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Simplification and BODMAS Rule

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Question 1Question →
What is the numerical value of the following mathematical expression evaluated using the BODMAS rule?
12.5% of 480−[334÷{1.25+12 of (3.6−1.8−0.7‾)}]×81512.5\% \text{ of } 480 - \left[ 3 \frac{3}{4} \div \left\{ 1.25 + \frac{1}{2} \text{ of } \left( 3.6 - \overline{1.8 - 0.7} \right) \right\} \right] \times \frac{8}{15}
Show answer & explanation

Answer: 59.2

Answer

The evaluated numerical value of the expression is 59.2.
Following strict BODMAS hierarchy—evaluating the vinculum (1.1), parentheses (2.5), 'of' operation (1.25), curly brackets (2.5), square bracket division (1.5), multiplication (0.8), percentage term (60), and final subtraction—gives 60 - 0.8 = 59.2.

Step-by-Step Solution

1
Evaluate the expression under the vinculum bar.
1.8 - 0.7 = 1.1
The vinculum has the highest priority and acts as an implicit innermost bracket.
2
Evaluate the terms inside the round brackets (parentheses).
3.6 - 1.1 = 2.5
Round brackets must be resolved after the vinculum.
3
Evaluate the 'of' operation inside the curly brackets.
(1/2) * 2.5 = 1.25
'Of' precedes addition and multiplication in the standard BODMAS order.
4
Complete the addition within the curly brackets.
1.25 + 1.25 = 2.5 = 5/2
Brackets must be fully simplified from inside out.
5
Perform division inside the square brackets.
(15/4) / (5/2) = (15/4) * (2/5) = 3/2 = 1.5
Square brackets are evaluated after inner curly brackets.
6
Multiply the square bracket result by 8/15.
1.5 * (8/15) = (3/2) * (8/15) = 4/5 = 0.8
Multiplication takes precedence over final subtraction.
7
Calculate the initial percentage 'of' term.
12.5% of 480 = 0.125 * 480 = 60
'Of' operation on percentage takes precedence before subtraction.
8
Subtract the bracketed product from the initial term.
60 - 0.8 = 59.2
Subtraction is performed last according to BODMAS.

Key Concept

BODMAS Order of Operations with Vinculum and Nested Brackets
Estimated Time:2m 0s
Question 2Question →
Evaluate the following numerical expression using the correct order of operations (BODMAS):
40−4×(6−2)÷2+540 - 4 \times (6 - 2) \div 2 + 5
What is the final result?
Show answer & explanation

Answer: 37

Answer

The final result of the expression is 37.
Following the BODMAS rule: first simplify the bracket (6−2)=4(6 - 2) = 4. Next, execute multiplication and division from left to right: 4×4=164 \times 4 = 16 and 16÷2=816 \div 2 = 8. The expression reduces to 40−8+540 - 8 + 5. Finally, carry out subtraction and addition from left to right: 40−8=3240 - 8 = 32, and 32+5=3732 + 5 = 37.

Step-by-Step Solution

1
Evaluate the expression inside the brackets
6−2=46 - 2 = 4
According to BODMAS, operations inside brackets (B) take highest priority.
2
Perform multiplication and division from left to right
4×4=164 \times 4 = 16, then 16÷2=816 \div 2 = 8
Multiplication and Division (DM) carry equal priority and are evaluated in order from left to right.
3
Perform addition and subtraction from left to right
40−8+5=32+5=3740 - 8 + 5 = 32 + 5 = 37
Addition and Subtraction (AS) carry equal priority and are evaluated sequentially from left to right.

Key Concept

BODMAS Order of Operations
Question 3Question →
What is the simplified value of the following mathematical expression obtained by applying the BODMAS rule?
96÷[4+{25−(12−8−3‾)×3}]96 \div \left[ 4 + \left\{ 25 - \left( 12 - \overline{8 - 3} \right) \times 3 \right\} \right]
Show answer & explanation

Answer: 12

Answer

12
Following the standard BODMAS precedence rule: first evaluate the vinculum 8−3‾=5\overline{8-3} = 5, then the round brackets (12−5)=7(12-5) = 7, then multiplication 7×3=217 \times 3 = 21, then curly brackets 25−21=425 - 21 = 4, then square brackets 4+4=84 + 4 = 8, and finally division 96÷8=1296 \div 8 = 12.

Step-by-Step Solution

1
Evaluate the expression under the vinculum (bar)
\overline{8 - 3} = 5
The vinculum takes precedence over other bracket operations.
2
Evaluate the operation inside the innermost round brackets
12 - 5 = 7
Resolve the expression within the round brackets next.
3
Perform multiplication inside the curly brackets
7×3=217 \times 3 = 21
Multiplication precedes subtraction within the curly brackets according to BODMAS.
4
Complete the subtraction inside the curly brackets
25 - 21 = 4
Evaluate the remaining subtraction inside the curly brackets.
5
Evaluate the addition inside the outer square brackets
4 + 4 = 8
Combine the terms within the square brackets to obtain the final divisor.
6
Perform the final division
96÷8=1296 \div 8 = 12
Divide the initial integer by the evaluated square bracket result.

Key Concept

Simplification and BODMAS Rule with Vinculum
Question 4Question →
What is the simplified numerical value of the following mathematical expression when evaluated using the standard BODMAS rule?
240÷[212×{14−(312+25% of (14−1.8+2.2‾))}]240 \div \left[ 2 \frac{1}{2} \times \left\{ 14 - \left( 3 \frac{1}{2} + 25\% \text{ of } \left( 14 - \overline{1.8 + 2.2} \right) \right) \right\} \right]
Show answer & explanation

Answer: 12

Answer

12
Following the strict hierarchical order of operations (BODMAS: Vinculum →\rightarrow Brackets →\rightarrow Orders →\rightarrow Division/Multiplication →\rightarrow Addition/Subtraction), the innermost vinculum 1.8+2.2‾\overline{1.8 + 2.2} evaluates to 44. Then 14−4=1014 - 4 = 10, and 25%25\% of 1010 equals 2.52.5. Adding this to 312(3.5)3 \frac{1}{2} (3.5) yields 66. Inside the curly brackets, 14−6=814 - 6 = 8. Inside the square brackets, 212(2.5)×8=202 \frac{1}{2} (2.5) \times 8 = 20. Finally, 240÷20=12240 \div 20 = 12.

Step-by-Step Solution

1
Evaluate the expression under the vinculum (bar)
\overline{1.8 + 2.2} = 4
The vinculum acts as the innermost grouping symbol and must be simplified first.
2
Simplify the innermost parenthetical difference
14 - 4 = 10
Subtract the vinculum result from 14 within the round brackets.
3
Calculate the percentage of the result from Step 2
25\% \text{ of } 10 = \frac{25}{100} \times 10 = 2.5
'Of' represents multiplication in percentage evaluation.
4
Complete the evaluation inside the round brackets
3 \frac{1}{2} + 2.5 = 3.5 + 2.5 = 6
Convert the mixed fraction 3123 \frac{1}{2} to decimal 3.53.5 and sum with 2.52.5.
5
Evaluate the expression inside the curly brackets
14 - 6 = 8
Subtract the round bracket total from 14.
6
Simplify the expression inside the square brackets
2 \frac{1}{2} \times 8 = 2.5 \times 8 = 20
Multiply the mixed fraction 2122 \frac{1}{2} by the curly bracket result.
7
Perform the final division outside the brackets
240÷20=12240 \div 20 = 12
Divide 240 by the completely simplified value of the square brackets.

Key Concept

BODMAS Rule with Vinculum and Multi-level Brackets
Question 5Question →

What is the final value of the expression 36÷4×3+(15−7)−1036 \div 4 \times 3 + (15 - 7) - 10?

Show answer & explanation

Answer: 25

Answer

The correct answer is 25.
Applying the BODMAS order of operations strictly: first simplify the bracket (15−7)=8(15 - 7) = 8. Next, evaluate multiplication and division from left to right: 36÷4=936 \div 4 = 9 and 9×3=279 \times 3 = 27. Finally, evaluate addition and subtraction left to right: 27+8−10=2527 + 8 - 10 = 25.

Step-by-Step Solution

1
Evaluate bracket expression
15 - 7 = 8
Brackets have the highest precedence in the BODMAS rule.
2
Perform division and multiplication from left to right
36 ÷ 4 = 9, then 9 × 3 = 27
Division and multiplication carry equal priority and are evaluated in order from left to right.
3
Perform addition and subtraction from left to right
27 + 8 - 10 = 25
Addition and subtraction are performed sequentially from left to right.

Key Concept

BODMAS Order of Operations
Estimated Time:45s
Question 6Question →
Evaluate the following mathematical expression using the standard BODMAS rule:
40% of 150+[72÷{18−(212×4+11−5‾)}]40\% \text{ of } 150 + \left[ 72 \div \left\{ 18 - \left( 2\frac{1}{2} \times 4 + \overline{11 - 5} \right) \right\} \right]
What is the final simplified numerical value?
Show answer & explanation

Answer: 96

Answer

The simplified numerical value of the given expression is 96.
Applying the standard BODMAS rule: first evaluate the vinculum 11−5‾=6\overline{11 - 5} = 6. Next, evaluate inside the round brackets: 2.5×4+6=162.5 \times 4 + 6 = 16. Then simplify inside the curly braces: 18−16=218 - 16 = 2. Following that, perform division inside the square brackets: 72÷2=3672 \div 2 = 36. Separately, evaluate the percentage term: 40% of 150=6040\% \text{ of } 150 = 60. Summing these two terms gives 60+36=9660 + 36 = 96.

Step-by-Step Solution

1
Evaluate the bar (vinculum) expression.
\overline{11 - 5} = 6
The vinculum (bar) has highest priority within bracket operations.
2
Simplify the terms within the round parentheses.
2\frac{1}{2} \times 4 + 6 = 10 + 6 = 16
Perform multiplication before addition inside parentheses.
3
Evaluate the expression inside the curly braces.
18 - 16 = 2
Subtract the result of the round brackets from 18.
4
Perform the division inside the square brackets.
72÷2=3672 \div 2 = 36
Divide 72 by the value obtained from curly braces.
5
Calculate the percentage component of the expression.
40\% \text{ of } 150 = \frac{40}{100} \times 150 = 60
The word 'of' indicates multiplication applied to the percentage value.
6
Perform the final addition.
60 + 36 = 96
Add the result of the percentage calculation to the result of the bracket evaluation.

Key Concept

Order of Operations (BODMAS Rule) with Vinculum, Nested Brackets, and Percentages
Estimated Time:1m 30s
Question 7Question →
Evaluate the following mathematical expression by strictly applying the BODMAS rule:
150% of 48−[14.5−{412×(12.8÷2.5+1.5‾−135)+2.8}]÷0.15150\% \text{ of } 48 - \left[ 14.5 - \left\{ 4 \frac{1}{2} \times \left( 12.8 \div \overline{2.5 + 1.5} - 1 \frac{3}{5} \right) + 2.8 \right\} \right] \div 0.15
What is the simplified numerical value?
Show answer & explanation

Answer: 42

Answer

The simplified numerical value of the given mathematical expression is 42.
Following the strict BODMAS order of operations: Vinculum -> Round brackets -> Curly brackets -> Square brackets -> Division -> 'Of' -> Subtraction gives the exact result 42.

Step-by-Step Solution

1
Evaluate the term under the vinculum (bar)
2.5 + 1.5 = 4
The vinculum has highest priority among grouping symbols.
2
Evaluate operations inside the round brackets (parentheses)
12.8 / 4 - 1.6 = 3.2 - 1.6 = 1.6
Division inside parentheses precedes subtraction, and 1 3/5 converts to decimal 1.6.
3
Evaluate operations inside the curly brackets
4.5 * 1.6 + 2.8 = 7.2 + 2.8 = 10
Multiplication precedes addition inside curly brackets, with 4 1/2 converting to 4.5.
4
Evaluate operations inside the square brackets
14.5 - 10 = 4.5
Subtract the evaluated inner expression from 14.5.
5
Perform the division following the bracket result
4.5 / 0.15 = 30
Division operation takes precedence over final subtraction.
6
Calculate the percentage 'of' expression
150% of 48 = (150 / 100) * 48 = 72
'Of' operation is evaluated before basic addition and subtraction.
7
Compute the final subtraction
72 - 30 = 42
Subtract the result of the bracketed division term from the percentage evaluation.

Key Concept

Order of Operations (BODMAS / PEMDAS) with Vinculum and Nested Brackets
Question 8Question →
Find the value of the given mathematical expression by applying the standard order of operations (BODMAS):
25−[12+{8÷2×(5−3+1‾)}]25 - [12 + \{8 \div 2 \times (5 - \overline{3 + 1})\}]
Show answer & explanation

Answer: 9

Answer

9
Following the BODMAS rule: evaluate the vinculum 3+1‾=4\overline{3 + 1} = 4, then round brackets (5−4)=1(5 - 4) = 1, then curly brackets {8÷2×1}=4\{8 \div 2 \times 1\} = 4, then square brackets [12+4]=16[12 + 4] = 16, and finally 25−16=925 - 16 = 9.

Step-by-Step Solution

1
Evaluate the expression under the vinculum (bar)
3 + 1 = 4
The vinculum has the highest precedence among brackets (VBODMAS).
2
Evaluate the innermost round bracket
5 - 4 = 1
Round brackets are evaluated after resolving the vinculum.
3
Evaluate division and multiplication inside curly brackets from left to right
8 ÷ 2 × 1 = 4 × 1 = 4
Division and multiplication have equal precedence and are resolved from left to right.
4
Evaluate addition inside square brackets
12 + 4 = 16
Square brackets are resolved next.
5
Perform final subtraction outside the brackets
25 - 16 = 9
Outer subtraction is performed as the final step.

Key Concept

Order of Operations (BODMAS / VBODMAS)
Estimated Time:45s
Question 9Question →
What is the simplified value of the following mathematical expression when evaluated strictly using the BODMAS rule?
25% of 160+[45÷{15−(3.5×2+8−5‾)}]×2.525\% \text{ of } 160 + \left[ 45 \div \left\{ 15 - \left( 3.5 \times 2 + \overline{8 - 5} \right) \right\} \right] \times 2.5
Show answer & explanation

Answer: 62.5

Answer

62.5
Evaluating step-by-step according to BODMAS: first the vinculum gives 3; the round bracket gives 3.5 × 2 + 3 = 10; the curly bracket gives 15 - 10 = 5; the square bracket gives 45 ÷ 5 = 9. Next, 25% of 160 yields 40. Then multiplication gives 9 × 2.5 = 22.5. Finally, adding 40 + 22.5 gives 62.5.

Step-by-Step Solution

1
Evaluate the expression under the bar (vinculum)
\overline{8 - 5} = 3
The bar (vinculum) acts as the innermost bracket and takes highest priority.
2
Evaluate the innermost round brackets, applying multiplication before addition
(3.5 \times 2 + 3) = (7 + 3) = 10
Within round brackets, multiplication precedes addition.
3
Evaluate the curly brackets
\{15 - 10\} = 5
Perform subtraction inside the curly brackets.
4
Evaluate the square brackets
[45÷5]=9[45 \div 5] = 9
Perform division inside the square brackets.
5
Calculate the percentage term ('of' operation)
25\% \text{ of } 160 = \frac{25}{100} \times 160 = 40
'Of' represents multiplication linked to percentage.
6
Perform multiplication before addition in the outer expression
9×2.5=22.59 \times 2.5 = 22.5
Multiplication takes precedence over addition.
7
Perform final addition
40 + 22.5 = 62.5
Add the result of the percentage term to the bracket evaluation term.

Key Concept

BODMAS Rule (Brackets, Orders, Division/Multiplication, Addition/Subtraction) with Vinculum and Percentages
Question 10Question →
What is the simplified value of the following mathematical expression when evaluated using the standard BODMAS rule?
25% of 180−[4.8+{12÷(313×0.8+0.4‾)}]25\% \text{ of } 180 - \left[ 4.8 + \left\{ 12 \div \left( 3\frac{1}{3} \times \overline{0.8 + 0.4} \right) \right\} \right]
Show answer & explanation

Answer: 37.237.2

Answer

The simplified value of the expression is 37.237.2.
Evaluating strictly according to the BODMAS hierarchical priority: first resolve the vinculum 0.8+0.4‾=1.2\overline{0.8 + 0.4} = 1.2, then the round brackets 103×1.2=4\frac{10}{3} \times 1.2 = 4, then the division in curly brackets 12÷4=312 \div 4 = 3, followed by square bracket addition 4.8+3=7.84.8 + 3 = 7.8, and finally subtracting this from 25% of 180=4525\% \text{ of } 180 = 45 gives 45−7.8=37.245 - 7.8 = 37.2.

Step-by-Step Solution

1
Evaluate the expression under the vinculum bar first
0.8+0.4‾=1.2\overline{0.8 + 0.4} = 1.2
According to the BODMAS rule, operations under a vinculum bar have the highest priority over all other brackets.
2
Convert the mixed fraction and evaluate the round brackets
313×1.2=103×1210=43\frac{1}{3} \times 1.2 = \frac{10}{3} \times \frac{12}{10} = 4
Convert 3133\frac{1}{3} to the improper fraction 103\frac{10}{3} and multiply by 1.21.2 (or 65\frac{6}{5}).
3
Evaluate the expression inside the curly brackets
12÷4=312 \div 4 = 3
Perform division of 1212 by the result of the round brackets (44).
4
Evaluate the expression inside the square brackets
4.8+3=7.84.8 + 3 = 7.8
Add 4.84.8 to the result obtained from the curly brackets (33).
5
Calculate the percentage term and perform the final subtraction
25% of 180=25100×180=4525\% \text{ of } 180 = \frac{25}{100} \times 180 = 45; then 45−7.8=37.245 - 7.8 = 37.2
'Of' represents multiplication for the percentage term, which is evaluated and then reduced by the square bracket result.

Key Concept

BODMAS Rule with Vinculum and Mixed Operations
Question 11Question →
Evaluate the following complex mathematical expression strictly adhering to the hierarchical order of operations (BODMAS rule):
{64% of 125+[133÷{216−(1.4×2.5−35+710‾)}]}×0.375\left\{ 64\% \text{ of } 125 + \left[ \frac{13}{3} \div \left\{ 2\frac{1}{6} - \left( 1.4 \times 2.5 - \overline{\frac{3}{5} + \frac{7}{10}} \right) \right\} \right] \right\} \times 0.375
What is the exact numerical value of the final simplified expression?
Show answer & explanation

Answer: -18.75

Answer

The simplified final value of the expression is -18.75.
Following the BODMAS rule strictly: first simplify under the vinculum (3/5 + 7/10 = 1.3), then inside the round brackets (1.4 * 2.5 - 1.3 = 2.2). Next, inside the curly brackets (13/6 - 2.2 = -1/30), then the division in the square brackets ((13/3) / (-1/30) = -130). Evaluating 64% of 125 gives 80. Combining inside the main bracket gives 80 + (-130) = -50. Finally, multiplying by 0.375 yields -18.75.

Step-by-Step Solution

1
Evaluate the expression under the vinculum bar
35+710=1.3\frac{3}{5} + \frac{7}{10} = 1.3
The vinculum (bar bracket) has the highest priority under BODMAS and must be evaluated first.
2
Simplify the innermost round brackets
1.4 \times 2.5 - 1.3 = 3.5 - 1.3 = 2.2
Perform multiplication inside the round brackets before subtraction, then subtract the vinculum result.
3
Evaluate the expression inside the inner curly brackets
2\frac{1}{6} - 2.2 = \frac{13}{6} - \frac{11}{5} = -\frac{1}{30}
Convert the mixed fraction and decimal to improper fractions and subtract.
4
Evaluate the square bracket division
\frac{13}{3} \div \left( -\frac{1}{30} \right) = \frac{13}{3} \times (-30) = -130
Dividing by a fraction is equivalent to multiplying by its reciprocal.
5
Calculate the percentage term '64% of 125'
64100×125=80\frac{64}{100} \times 125 = 80
'Of' operation takes precedence over addition.
6
Combine the terms within the main outer brackets
80 + (-130) = -50
Add the result of the percentage term to the square bracket result.
7
Multiply by the outer factor 0.375
−50×0.375=−18.75-50 \times 0.375 = -18.75
Perform final multiplication to complete the simplification.

Key Concept

BODMAS order of operations with nested brackets, vinculum, fractions, decimals, and percentage operations.
Estimated Time:3m 0s
Question 12Question →
What is the simplified value of the following mathematical expression when evaluated using the standard BODMAS rule?
60−[15+{20÷5+3×(8−4+2‾)}]60 - [15 + \{20 \div 5 + 3 \times (8 - \overline{4 + 2})\}]
Show answer & explanation

Answer: 3535

Answer

The simplified value of the expression is 3535.
Following the BODMAS rule strictly: first resolve the vinculum 4+2‾=6\overline{4 + 2} = 6, then the round brackets (8−6)=2(8 - 6) = 2. Inside the curly brackets, division and multiplication are evaluated before addition (20÷5+3×2=4+6=1020 \div 5 + 3 \times 2 = 4 + 6 = 10). Adding this to 1515 inside the square brackets gives 2525. Subtracting 2525 from 6060 gives the correct simplified result of 3535.

Step-by-Step Solution

1
Evaluate the expression under the vinculum bar.
4+2‾=6\overline{4 + 2} = 6
Operations under a vinculum (line bracket) take highest priority.
2
Simplify the innermost round brackets (8−6)(8 - 6).
8−6=28 - 6 = 2
Parentheses must be evaluated next.
3
Evaluate the terms inside the curly brackets {20÷5+3×2}\{20 \div 5 + 3 \times 2\}. Perform division and multiplication before addition.
20÷5=420 \div 5 = 4 and 3×2=63 \times 2 = 6, so 4+6=104 + 6 = 10
According to BODMAS, division and multiplication precede addition.
4
Simplify the square brackets [15+10][15 + 10].
15+10=2515 + 10 = 25
Resolve the remaining bracket structure.
5
Perform the final subtraction 60−2560 - 25.
3535
Complete the outermost operation.

Key Concept

Simplification using hierarchical order of operations (BODMAS / Vinculum rule)
Question 13Question →

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

20+4×[36÷{12−(3+7−4‾)}]20 + 4 \times \left[ 36 \div \left\{ 12 - \left( 3 + \overline{7 - 4} \right) \right\} \right]
Show answer & explanation

Answer: 44

Answer

44
Following the BODMAS order of operations, we first evaluate the vinculum line to get 3, then solve the round bracket (3 + 3 = 6), followed by the curly bracket (12 - 6 = 6), and then the square bracket (36 ÷ 6 = 6). Finally, performing multiplication before addition gives 20 + (4 × 6) = 20 + 24 = 44.

Step-by-Step Solution

1
Simplify the expression under the vinculum (bar)
7 - 4 = 3
The vinculum has the highest priority and must be evaluated first.
2
Simplify the innermost round brackets
3 + 3 = 6
Perform addition inside the parentheses.
3
Simplify the curly brackets
12 - 6 = 6
Subtract the result of the round brackets from 12.
4
Simplify the square brackets
36 ÷ 6 = 6
Perform division inside the square brackets.
5
Apply multiplication before addition in the outer expression
4 × 6 = 24
Multiplication has higher priority than addition according to BODMAS.
6
Perform final addition
20 + 24 = 44
Add 20 to 24 to get the final simplified answer.

Key Concept

Simplification and BODMAS Rule
Question 14Question →
What is the simplified numerical value of the following mathematical expression when evaluated using the correct BODMAS order of operations?
20% of 150−[3.5+2×{7.2−(1.4+3.8−1.6‾)÷0.6}]20\% \text{ of } 150 - \left[ 3.5 + 2 \times \left\{ 7.2 - \left( 1.4 + \overline{3.8 - 1.6} \right) \div 0.6 \right\} \right]
Show answer & explanation

Answer: 24.1

Answer

24.1
Evaluating the expression by strictly following the VBODMAS hierarchy (Vinculum -> Brackets -> Of/Orders -> Division -> Multiplication -> Addition -> Subtraction) yields the step-by-step values: vinculum gives 2.2, round brackets give 3.6, division inside curly braces gives 6, curly braces give 1.2, multiplication inside square brackets gives 2.4, square brackets give 5.9, percentage gives 30, and final subtraction gives 24.1.

Step-by-Step Solution

1
Evaluate the expression under the vinculum (bar)
\overline{3.8 - 1.6} = 2.2
The vinculum has the highest priority in the hierarchy of brackets.
2
Simplify the terms within the parentheses (round brackets)
1.4 + 2.2 = 3.6
Complete the inner addition inside the round brackets.
3
Perform division inside the braces (curly brackets)
3.6÷0.6=63.6 \div 0.6 = 6
Division takes precedence over subtraction inside the curly brackets.
4
Perform subtraction inside the braces (curly brackets)
7.2 - 6 = 1.2
Complete the remaining operation inside the curly brackets.
5
Perform multiplication inside the square brackets
2×1.2=2.42 \times 1.2 = 2.4
Multiplication takes precedence over addition inside the square brackets.
6
Perform addition inside the square brackets
3.5 + 2.4 = 5.9
Complete the final operation inside the square brackets.
7
Calculate the percentage value
20\% \text{ of } 150 = \frac{20}{100} \times 150 = 30
Evaluate the 'Of' operation / percentage computation.
8
Subtract the bracket result from the percentage value
30 - 5.9 = 24.1
Execute the final subtraction outside all brackets.

Key Concept

Hierarchy of Order of Operations (BODMAS / VBODMAS)
Question 15Question →
What is the final numerical value obtained by evaluating the following mathematical expression strictly according to the BODMAS rule?
50−[52÷{4.5+45×(3.7−1.8−0.6‾)}]50 - \left[ 52 \div \left\{ 4.5 + \frac{4}{5} \times \left( 3.7 - \overline{1.8 - 0.6} \right) \right\} \right]
Show answer & explanation

Answer: 42

Answer

42
Following VBODMAS rule strictly:
1. Vinculum: 1.8 - 0.6 = 1.2
2. Round brackets: 3.7 - 1.2 = 2.5
3. Multiplication in curly brackets: (4/5) * 2.5 = 2
4. Addition in curly brackets: 4.5 + 2 = 6.5
5. Square bracket division: 52 / 6.5 = 8
6. Outer subtraction: 50 - 8 = 42.

Step-by-Step Solution

1
Evaluate the vinculum (bar line above numbers)
\overline{1.8 - 0.6} = 1.2
According to BODMAS (or VBODMAS), the vinculum takes precedence over round brackets.
2
Simplify the terms inside the parentheses (round brackets)
3.7 - 1.2 = 2.5
Parentheses are evaluated next after the vinculum.
3
Evaluate the multiplication inside the curly brackets
\frac{4}{5} \times 2.5 = 0.8 \times 2.5 = 2.0
Within curly brackets, multiplication precedes addition.
4
Complete the addition inside the curly brackets
4.5 + 2.0 = 6.5
Completing all operations within the curly brackets.
5
Evaluate the division inside the square brackets
52÷6.5=852 \div 6.5 = 8
Simplifying the entire square bracket term.
6
Perform the final subtraction outside all brackets
50 - 8 = 42
Final arithmetic step to find the value of the expression.

Key Concept

Order of Operations (BODMAS / VBODMAS)
Question 16Question →
Calculate the exact numerical value of the following expression by applying the standard BODMAS/VBODMAS order of operations:
45% of 160−[12.5+{34×(36÷3−4.2+1.8‾)+5.5}÷0.5]45\% \text{ of } 160 - \left[ 12.5 + \left\{ \frac{3}{4} \times \left( 36 \div 3 - \overline{4.2 + 1.8} \right) + 5.5 \right\} \div 0.5 \right]
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Answer: 39.5

Answer

The simplified numerical value of the given expression is 39.5.
Evaluating step by step according to VBODMAS rules yields 39.5. First, the vinculum gives 6. The round bracket gives 36 ÷ 3 - 6 = 6. The curly bracket gives (3/4) × 6 + 5.5 = 10. The square bracket gives 12.5 + 10 ÷ 0.5 = 32.5. Finally, 45% of 160 = 72, and 72 - 32.5 = 39.5.

Step-by-Step Solution

1
Evaluate the expression under the vinculum (bar)
\overline{4.2 + 1.8} = 6
The vinculum acts as a top-priority bracket, so the addition under the bar must be executed before other operations.
2
Simplify the innermost round brackets ( )
36 \div 3 - 6 = 12 - 6 = 6
Inside the round bracket, division precedes subtraction according to BODMAS.
3
Simplify the curly brackets { }
\frac{3}{4} \times 6 + 5.5 = 4.5 + 5.5 = 10
Inside the curly bracket, multiplication of fractions precedes addition.
4
Simplify the square brackets [ ]
12.5 + 10 \div 0.5 = 12.5 + 20 = 32.5
Inside the square bracket, division by decimal (10 / 0.5 = 20) takes precedence over addition.
5
Calculate the percentage term ('of' operation)
45\% \text{ of } 160 = 0.45 \times 160 = 72
The 'of' operation represents multiplication for percentage evaluation.
6
Perform the final subtraction
72 - 32.5 = 39.5
Subtract the fully simplified bracket result from the percentage term.

Key Concept

BODMAS / VBODMAS Rule with Nested Brackets, Percentages, and Vinculum
Estimated Time:2m 0s
Question 17Question →
What is the simplified numerical value of the mathematical expression 36−[18÷{6−(4−3−1‾)}×2]36 - \left[ 18 \div \left\{ 6 - \left( 4 - \overline{3 - 1} \right) \right\} \times 2 \right] when evaluated strictly adhering to the VBODMAS rule?
Show answer & explanation

Answer: 2727

Answer

The simplified numerical value of the given expression is 27.
First resolve the vinculum 3−1‾=2\overline{3-1} = 2. Next, simplify the round bracket (4−2)=2(4-2) = 2, then the curly bracket {6−2}=4\{6-2\} = 4. Inside the square bracket, evaluate division before multiplication from left to right: 18÷4=4.518 \div 4 = 4.5, and 4.5×2=94.5 \times 2 = 9. Finally, subtract from 36 to get 36−9=2736 - 9 = 27.

Step-by-Step Solution

1
Evaluate the expression under the bar/vinculum
\overline{3 - 1} = 2
According to VBODMAS rules, vinculum (bar) has highest priority over standard operations.
2
Simplify the innermost round bracket
(4 - 2) = 2
Resolve terms within parenthesis after vinculum.
3
Simplify the curly bracket
\{6 - 2\} = 4
Perform subtraction inside curly braces.
4
Evaluate operations inside the square bracket from left to right
[18 \div 4 \times 2] = 4.5 \times 2 = 9
Division and multiplication have equal priority and must be evaluated left to right.
5
Perform the final outer subtraction
36 - 9 = 27
Complete the remaining operation.

Key Concept

VBODMAS / BODMAS Order of Operations
Question 18Question →
What is the numerical value of the mathematical expression 80−[15+(12÷3×2)]80 - [15 + (12 \div 3 \times 2)] when simplified using the standard BODMAS rule?
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Answer: 57

Answer

The simplified numerical value of the given expression is 57.
Evaluating the expression following the strict BODMAS order of operations: first simplify the innermost round brackets by doing division (12÷3=412 \div 3 = 4) then multiplication (4×2=84 \times 2 = 8). Next, add the numbers inside the square brackets (15+8=2315 + 8 = 23). Finally, subtract 23 from 80 to obtain 57.

Step-by-Step Solution

1
Perform division inside the round brackets.
12÷3=412 \div 3 = 4
According to the BODMAS rule, division takes precedence over multiplication within brackets.
2
Perform multiplication to complete the round bracket evaluation.
4×2=84 \times 2 = 8
Complete the operations contained within the innermost parentheses.
3
Perform addition inside the square brackets.
15+8=2315 + 8 = 23
Simplify the terms remaining inside the square brackets.
4
Subtract the result of the brackets from the outer value.
80−23=5780 - 23 = 57
Perform final subtraction to determine the simplified answer.

Key Concept

BODMAS Rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction)
Question 19Question →
Evaluate the following mathematical expression using the standard BODMAS (VBODMAS) rule:
40% of 250−[15+{45÷(2+14 of (18−8−2‾))}]40\% \text{ of } 250 - \left[ 15 + \left\{ 45 \div \left( 2 + \frac{1}{4} \text{ of } \left( 18 - \overline{8 - 2} \right) \right) \right\} \right]
What is the final simplified value of the expression?
Show answer & explanation

Answer: 76

Answer

The simplified value of the expression is 76.
Following the strict hierarchical order of operations (VBODMAS), resolving the bar vinculum first gives 6, then the inner parenthesis yields 12. Taking 1/4 of 12 gives 3, and adding 2 yields 5. Dividing 45 by 5 yields 9, and adding 15 yields 24 inside the main bracket. Subtracting 24 from 40% of 250 (which equals 100) gives the correct answer of 76.

Step-by-Step Solution

1
Evaluate the expression under the vinculum bar: 8−2‾\overline{8 - 2}.
8−2‾=6\overline{8 - 2} = 6
According to VBODMAS, operations under a vinculum take highest priority.
2
Evaluate the innermost round bracket: (18−6)(18 - 6).
18−6=1218 - 6 = 12
Resolve terms within the round parentheses.
3
Evaluate the 'of' operation inside the round bracket context: 14 of 12\frac{1}{4} \text{ of } 12.
14×12=3\frac{1}{4} \times 12 = 3
'Of' precedes basic addition and division.
4
Complete the addition inside the innermost bracket: (2+3)(2 + 3).
2+3=52 + 3 = 5
Finalize inner parentheses.
5
Evaluate the division inside the curly brackets: {45÷5}\{45 \div 5\}.
45÷5=945 \div 5 = 9
Perform division inside curly brackets.
6
Evaluate the addition inside the square brackets: [15+9][15 + 9].
15+9=2415 + 9 = 24
Resolve the square brackets.
7
Evaluate the percentage term: 40% of 25040\% \text{ of } 250.
40100×250=100\frac{40}{100} \times 250 = 100
Calculate the percentage value independently.
8
Perform the final subtraction: 100−24100 - 24.
100−24=76100 - 24 = 76
Subtract the bracket result from the percentage value.

Key Concept

BODMAS / VBODMAS Order of Operations

Alternative Method

Calculate the percentage term 40% of 250 = 100 first, then systematically simplify the bracket from innermost (vinculum) to outermost to subtract from 100.
Estimated Time:1m 15s
Question 20Question →

What is the value of the mathematical expression 24+4×[15−{12÷4+(8−5−2‾)}]24 + 4 \times \left[ 15 - \left\{ 12 \div 4 + (8 - \overline{5 - 2}) \right\} \right]?

Show answer & explanation

Answer: 52

Answer

The simplified value of the expression is 52.
Following the VBODMAS hierarchy: first evaluate the bar line 5−2‾=3\overline{5-2} = 3, then the round brackets (8−3)=5(8-3) = 5, then division inside the curly braces 12÷4=312 \div 4 = 3, followed by addition inside curly braces 3+5=83+5 = 8. Next, subtract within square brackets 15−8=715-8 = 7. Finally, multiply before adding: 4×7=284 \times 7 = 28, and 24+28=5224 + 28 = 52.

Step-by-Step Solution

1
Evaluate the vinculum bar 5−2‾\overline{5 - 2}
5−2=35 - 2 = 3
According to VBODMAS rules, operations under a vinculum (bar) have the highest priority among bracket operations.
2
Evaluate the expression inside the round brackets (8−3)(8 - 3)
8−3=58 - 3 = 5
Round brackets (parentheses) are simplified next.
3
Evaluate the expression inside the curly braces {12÷4+5}\{12 \div 4 + 5\}
12÷4=312 \div 4 = 3, then 3+5=83 + 5 = 8
Inside the curly braces, division takes precedence over addition.
4
Evaluate the expression inside the square brackets [15−8][15 - 8]
15−8=715 - 8 = 7
Square brackets are solved after round and curly brackets.
5
Perform multiplication before final addition
4×7=284 \times 7 = 28
Multiplication takes precedence over addition outside the brackets.
6
Perform the final addition
24+28=5224 + 28 = 52
Complete the final addition step to obtain the result.

Key Concept

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