} \right) \right\} + 2.5 \right] \times 2
Show answer & explanation

Answer: 16

Answer

16
Evaluating the expression according to VBODMAS rules step-by-step: first the vinculum gives 1.5; adding inside round brackets gives 3; dividing inside curly braces gives 4; multiplying and adding inside square brackets gives 14.5; finally multiplying by 2 gives 29, and subtracting from 45 yields 16.

Step-by-Step Solution

1
Evaluate the expression under the vinculum (bar)
\overline{2.7 - 1.2} = 1.5
According to VBODMAS, operations under a vinculum must be simplified first.
2
Simplify the expression inside the round brackets (parentheses)
1.5 + 1.5 = 3
Parentheses have priority after the vinculum is resolved.
3
Evaluate the division inside the curly braces
12÷3=412 \div 3 = 4
Operations within braces are evaluated next.
4
Simplify the expression inside the square brackets
3 \times 4 + 2.5 = 12 + 2.5 = 14.5
Inside brackets, multiplication takes precedence over addition.
5
Perform final operations outside brackets using standard operator precedence
45 - 14.5 \times 2 = 45 - 29 = 16
Multiplication must be executed before subtraction.

Key Concept

Hierarchy of operations in VBODMAS (Vinculum, Brackets, Orders, Division, Multiplication, Addition, Subtraction)
Question 32Question →
What is the simplified numerical value of the mathematical expression 25−[10+{8÷(6−4−2‾)}]25 - \left[ 10 + \left\{ 8 \div \left( 6 - \overline{4 - 2} \right) \right\} \right] when evaluated using the standard BODMAS rule?
Show answer & explanation

Answer: 1313

Answer

The correct simplified value of the given expression is 13.
Evaluating the expression step-by-step using VBODMAS rules:
1. Vinculum: 4−2‾=2\overline{4 - 2} = 2
2. Round brackets: 6−2=46 - 2 = 4
3. Curly brackets: 8÷4=28 \div 4 = 2
4. Square brackets: 10+2=1210 + 2 = 12
5. Final subtraction: 25−12=1325 - 12 = 13.
Thus, the correct value is 13.

Step-by-Step Solution

1
Evaluate the expression under the vinculum (bar)
4−2‾=2\overline{4 - 2} = 2
According to VBODMAS, operations under a vinculum (bar) have the highest precedence.
2
Simplify the innermost round brackets
6−2=46 - 2 = 4
Substitute the vinculum result into the round brackets (6−2)(6 - 2).
3
Evaluate the division inside the curly brackets
8÷4=28 \div 4 = 2
Division within the curly braces {8÷4}\{8 \div 4\} takes precedence.
4
Evaluate the addition inside the square brackets
10+2=1210 + 2 = 12
Add the terms inside the square brackets [10+2][10 + 2].
5
Perform the final subtraction
25−12=1325 - 12 = 13
Subtract the bracket result from 25.

Key Concept

Order of operations following the VBODMAS rule (Vinculum, Brackets, Orders, Division, Multiplication, Addition, Subtraction)
Question 33Question →
Evaluate the expression given below by applying the standard order of operations (VBODMAS):
2.5×[18÷{4.5+12 of (7.8−3.4+1.4‾)}]+3.52.5 \times \left[ 18 \div \left\{ 4.5 + \frac{1}{2} \text{ of } \left( 7.8 - \overline{3.4 + 1.4} \right) \right\} \right] + 3.5
Which of the following represents the correct simplified result?
Show answer & explanation

Answer: 11

Answer

The correct simplified result is 11.
Evaluating step-by-step using VBODMAS order yields: Vinculum gives 4.8; Round bracket yields 7.8 - 4.8 = 3.0; 'of' operation gives 0.5 * 3.0 = 1.5; Curly brackets give 4.5 + 1.5 = 6.0; Square bracket gives 18 / 6.0 = 3; Final calculation gives 2.5 * 3 + 3.5 = 7.5 + 3.5 = 11.

Step-by-Step Solution

1
Evaluate the expression under the vinculum (bar line).
\overline{3.4 + 1.4} = 4.8
According to VBODMAS, the vinculum takes precedence over all standard brackets.
2
Simplify the innermost round brackets.
7.8 - 4.8 = 3.0
Resolve terms within parenthetical brackets next.
3
Execute the 'of' operation inside the curly brackets.
\frac{1}{2} \text{ of } 3.0 = 1.5
The 'of' operator represents multiplication with higher priority than division and standard addition.
4
Complete the addition within the curly brackets.
4.5 + 1.5 = 6.0
Finish evaluating all operations contained within the curly brackets.
5
Perform division inside the square brackets.
18÷6.0=318 \div 6.0 = 3
Evaluate the remaining square bracket operation.
6
Perform final multiplication and addition operations from left to right according to operator precedence.
2.5 \times 3 + 3.5 = 7.5 + 3.5 = 11
Multiplication takes precedence over final addition.

Key Concept

VBODMAS Rule (Vinculum, Brackets, Of, Division, Multiplication, Addition, Subtraction)
Estimated Time:1m 15s
Question 34Question →

What is the simplified numerical value of the expression 15+{20−(8÷6−2‾)}15 + \left\{ 20 - \left( 8 \div \overline{6 - 2} \right) \right\} when evaluated using the standard BODMAS rule?

Show answer & explanation

Answer: 33

Answer

The simplified numerical value of the expression is 33.
Applying VBODMAS order (Vinculum →\rightarrow Brackets →\rightarrow Division →\rightarrow Subtraction →\rightarrow Addition) yields: 6−2‾=4\overline{6-2} = 4, 8÷4=28 \div 4 = 2, 20−2=1820 - 2 = 18, and 15+18=3315 + 18 = 33.

Step-by-Step Solution

1
Evaluate the expression under the vinculum (bar)
6−2‾=4\overline{6 - 2} = 4
The vinculum (bar line) takes precedence over standard operators.
2
Perform division inside the round brackets
8÷4=28 \div 4 = 2
Operations inside the innermost round brackets are evaluated next.
3
Perform subtraction inside the curly brackets
20−2=1820 - 2 = 18
Evaluate the expression enclosed in the curly brackets.
4
Perform final addition outside brackets
15+18=3315 + 18 = 33
Complete the evaluation by adding the remaining outer terms.

Key Concept

BODMAS / VBODMAS Rule (Order of Operations with Vinculum and Brackets)
Question 35Question →

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

25% of 120−[4×{15−(18÷7−4‾)}]÷1.525\% \text{ of } 120 - \left[ 4 \times \left\{ 15 - \left( 18 \div \overline{7 - 4} \right) \right\} \right] \div 1.5
Show answer & explanation

Answer: 6

Answer

6
Evaluating the vinculum 7−4‾\overline{7 - 4} yields 33. The round bracket becomes 18÷3=618 \div 3 = 6. The curly bracket yields 15−6=915 - 6 = 9. The square bracket evaluates to 4×9=364 \times 9 = 36. Concurrently, 25%25\% of 120120 equals 3030. Following operator hierarchy, division is executed next: 36÷1.5=2436 \div 1.5 = 24. Finally, performing subtraction gives 30−24=630 - 24 = 6.

Step-by-Step Solution

1
Evaluate the expression under the bar (vinculum)
7−4‾=3\overline{7 - 4} = 3
According to BODMAS, vinculum (bar bracket) has the highest priority among all grouping symbols.
2
Evaluate the innermost round bracket
18÷3=618 \div 3 = 6
Perform division inside the round bracket after resolving the vinculum.
3
Evaluate the curly bracket
15−6=915 - 6 = 9
Subtract the result of the round bracket from 15 inside the curly bracket.
4
Evaluate the square bracket and the percentage term
4×9=364 \times 9 = 36 and 25% of 120=25100×120=3025\% \text{ of } 120 = \frac{25}{100} \times 120 = 30
Multiply 4 by the curly bracket result, and independently calculate the percentage term.
5
Perform division before final subtraction
36÷1.5=2436 \div 1.5 = 24
BODMAS mandates performing division before subtraction.
6
Perform the final subtraction
30−24=630 - 24 = 6
Subtract the quotient from the percentage value.

Key Concept

BODMAS Order of Operations with Vinculum and Mixed Numbers
Question 36Question →

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

45−[15+{24÷(3+12 of (16−8−2‾))}]45 - \left[ 15 + \left\{ 24 \div \left( 3 + \frac{1}{2} \text{ of } \left( 16 - \overline{8 - 2} \right) \right) \right\} \right]
Show answer & explanation

Answer: 27

Answer

The simplified numerical value of the given expression is 27.
Evaluating step-by-step using VBODMAS order of precedence (Vinculum -> Brackets -> Of -> Division -> Multiplication -> Addition -> Subtraction) yields the simplified result 27.

Step-by-Step Solution

1
Evaluate the vinculum (bar) operation
\overline{8 - 2} = 6
According to VBODMAS, operations under a vinculum take precedence over standard bracket operations.
2
Simplify the innermost subtraction inside the round brackets
16 - 6 = 10
Subtracted the value obtained from the vinculum within the innermost parentheses.
3
Evaluate the 'of' operator
\frac{1}{2} \text{ of } 10 = 5
The 'of' operator represents multiplication with priority immediately following brackets.
4
Complete the addition in the round brackets
3 + 5 = 8
Evaluated the remaining addition within the round brackets.
5
Perform division inside the curly brackets
24÷8=324 \div 8 = 3
Divided 24 by the simplified result of the round brackets.
6
Perform addition inside the square brackets
15 + 3 = 18
Added 15 to the result from the curly brackets.
7
Perform final subtraction
45 - 18 = 27
Subtracted the square bracket result from 45 to obtain the final simplified value.

Key Concept

Order of Operations (VBODMAS Rule)
Estimated Time:1m 30s
Question 37Question →
What is the simplified numerical value of the mathematical expression given below when evaluated strictly according to the VBODMAS rule?
15% of 200−[36÷{18−(2×7−4‾)}]×3.515\% \text{ of } 200 - \left[ 36 \div \left\{ 18 - \left( 2 \times \overline{7 - 4} \right) \right\} \right] \times 3.5
Show answer & explanation

Answer: 19.519.5

Answer

The simplified numerical value of the expression is 19.519.5.
Following the VBODMAS hierarchy, we first solve the bar term 7−4‾=3\overline{7-4} = 3, giving (2×3)=6(2 \times 3) = 6 inside the inner bracket. Next, the curly bracket simplifies to 18−6=1218 - 6 = 12. The square bracket simplifies to 36÷12=336 \div 12 = 3. Evaluating 15% of 200=3015\% \text{ of } 200 = 30 and the product 3×3.5=10.53 \times 3.5 = 10.5, we get 30−10.5=19.530 - 10.5 = 19.5.

Step-by-Step Solution

1
Evaluate the expression under the Vinculum (bar)
7−4‾=3\overline{7 - 4} = 3
According to VBODMAS, operations under the vinculum have the highest priority.
2
Evaluate the innermost round bracket ()( )
2×3=62 \times 3 = 6
Resolve the multiplication inside the round brackets.
3
Evaluate the curly bracket {}\{ \}
18−6=1218 - 6 = 12
Perform subtraction inside the curly brackets.
4
Evaluate the square bracket [][ ]
36÷12=336 \div 12 = 3
Perform division inside the square brackets.
5
Calculate the percentage portion
15% of 200=15100×200=3015\% \text{ of } 200 = \frac{15}{100} \times 200 = 30
'Of' represents multiplication in percentage evaluation.
6
Perform multiplication before final subtraction
3×3.5=10.53 \times 3.5 = 10.5
Multiplication takes precedence over final subtraction.
7
Perform final subtraction
30−10.5=19.530 - 10.5 = 19.5
Subtract the result of the bracketed expression term from the percentage term.

Key Concept

Order of Operations (VBODMAS Rule)
Estimated Time:1m 30s
Question 38Question →

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

18% of 250+[34−{12×2.5−(14÷2+8−3‾)}]18\% \text{ of } 250 + \left[ 34 - \left\{ 12 \times 2.5 - \left( 14 \div 2 + \overline{8 - 3} \right) \right\} \right]
Show answer & explanation

Answer: 61

Answer

61
Following the VBODMAS priority rule, we first clear the vinculum 8−3‾=5\overline{8-3}=5. Next, within the round brackets, division precedes addition: 14÷2+5=7+5=1214 \div 2 + 5 = 7 + 5 = 12. Inside the curly brackets, multiplication precedes subtraction: 12×2.5−12=30−12=1812 \times 2.5 - 12 = 30 - 12 = 18. The square bracket reduces to 34−18=1634 - 18 = 16. Evaluating 18%18\% of 250250 gives 4545. Adding 45+1645 + 16 yields the correct final result of 61.

Step-by-Step Solution

1
Evaluate the vinculum bar term
\overline{8 - 3} = 5
According to VBODMAS, operations under a vinculum (bar) must be simplified first.
2
Simplify the innermost round brackets
(14 \div 2 + 5) = 7 + 5 = 12
Division takes precedence over addition inside the parentheses.
3
Simplify the curly brackets
\{ 12 \times 2.5 - 12 \} = 30 - 12 = 18
Multiplication is performed before subtraction inside the brace group.
4
Simplify the square brackets
[ 34 - 18 ] = 16
Complete the bracket hierarchy by evaluating the outer square brackets.
5
Evaluate the 'of' percentage term
18\% \text{ of } 250 = \frac{18}{100} \times 250 = 45
The percentage 'of' operator is calculated as multiplication.
6
Perform the final addition
45 + 16 = 61
Combine the percentage term with the simplified bracket result.

Key Concept

VBODMAS Rule (Vinculum, Brackets, Of, Division, Multiplication, Addition, Subtraction)
Question 39Question →

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

16.5+{4.5×[12−(3.2+4.8−1.6‾÷0.8)]}16.5 + \left\{ 4.5 \times \left[ 12 - \left( 3.2 + \overline{4.8 - 1.6} \div 0.8 \right) \right] \right\}
Show answer & explanation

Answer: 38.138.1

Answer

The simplified numerical value of the expression is 38.138.1.
Following the VBODMAS priority sequence: resolving the vinculum gives 3.23.2; evaluating division inside the round bracket yields 3.2÷0.8=43.2 \div 0.8 = 4; finishing the round bracket yields 3.2+4=7.23.2 + 4 = 7.2; evaluating the square bracket gives 12−7.2=4.812 - 7.2 = 4.8; evaluating the curly bracket gives 4.5×4.8=21.64.5 \times 4.8 = 21.6; finally, adding 16.5+21.616.5 + 21.6 yields 38.138.1.

Step-by-Step Solution

1
Evaluate the expression under the vinculum (bar)
4.8−1.6‾=3.2\overline{4.8 - 1.6} = 3.2
According to the VBODMAS rule, operations under a vinculum take highest priority.
2
Evaluate the division inside the innermost round bracket
3.2÷0.8=43.2 \div 0.8 = 4
Division takes precedence over addition within parentheses.
3
Complete the evaluation inside the round bracket
3.2+4=7.23.2 + 4 = 7.2
Add the remaining terms within the round bracket.
4
Evaluate the expression inside the square bracket
12−7.2=4.812 - 7.2 = 4.8
Subtract the result of the round bracket from 1212.
5
Evaluate the multiplication inside the curly bracket
4.5×4.8=21.64.5 \times 4.8 = 21.6
Multiply the term outside the square bracket by the simplified square bracket value.
6
Perform the final addition
16.5+21.6=38.116.5 + 21.6 = 38.1
Add the initial constant to the simplified curly bracket term.

Key Concept

Order of Operations (VBODMAS Rule)
Estimated Time:1m 30s
Question 40Question →
What is the final numerical value of the following expression when evaluated strictly according to the VBODMAS rule?
12.5×4−[16+{25÷(3.5+2.8−1.3‾)}]12.5 \times 4 - \left[ 16 + \left\{ 25 \div \left( 3.5 + \overline{2.8 - 1.3} \right) \right\} \right]
Show answer & explanation

Answer: 29

Answer

The simplified numerical value of the expression is 29.
Applying VBODMAS step-by-step resolves the vinculum first (2.8 - 1.3 = 1.5), then the round brackets (3.5 + 1.5 = 5), curly brackets (25 / 5 = 5), square brackets (16 + 5 = 21), and finally the multiplication and subtraction (50 - 21 = 29).

Step-by-Step Solution

1
Evaluate the vinculum (bar) operation first
\overline{2.8 - 1.3} = 1.5
According to VBODMAS, the vinculum takes top priority over all other operations.
2
Simplify the expression inside the innermost round brackets
3.5 + 1.5 = 5
Next in hierarchy are the round brackets (parentheses).
3
Simplify the expression inside the curly brackets
25÷5=525 \div 5 = 5
Evaluate operations inside curly braces next.
4
Simplify the expression inside the square brackets
16 + 5 = 21
Complete the evaluation of the outer square brackets.
5
Perform the multiplication and final subtraction outside the brackets
12.5 \times 4 = 50 \text{ and then } 50 - 21 = 29
Perform multiplication before final subtraction following standard operator precedence.

Key Concept

VBODMAS Rule (Vinculum, Brackets, Orders, Division, Multiplication, Addition, Subtraction)
Estimated Time:1m 30s
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