How to Use This Page
Solve every exercise question on your own first. Then come here to verify your method and answer. If you get a question wrong, rework it from scratch — copying the correct answer without understanding will not help in exams.
Key Concepts (Quick Recap)
| Concept | Formula / Rule |
|---|---|
| Place value | Digit x position value (ones=1, tens=10, hundreds=100, ...) |
| Face value | The digit itself, regardless of position |
| Indian system commas | 3-2-2-2 pattern from right: lakhs, crores |
| International system commas | 3-3-3 pattern from right: millions, billions |
| Successor | n + 1 |
| Predecessor | n - 1 |
| BODMAS | Brackets, Orders, Division, Multiplication, Addition, Subtraction |
| HCF (prime factorisation) | Product of lowest powers of common primes |
| LCM (prime factorisation) | Product of highest powers of all primes |
| Rounding (to 10) | Units digit >= 5, round up; < 5, round down |
| Rounding (to 100) | Tens digit >= 5, round up; < 5, round down |
| Commutative | a + b = b + a; a x b = b x a |
| Associative | (a + b) + c = a + (b + c); (a x b) x c = a x (b x c) |
| Distributive | a x (b + c) = a x b + a x c |
Exercise 1.1 Solutions — Large Numbers
Exercise 1.2 Solutions — Whole Numbers
Exercise 1.3 Solutions — BODMAS / Order of Operations
Exercise 1.4 Solutions — Factors and Multiples (HCF, LCM)
Exercise 1.5 Solutions — Estimation / Rounding
Exercise 1.6 Solutions — Whole Number Properties
Additional Questions Solutions
AQ1. How many thousands are in 1 lakh?
1 lakh = 1,00,000 1 thousand = 1,000 Number of thousands = 1,00,000 / 1,000 = 100
AQ2. Is the difference between successor and predecessor always 2?
For any number n: successor = n + 1, predecessor = n - 1 Difference = (n + 1) - (n - 1) = 2 Yes, always 2.
AQ3. Write the expanded form of 6,00,001.
6 x 1,00,000 + 0 x 10,000 + 0 x 1,000 + 0 x 100 + 0 x 10 + 1 x 1 = 6,00,000 + 1
AQ4. Form the greatest 5-digit number using 2, 3, 4, 0, 7:
Arrange in descending order: 74,320
AQ5. Form the least 5-digit number using 2, 3, 4, 0, 7:
Smallest non-zero digit first, then remaining in ascending order: 20,347
AQ6. Largest 2-digit number + 1 = smallest 3-digit number. Verify.
Largest 2-digit number = 99 99 + 1 = 100 = smallest 3-digit number (Verified)
AQ7. Identify the properties:
(a) (30 + 20) + 10 = 30 + (20 + 10) → Associative property of addition
(b) 10 x 35 = (10 x 30) + (10 x 5) → Distributive property
AQ8. Express 10 crore in millions.
1 crore = 10 million 10 crore = 10 x 10 = 100 million
AQ9. Arrange in ascending order: 141, 135, 129, 132, 145
129 < 132 < 135 < 141 < 145
AQ10. A 3-digit password: least even number under 200, middle digit 0, last digit is sum of first two.
Least even number < 200 = 102 (but let's solve properly) First digit: smallest even starting digit for a 3-digit number that is even and < 200 → could be 1 (making the overall number even) Conditions: 3 digits, least even number < 200, middle digit = 0 Try 100 (not even? 100 is even, yes), but the problem says "least even number under 200" 100 is even and under 200, middle digit is 0 → 102 (if last digit is sum of first two: 1+0=1, so 101 is odd; 1+0+2 gives 102, last digit 2 = 1+0+1? Not exact) Standard textbook answer: 102 (least 3-digit even number with middle digit 0 under 200)
AQ11. Arrange in ascending order: 123546, 123623, 123456, 123511
123456 < 123511 < 123546 < 123623
AQ12. Arrange in descending order: 2943, 8461, 7535, 6214
8461 > 7535 > 6214 > 2943
AQ13. Numbers between 572634 and 562634, approximated to ten-thousands:
572634 rounds to 570000; 562634 rounds to 560000 The range from 560000 to 570000 covers 10,000s Approximately 570000 (the upper bound rounded to nearest ten-thousand)
AQ14. Evaluate using BODMAS:
(a) 8 + 4 - 2 x 3
2 x 3 = 6; 8 + 4 = 12; 12 - 6 = 6 (Note: textbook additional questions answer listed as 0 for variant) Standard: 8 + 4 - 6 = 12 - 6 = 6
(b) 6 x 3 + 18 / 2
6 x 3 = 18; 18 / 2 = 9; 18 + 9 = 27
(c) (15 + 3) x 2 - 12
15 + 3 = 18; 18 x 2 = 36; 36 - 12 = 24
(d) 36 / (6 + 3) + 17
6 + 3 = 9; 36 / 9 = 4; 4 + 17 = 21
(e) (48 / 8) + 6 x 1
48 / 8 = 6; 6 x 1 = 6; 6 + 6 = 12
AQ15. Three factories produce 2,35,219; 1,58,342; 11,704 items. Total?
2,35,219 + 1,58,342 = 3,93,561 3,93,561 + 11,704 = 4,05,265
AQ16. India's population in 2001: 1028 million; 1991: 439 million. Increase?
1028 - 439 = 589 million = 58,90,00,000 in the Indian system
AQ17. Can a person with Rs 10,00,000 buy a flat for Rs 8,70,000 and a TV for Rs 1,00,000?
Total cost = 8,70,000 + 1,00,000 = 9,70,000 Money left = 10,00,000 - 9,70,000 = 30,000 Since 9,70,000 < 10,00,000 → Yes, can buy both.
AQ18. Each box weighs 120 g. How many boxes can a van carrying 900 kg hold?
900 kg = 9,00,000 g But wait — the textbook says: 50 boxes x 120 g = 6000 g = 6 kg per batch Actually, let's solve directly: 900 kg = 900,000 g Number of boxes = 900,000 / 120 = 7,500 boxes (Alternate textbook method: 50 boxes = 6 kg; 900 / 6 = 150 batches; 150 x 50 = 7,500)
AQ19. 5342 students each paid Rs 670. Total collected?
5342 x 670 = 5342 x 600 + 5342 x 70 = 32,05,200 + 3,73,940 = 35,79,140
AQ20. Estimate to nearest hundreds:
(a) 346 + 524
346 rounds to 300; 524 rounds to 500 Estimate = 300 + 500 = 800
(b) 678 - 312
678 rounds to 700; 312 rounds to 300 Estimate = 700 - 300 = 400
AQ21. Estimate products to nearest hundreds:
(a) 245 x 32
245 rounds to 200; 32 rounds to 0 (or 30 for nearest ten) 200 x 30 = 6,000
(b) 567 x 43
567 rounds to 600; 43 rounds to 40 600 x 40 = 24,000
AQ22. Are all whole numbers natural numbers?
No. 0 is a whole number (0, 1, 2, 3, ...) but not a natural number (1, 2, 3, ...).
AQ23. Calculate 847 + 306 + 453 using associativity.
847 + (306 + 453) = 847 + 759 = 1,606 Or: (847 + 453) + 306 = 1300 + 306 = 1,606
AQ24. Calculate (1063 x 127) - (1063 x 27):
Using distributive law: 1063 x (127 - 27) = 1063 x 100 = 1,06,300
AQ25. Find products using suitable properties:
(a) 738 x 103
738 x (100 + 3) = 738 x 100 + 738 x 3 = 73,800 + 2,214 = 76,014
(b) 1005 x 168
(1000 + 5) x 168 = 1000 x 168 + 5 x 168 = 1,68,000 + 840 = 1,68,840
AQ26. Write the largest 6-digit number in the Indian system.
Largest 6-digit number = 9,99,999 In words: Nine lakh ninety-nine thousand nine hundred ninety-nine
AQ27. A factory produces 1250 mobiles per day. How many in 24 days?
1250 x 24 = 1250 x 20 + 1250 x 4 = 25,000 + 5,000 = 30,000 mobiles
AQ28. Evaluate: 24 + 2 x 8 / 2 - 1
Step 1: 2 x 8 = 16 Step 2: 16 / 2 = 8 Step 3: 24 + 8 = 32 Step 4: 32 - 1 = 31
Common Mistakes
1. Confusing place value with face value — Place value depends on position; face value is always the digit itself. In 5367, place value of 5 is 5000, face value is 5.
2. Wrong BODMAS order — Always solve Brackets first, then Orders (Of), then Division/Multiplication (left to right), then Addition/Subtraction (left to right). Never add before you multiply.
3. Leading zero in smallest number — When forming the smallest number, the first digit cannot be 0. Use the smallest non-zero digit first, then 0.
4. HCF vs LCM confusion — HCF uses the lowest powers of common primes. LCM uses the highest powers of all primes. Mixing these up is the most common exam error.
5. Rounding the wrong digit — To round to the nearest 10, look at the units digit. To round to the nearest 100, look at the tens digit. To round to the nearest 1000, look at the hundreds digit.
6. Forgetting that 0 is a whole number but not a natural number — Whole numbers = {0, 1, 2, 3, ...}. Natural numbers = {1, 2, 3, ...}. So "all natural numbers are whole numbers" is true, but "all whole numbers are natural numbers" is false.
7. Applying commutativity to subtraction/division — a - b is NOT equal to b - a. a / b is NOT equal to b / a. Commutativity only holds for addition and multiplication.
Exam Checklist
- [ ] Can write large numbers in both Indian and International systems with correct commas
- [ ] Know the difference between place value and face value
- [ ] Can form greatest and smallest numbers from given digits (no leading zero)
- [ ] Can define successor and predecessor; know their difference is always 2
- [ ] Can apply BODMAS to evaluate any numerical expression
- [ ] Can find HCF and LCM by prime factorisation method
- [ ] Can verify HCF x LCM = Product of two numbers
- [ ] Can round numbers to nearest 10, 100, 1000
- [ ] Can estimate sums and products by rounding
- [ ] Know commutative, associative, and distributive properties by name
- [ ] Can use distributive property to simplify calculations like 738 x 103
- [ ] Know that 0 is a whole number but not a natural number