Simplification (BODMAS) Practice Quiz: WBPSC Clerkship 2024
A little practice. A step forward.
Twelve sums on the BODMAS order, each with a worked explanation. 📖 Read the detailed topic
What is the value of $48 \div 6 \times 2$?
Division and multiplication are of equal rank, so work left to right: $48 \div 6 = 8$, then $8 \times 2 = 16$. Multiplying first gives $48 \div 12 = 4$, which is wrong.
- Division and multiplication go left to right
- Multiplication does not come before division
- Multiplying first and writing 4
- D and M share a row: whichever comes first
- Right: $48 \div 6 = 8$, $8 \times 2 = 16$
- Wrong: $6 \times 2 = 12$, $48 \div 12 = 4$
What is the value of $15 - 3 \times 4 + 18 \div 6$?
Multiplication and division first: $3 \times 4 = 12$ and $18 \div 6 = 3$. Then $15 - 12 + 3 = 6$. Working strictly left to right gives 11, which is wrong. Sums like this come up often, so write each step on its own line.
- Multiply and divide first, add and subtract last
- One operation per step
- Doing every sign in plain left-to-right order gives 11
- Add and subtract come last
| Step | Working | Result |
|---|---|---|
| Multiply | 3 × 4 | 12 |
| Divide | 18 ÷ 6 | 3 |
| Subtract, add | 15 − 12 + 3 | 6 |
What is the value of $7 + 3 \times (12 - 8) \div 2$?
Brackets first: $12 - 8 = 4$. Then $3 \times 4 = 12$ and $12 \div 2 = 6$ (left to right). Finally $7 + 6 = 13$. Adding $7 + 3 = 10$ first would give 20, which is wrong.
- Brackets first
- Addition last
- Adding 7 + 3 first to get 20
- B first, A last
What is the value of $100 - [20 + \{15 - (8 - 3)\}]$?
Work from the inside out: $(8 - 3) = 5$, then $\{15 - 5\} = 10$, then $[20 + 10] = 30$. Finally $100 - 30 = 70$. Mistakes here usually come from mixing up the bracket order, so rewrite the sum after opening each bracket.
- Order: ( ) then { } then [ ]
- Rewrite the sum after each bracket
- Trying to open the outer bracket first
- Inside out, like peeling an onion
| Step | Working | Result |
|---|---|---|
| Small bracket ( ) | 8 − 3 | 5 |
| Curly bracket { } | 15 − 5 | 10 |
| Square bracket [ ] | 20 + 10 | 30 |
| Last | 100 − 30 | 70 |
What is the value of $\frac{3}{5}$ of $150 \div 9 + 4$?
'Of' first: $\frac{3}{5} \times 150 = 90$. Then $90 \div 9 = 10$. Finally $10 + 4 = 14$. Forgetting the last addition gives 10. Remember that 'of' means multiply, but it ranks above ordinary multiplication and division.
- 'Of' is worked before division
- 'Of' means multiply, but first
- Forgetting the final + 4
- The O in BODMAS stands for of
What is the value of $0.6 \times 0.5 + 1.2 \div 0.4 - 0.8$?
Multiplication and division first: $0.6 \times 0.5 = 0.3$ and $1.2 \div 0.4 = 3$. Then $0.3 + 3 - 0.8 = 2.5$. In decimal sums, recheck the position of the decimal point in the last step.
- Decimals follow the same order
- 1.2 ÷ 0.4 = 12 ÷ 4 = 3
- Writing 0.6 × 0.5 = 3 (losing the decimal point)
- Multiply both numbers in a division by 10 to clear the decimal
| Part | Working | Result |
|---|---|---|
| Multiplication | 0.6 × 0.5 | 0.3 |
| Division | 1.2 ÷ 0.4 | 3 |
| Add/subtract | 0.3 + 3 − 0.8 | 2.5 |
What is the value of $\frac{3}{4} + \frac{1}{2} \times \frac{2}{3}$?
Multiply first: $\frac{1}{2} \times \frac{2}{3} = \frac{1}{3}$. Then $\frac{3}{4} + \frac{1}{3} = \frac{9}{12} + \frac{4}{12} = \frac{13}{12} = 1\frac{1}{12}$. Adding first would give $\frac{5}{4} \times \frac{2}{3} = \frac{5}{6}$, which is wrong.
- Multiplication before addition, even with fractions
- Use the common denominator 12
- Adding first and getting $\frac{5}{6}$
- Multiply first, add later: fractions or not
| Step | Working |
|---|---|
| Multiply | $\frac{1}{2} \times \frac{2}{3} = \frac{1}{3}$ |
| Common denominator | $\frac{3}{4} = \frac{9}{12}$, $\frac{1}{3} = \frac{4}{12}$ |
| Add | $\frac{13}{12} = 1\frac{1}{12}$ |
What is the value of $5 + 5 \times 5 - 5 \div 5$?
Multiplication and division first: $5 \times 5 = 25$ and $5 \div 5 = 1$. Then $5 + 25 - 1 = 29$. Plain left-to-right working gives 9, which is wrong. Do not be put off by the five 5s; decide the order from the signs, not the numbers.
- Multiply and divide first
- Add and subtract afterwards
- Going straight left to right and getting 9
- Five fives: 5 + 25 − 1
What is the value of $30 - 2 \times (3 + 4) + 6 \div 2$?
Bracket first: $3 + 4 = 7$. Then $2 \times 7 = 14$ and $6 \div 2 = 3$. Finally $30 - 14 + 3 = 19$. This sum uses all three stages: brackets, then multiplication and division, then addition and subtraction.
- Brackets, then multiply/divide, then add/subtract
- All three stages are used
- Reading 30 − 14 + 3 as 30 − 17
- B, D/M, A/S: three stages
| Step | Working | Result |
|---|---|---|
| Bracket | 3 + 4 | 7 |
| Multiply | 2 × 7 | 14 |
| Divide | 6 ÷ 2 | 3 |
| Subtract, add | 30 − 14 + 3 | 19 |
What is the value of $40 - \overline{10 - 5} \times 3$?
The bar (vinculum) acts as a bracket: $\overline{10 - 5} = 5$. Then $5 \times 3 = 15$. Finally $40 - 15 = 25$. Without the bar it would be $40 - 10 - 15 = 15$.
- The part under the bar goes first
- Without the bar the answer changes
- Ignoring the bar and getting 15
- Bar = bracket, and it goes first
What is the value of $3 + 4^{2} \div 8 - 1$?
Power first: $4^{2} = 16$. Then $16 \div 8 = 2$. Finally $3 + 2 - 1 = 4$. Reading it as $(3 + 4)^{2}$ is wrong because there is no bracket. A power ranks above division in the order of work.
- Powers (Orders) before division
- Without brackets the power applies only to its own number
- Treating $4^{2}$ as $(3+4)^{2}$
- O stands for Of and Orders (powers)
What is the value of $\frac{12 + 18 \div 3}{4 \times 2 - 3}$?
The fraction bar acts as a bracket, so simplify the numerator and the denominator separately. Numerator: $12 + 6 = 18$. Denominator: $8 - 3 = 5$. The value is $\frac{18}{5} = 3.6$. Whenever you see a fraction bar, think of the top and bottom as two separate sums.
- Fraction bar = bracket
- Simplify top and bottom separately
- Adding 12 + 18 first in the numerator
- Treat the top and bottom as two separate sums
| Part | Working | Result |
|---|---|---|
| Numerator | 12 + 18 ÷ 3 = 12 + 6 | 18 |
| Denominator | 4 × 2 − 3 = 8 − 3 | 5 |
| Value | 18 ÷ 5 | 3.6 |
📊 Topic Analysis
Twelve sums on the BODMAS order, each with a worked explanation.
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