ICSE Class 6 Maths Whole Numbers Step-by-Step Solutions
ICSE Class 6 Maths Chapter 2 at a glance
ICSE Class 6 Maths Chapter 2, Operations on Whole Numbers, teaches students how whole numbers behave under addition, subtraction, multiplication and division. This replacement page for RS Aggarwal Mathematics Solutions Class 6 ICSE Chapter 2 Operations on Whole Numbers focuses on the methods students need most: operation properties, division algorithm verification, order of operations, number patterns and common error correction.
Key rules for RS Aggarwal Mathematics Solutions Class 6 ICSE Chapter 2 Operations on Whole Numbers
Concept snapshot: Properties are legal shortcuts. Commutative means numbers may swap places, associative means brackets may move, and distributive means multiplication may be split across addition or subtraction.
| Rule | Statement | Use |
|---|---|---|
| Commutative addition | a+b=b+a | Swap addends. |
| Commutative multiplication | a\times b=b\times a | Swap factors. |
| Associative addition | (a+b)+c=a+(b+c) | Move brackets in addition. |
| Associative multiplication | (a\times b)\times c=a\times(b\times c) | Group convenient factors. |
| Identity | a+0=a, a\times1=a | Zero and one keep values unchanged in these cases. |
| Zero property | a\times0=0 | Any number multiplied by zero gives zero. |
| Division algorithm | \text{Dividend}=\text{Divisor}\times\text{Quotient}+\text{Remainder} | Verify division answers. |
Worked solutions for Chapter 2 Operations on Whole Numbers
Exercise 2(A): fill in the blanks and verify operations
Question 1: 168+259=259+168, 0+317=317, (37+68)+56=37+(68+56), 8+3\times4=20, and 18\times(17+23)=(18\times17)+(18\times23).
Final answers: 259,\ 0,\ 56,\ 68,\ 20,\ 17,\ 23.
Question 2: Use identity and zero rules: 237\times1=237, 56\times0=0, 0\div53=0, 37\times59=59\times37, 0\times138=0, 73\div73=1.
Final answers: 237,\ 0,\ 0,\ 37,\ 0,\ 1.
Question 3: 29\times124=3596, and 3605-3596=9. Verification: 29\times124+9=3605.
Final answer: quotient 124, remainder 9.
Question 4: 45\times16+9=729. Question 5: largest 5-digit number =99999; 57\times1754=99978; answer 99978. Question 6: 63\times1587=99981, remainder from 100000 is 19, so add 44; answer 100044. Question 7: 1653=45\times d+33, so d=(1653-33)\div45=36.
Final answers: 729,\ 99978,\ 100044,\ 36.
Question 8: 576\times285+576\times115=576\times400=230400; 385\times178-385\times78=38500; 365\times645+135\times645=322500; 407\times168-307\times168=16800.
Final answers: 230400,\ 38500,\ 322500,\ 16800.
Questions 9 to 12: Convenient grouping gives 64800,\ 65800,\ 16800,\ 1000000. Division verification gives 42 R 26, 53 R 37, and 123 R 84. Simplification gives 39,\ 18,\ 37,\ 1,\ 6.
Final answers: as listed.
Exercise 2(B): patterns and magic-square method
Pattern answers: 555\div15=37, 666\div18=37, 777\div21=37; 999999\times5=4999995, 999999\times6=5999994, 999999\times7=6999993; 12345679\times45=555555555, 12345679\times54=666666666, 12345679\times63=777777777.
Five-number pattern: The sum equals 5\times\text{middle number}. For 75, the row is 13+14+15+16+17=75. No row gives 92 because 92\div5=18.4.
Magic square method: \text{missing number}=\text{magic sum}-\text{sum of known numbers in the same line}.
Exercise 2(C): multiple-choice solutions
MCQ 1: smallest whole number is 0, so option d. MCQ 2: 1000\div7 leaves remainder 6, so answer 1001, option c. MCQ 3: 9999\div13 leaves remainder 2, so answer 9997, option b. MCQ 4: 10003=11\times909+4, so subtract 4, option d.
Extra worked examples for practice
Worked Example 1: Distributive law
Step 1: Evaluate 425\times64+425\times36.
425\times64+425\times36=425\times(64+36)=425\times100=42500
Final answer: 42500.
Worked Example 2: Division algorithm
Step 1: For 5487\div42, 42\times130=5460.
Step 2: Remainder =5487-5460=27.
42\times130+27=5487
Final answer: quotient 130, remainder 27.
Worked Example 3: Order of operations
Step 1: Simplify 48-24\div6+5\times3.
48-24\div6+5\times3=48-4+15=59
Final answer: 59.
Examiner’s mindset
Show the rule and the working. In a division question, marks are usually earned by identifying quotient and remainder and then verifying with \text{Dividend}=\text{Divisor}\times\text{Quotient}+\text{Remainder}. In simplification, show multiplication and division before addition and subtraction.
Common mistakes students make
- Adding before multiplying: 8+3\times4=20, not 44.
- Applying commutative property to subtraction: 9-4\neq4-9.
- Ignoring the remainder condition: remainder must be smaller than divisor.
- Confusing zero cases: 0\div53=0, but division by 0 is not defined.
Quick answer index
| Exercise | Answer |
|---|---|
| 2(A) Q1-Q2 | 259,\ 0,\ 56,\ 68,\ 20,\ 17,\ 23; 237,\ 0,\ 0,\ 37,\ 0,\ 1 |
| 2(A) Q3-Q7 | 124 R 9; 729; 99978; 100044; 36 |
| 2(A) Q8-Q12 | 230400,\ 38500,\ 322500,\ 16800; grouping, verification and simplification answers shown above |
| 2(B) | Pattern answers and magic-square method shown above |
| 2(C) MCQ 1-4 | d,\ c,\ b,\ d |
Sources and syllabus alignment
This article follows the standard Class 6 treatment of whole numbers, operation properties and the division algorithm. For official reference, use the CISCE official website and the NCERT textbook portal. Related ICSE Board pages: ICSE solutions, Class 6 ICSE solutions, and ICSE Class 6 syllabus.
Frequently Asked Questions
What is the main idea of ICSE Class 6 Maths Chapter 2 whole numbers?
The main idea is to use properties of whole numbers, the division algorithm and correct order of operations to calculate accurately and show clear working.
How do I verify a division answer in RS Aggarwal Class 6 ICSE Maths?
Use \text{Dividend}=\text{Divisor}\times\text{Quotient}+\text{Remainder}. Also check that the remainder is smaller than the divisor.
Why do we multiply before adding in expressions like 8+3\times4?
Multiplication has higher priority than addition, so 8+3\times4=8+12=20.
Which property helps in 576\times285+576\times115?
The distributive property helps because 576 is common: 576\times285+576\times115=576\times(285+115).
Are whole numbers and natural numbers the same?
No. Whole numbers include 0, so they are 0,1,2,3,\ldots. Natural numbers are usually taken as 1,2,3,\ldots in Class 6.