Integers Class 6 ICSE Questions — Mathematics Chapter 2
The integers class 6 ICSE questions in this chapter start from one idea: every natural number has a negative partner. The chapter, from the Class 6 Mathematics book, explains what integers are, how to compare them, and how to add, subtract, multiply, and divide them. You will also meet absolute value and the DMAS order for mixed operations.
Download Integers Class 6 ICSE Mathematics Chapter 2 PDF
Download the Integers Class 6 ICSE Mathematics chapter PDF to revise offline or print for practice. It is the full chapter as printed in the book — 12 pages, 5 sections, 34 questions.
What is inside Chapter 2
12 pages · 5 sections · 20 worked examples · 34 exercise questions
| Section | Title |
|---|---|
| 2.1 | INTEGERS |
| 2.2 | ABSOLUTE VALUE OF AN INTEGER |
| 2.3 | COMPARING INTEGERS |
| 2.5 | FOUR FUNDAMENTAL OPERATIONS ON INTEGERS |
| 2.6 | COMBINATION OF FOUR FUNDAMENTAL OPERATIONS |
- EXERCISE 2 (A): 16 questions
- EXERCISE 2(C): 10 questions
- Revision Exercise (Chapter 2): 8 questions
2.1 INTEGERS
The chapter defines integers as a collection of three groups. First come the negatives of all natural numbers: -4, -3, -2, -1. Then zero, and then the natural numbers themselves: 1, 2, 3, 4, \dots. The list of negatives runs on forever to the left, and the list of naturals runs on forever to the right.
The chapter labels four subgroups clearly. Positive integers are 1, 2, 3, 4, 5, \dots. Negative integers are -1, -2, -3, -4, -5, \dots. Zero is neither positive nor negative. The set 0, 1, 2, 3, 4, 5, \dots forms the non-negative integers.
Why do these labels matter? Every sign rule in the later sections rests on them. If you know zero is neither positive nor negative, you will never misplace it when comparing integers. The same labels reappear when the chapter discusses absolute value in section 2.2.
If you need to revise natural numbers first, the Class 6 Maths book begins with a chapter on the number system. That number system chapter defines natural numbers before this chapter extends them into integers.
2.2 ABSOLUTE VALUE OF AN INTEGER
The absolute value of an integer is its numerical value without its sign. You write the integer between two vertical bars. The absolute value of -45 is |-45| = 45, and the absolute value of +19 is |+19| = 19. For any integer a, its absolute value |a| is always non-negative.
Three facts follow. The absolute value of a negative number is always greater than the number itself: |-8| = 8, which is greater than -8. The absolute value of a positive number equals the number: |8| = 8. And |a| = a happens only when a is zero or positive, as in |0| = 0 and |3| = 3.
Worked pattern with new numbers: evaluate |-9| + |-4|. First strip the signs: |-9| = 9 and |-4| = 4. Then add: 9 + 4 = 13. Now evaluate -|-7|. The bars give |-7| = 7, and the minus sign outside flips it to -7.
A common mistake is writing |-5| = -5. That is wrong: the bars strip the sign, so |-5| = 5. The negative sign only survives when it sits outside the bars, as in -|-5| = -5.
2.3 COMPARING INTEGERS
Four rules govern comparison. Every positive integer is greater than every negative integer and greater than zero. Every negative integer is smaller than every positive integer and smaller than zero. Zero is greater than every negative integer and smaller than every positive integer. For two negative integers, the one with the smaller absolute value is greater.
Example with new numbers: compare -24 and -31. Their absolute values are 24 and 31. Since 24 \lt 31, the smaller absolute value belongs to -24. Therefore -24 \gt -31.
The chapter calls positive and negative integers together directed numbers. They carry direction in real life. If moving 7 m east is +7, then -7 means moving 7 m west. If a profit of \text{₹} 40 is +40, a loss of \text{₹} 40 is -40.
A rise in temperature by 15^\circ \text{C} is +15, and a fall of 9^\circ \text{C} is -9. Heights above sea level are positive; depths below are negative.
Worked pattern: a diver at 120 m below the water surface rises 35 m. Below the surface is negative, so the start is -120. Rising 35 m adds +35. The result is -120 + 35 = -85. The diver ends 85 m below the surface. The same logic appears in temperature problems: add the rise, add the fall, and read the sign of the final value.
2.5 FOUR FUNDAMENTAL OPERATIONS ON INTEGERS
Addition follows two rules. When integers share a sign, add their absolute values and keep that sign. For like signs, (+46) + (+19) = +65 and (-14) + (-27) = -41. When signs differ, subtract the smaller absolute value from the larger and keep the sign of the larger.
Worked pattern for unlike signs: add (-63) + (+28). The absolute values are 63 and 28. Their difference is 63 - 28 = 35. The integer with the larger absolute value is -63, so the result carries its sign: -35.
Subtraction changes the sign of the integer being subtracted, then adds. For (+9) - (-4), change -4 to +4 and add: 9 + 4 = 13. A common mistake is treating (-9) - (-6) as -9 - 6 = -15. The correct working changes the sign: -9 + 6 = -3.
Multiplication and division share the same sign rule. Same signs give a positive result; unlike signs give a negative result. For example, (-72) \div (+8) = -9 and (+72) \div (+8) = +9.
| Operation | Same signs | Unlike signs |
|---|---|---|
| Multiplication | (+6) \times (+4) = +24, (-6) \times (-4) = +24 | (-6) \times (+4) = -24 |
| Division | (+15) \div (+3) = +5, (-15) \div (-3) = +5 | (+15) \div (-3) = -5 |
The chapter lists key properties. Addition is commutative, associative, has 0 as identity, and every integer has an additive inverse. Multiplication is commutative, associative, has 1 as identity, and a \times 0 = 0. Distributivity connects the two. Division by zero is not defined, while 0 \div a = 0 for non-zero a.
Watch for these common sign mistakes when you work through the exercises.
- Writing |-5| = -5 — the bars strip the sign, so |-5| = 5.
- Subtracting a negative wrongly: (-9) - (-6) is -9 + 6 = -3, not -15.
- Adding unlike signs by adding values: (+46) + (-19) is +27, not +65. Subtract the absolute values first.
2.6 COMBINATION OF FOUR FUNDAMENTAL OPERATIONS
The four fundamental operations are addition, subtraction, multiplication, and division. When an expression mixes them, simplify in the order given by the acronym DMAS. D stands for division, M for multiplication, A for addition, S for subtraction. Division and multiplication come before addition and subtraction.
Worked pattern with new numbers: evaluate 20 - 12 \div 3 + 4 \times (-5). Division first: 12 \div 3 = 4, giving 20 - 4 + 4 \times (-5). Multiplication next: 4 \times (-5) = -20, giving 20 - 4 - 20. Then add and subtract: 20 - 4 - 20 = -4.
A common mistake is doing multiplication before division. For 12 \div 3 \times 2, division must come first: 12 \div 3 = 4, then 4 \times 2 = 8. Doing multiplication first gives 3 \times 2 = 6, then 12 \div 6 = 2, which is wrong. The DMAS order fixes the result.
The chapter applies DMAS to every expression with mixed operations. Whether the numbers are large or small, the order never changes: divide, then multiply, then add, then subtract. Write down each step so you can see which operation you performed.
What to practise from Integers Class 6 ICSE
This chapter has three blocks of questions. Use the table to match each exercise to the section it tests. The integers class 6 ICSE questions in EXERCISE 2 (A) cover absolute value and comparison. EXERCISE 2(C) checks DMAS evaluation, and the Revision Exercise pulls the whole chapter together.
| Exercise | Questions | Tests |
|---|---|---|
| EXERCISE 2 (A) | 16 | Sections 2.2 and 2.3: absolute value, comparing and ordering integers, opposites of quantities, temperature and direction problems |
| EXERCISE 2(C) | 10 | Section 2.6: DMAS evaluation |
| Revision Exercise (Chapter 2) | 8 | The whole chapter |
Work the exercises in order. Finish EXERCISE 2 (A) before attempting the Revision Exercise, since later questions assume the earlier skills. For the official ICSE syllabus and examination details, visit the CISCE board site.
You can also browse the Class 6 ICSE books collection for the other chapters in this book.
Integers Class 6 ICSE frequently asked questions
Which integers class 6 ICSE questions should I practise first?
Start with EXERCISE 2 (A) after reading sections 2.2 and 2.3. It tests absolute value, comparison, and directed numbers. Then move to EXERCISE 2(C) for DMAS, and finish with the Revision Exercise to check the whole chapter.
What is the absolute value of a negative integer?
The absolute value of a negative integer is its positive numerical value. For |-12|, the answer is 12. The bars remove the sign, so the absolute value is always non-negative.
How do I add integers with different signs?
Subtract the smaller absolute value from the larger, then keep the sign of the integer with the larger absolute value. For (+46) + (-19), the difference is 27 and the sign is positive.
What does the DMAS rule mean in integers?
DMAS stands for division, multiplication, addition, subtraction. It gives the order for simplifying expressions that mix operations. Division and multiplication come before addition and subtraction.
Reference: ICSE Class 6 Mathematics textbook material, chapter 2: Integers — CISCE-aligned.