Kit Library / Mathematics / Arithmetic
⚡ Topic Learning KitShared by a Veda learner · Generated with Veda AI
Veda Bites are swipeable micro-lessons — each one teaches exactly one idea. The bites below come from this kit — swipe through them in the app.
💡 Key Idea
Wrong order = wrong answer. Always.
BODMAS tells you the exact sequence to evaluate any arithmetic expression so everyone gets the same answer.
↳ Always follow BODMAS from left to right within the same priority level.
📖 Definition
B-O-D-M-A-S decoded in seconds.
↳ Division and multiplication have equal priority; do them left to right.
⚠️ Common Mistake
Skipping brackets? You just lost marks.
↳ Brackets are solved from inside out, not left to right.
⚙️ Process
Break it down, layer by layer.
Simplify: $10 \times 10 + [400 \div (100 - (50 - 3 \times 10))]$
↳ Work from the innermost bracket outward, then apply BODMAS.
✏️ Example
One crossed number changes everything.
↳ Never change the numbers; only simplify step by step.
➗ Formula
The only formula you need for simplification.
↳ Memorize the hierarchy: B > O > D/M > A/S.
⭐ Important Fact
From 10 to 99 — how many?
Two-digit natural numbers range from 10 to 99 inclusive. Count = $99 - 10 + 1 = 90$.
↳ There are exactly 90 two-digit natural numbers.
Count without listing.
Number of two-digit numbers = $99 - 10 + 1 = 90$. Similarly, three-digit numbers = $999 - 100 + 1 = 900$.
↳ Use $\text{last} - \text{first} + 1$ for any consecutive range.
⚠️ Common Mistake
Inner brackets first — always.
↳ Always start with the deepest bracket.
🎯 Exam Tip
Show your steps, save your marks.
In simplification problems, write each step on a new line. This helps you avoid errors and earns partial credit even if the final answer is wrong.
↳ Step-by-step presentation reduces mistakes and secures method marks.
🧠 Memory Trick
Big Elephants Destroy Mice And Snakes.
Use Big Elephants Destroy Mice And Snakes to recall Brackets, Orders, Division, Multiplication, Addition, Subtraction.
↳ A silly sentence can lock in the order for life.
🌍 Real World
From billing to coding, order is key.
Spreadsheets, programming languages, and calculators all follow a fixed order of operations. Knowing BODMAS helps you predict and debug results.
↳ BODMAS is the universal language of calculation.
🛠️ Application
Fractions and brackets together? No problem.
↳ Always simplify the bracket fully before dividing.
🚫 Warning
Left to right, not D before M.
↳ D and M are equal — go left to right.
❓ Did You Know
Different words, same math.
In some countries, the order is remembered as PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction). The logic is identical to BODMAS.
↳ BODMAS and PEMDAS are two names for the same priority rules.
This topic covers the correct order of operations (BODMAS) for simplifying arithmetic expressions, including brackets, multiplication, division, addition, and subtraction. It also addresses common errors like misapplying…
Full explanation, worked examples & memory tricks in the app
All 17 questions, laddered from warm-up to topper-level, each with its answer and the reasoning behind it.
Q1. What is the correct order of operations in BODMAS?
BeginnerB · Brackets, Orders, Division/Multiplication, Addition/Subtraction
BODMAS stands for Brackets, Orders, Division/Multiplication, Addition/Subtraction, in that order.
Q2. How many two-digit natural numbers are there?
BeginnerC · 90
The smallest two-digit number is 10 and the largest is 99. Count = $99 - 10 + 1 = 90$.
Q3. In the expression $10 \times 10 + [400 \div (100 - (\overline{50 - 3 \times 10}))]$, what is the value inside the overline first?
BeginnerB · 20
Inside the overline: $50 - 3 \times 10 = 50 - 30 = 20$.
Q4. What does the overline (vinculum) in an expression indicate?
BeginnerD · It is a grouping symbol like parentheses.
The overline groups terms together, so you simplify the expression under it first.
Q5. Which of the following expressions correctly uses the formula for counting consecutive integers from 10 to 99?
BeginnerB · $99 - 10 + 1$
The formula is last − first + 1, so $99 - 10 + 1 = 90$.
Q6. The number of two-digit natural numbers is 90, calculated as $99 - 10 + 1$.
BeginnerA · True
The number of two-digit natural numbers is 90, calculated as $99 - 10 + 1$.
Q7. Simplify: $10 \times 10 + [400 \div (100 - (\overline{50 - 3 \times 10}))]$
IntermediateA · 105
First simplify the overline: $50 - 30 = 20$. Then $100 - 20 = 80$. Then $400 \div 80 = 5$. Then $10 \times 10 = 100$. Finally $100 + 5 = 105$.
Q8. What is the first step in simplifying $\frac{1}{13}[7 + 2 \times 5 \times 11 + 2]$?
IntermediateD · Multiply $2 \times 5 \times 11$
According to BODMAS, simplify inside the brackets first. Inside, do multiplication before addition: $2 \times 5 \times 11 = 110$.
Q9. A student calculates the number of two-digit numbers as $99 - 10 = 89$. What mistake did they make?
IntermediateB · They forgot to add 1 to include both endpoints.
The correct formula is last − first + 1. So $99 - 10 + 1 = 90$. Subtracting only gives 89, which is off by one.
Q10. In the expression $100 - (\overline{50 - 3 \times 10})$, what is the value after simplifying the overline?
IntermediateB · 80
First simplify the overline: $50 - 3 \times 10 = 50 - 30 = 20$. Then $100 - 20 = 80$.
Q11. Which operation should be performed first in the expression $25 + 2 + 24 \times 2 + 15 \times 5$?
IntermediateD · Multiplication
According to BODMAS, multiplication is done before addition. So compute $24 \times 2$ and $15 \times 5$ first.
Q12. What is the value of $400 \div (100 - (\overline{50 - 3 \times 10}))$?
IntermediateC · 5
Simplify the overline: $50 - 30 = 20$. Then $100 - 20 = 80$. Then $400 \div 80 = 5$.
Q13. What is the value of $\frac{1}{13}[7 + 2 \times 5 \times 11 + 2]$?
AdvancedA · $\frac{119}{13}$
Simplify inside brackets: $2 \times 5 \times 11 = 110$, then $7 + 110 + 2 = 119$. Then multiply by $\frac{1}{13}$: $\frac{119}{13}$, which is not an integer.
Q14. A student simplifies $10 \times 10 + [400 \div (100 - (\overline{50 - 3 \times 10}))]$ and gets 100. Where did they likely go wrong?
AdvancedB · They forgot to add the result of $400 \div 80$ to $100$.
The correct simplification gives $100 + 5 = 105$. Getting 100 means they omitted the final addition of 5.
Q15. If a month starts on Monday, what day of the week is the 15th?
AdvancedB · Monday
The pattern repeats every 7 days. The 1st is Monday, so the 8th is Monday, and the 15th is also Monday.
Q16. Which of the following is the correct simplification of $25 + 2 + 24 \times 2 + 15 \times 5$?
AdvancedB · 150
First do multiplications: $24 \times 2 = 48$, $15 \times 5 = 75$. Then add: $25 + 2 + 48 + 75 = 150$.
Q17. In the expression $(20+5)+2+(16+8)\times 2+(10+5)\times (3+2)$, which of the following steps is incorrect if the final answer is miscalculated?
AdvancedA · Adding all components from left to right without considering brackets.
The correct method requires following BODMAS/PEMDAS, which means simplifying brackets first. If a student adds all components from left to right without respecting the brackets, they will arrive at an incorrect answer.
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