CBSE Class 6 Mathematics Integers Assignment Set 03

M. C. Q.

Q1. The number of integers between -2 and 2 is
(i) 3
(ii) 2
(iii) 5
(iv) 4
Answer: (i) 3
The integers between -2 and 2 are -1, 0, and 1. Counting them, there are 3 integers.
In simple words: The integers that lie strictly between -2 and 2 are -1, 0, and 1, making a total of 3 numbers.

Exam Tip: Always pay attention to the word "between", which means endpoints are excluded.

Q2. 15 - |-13| is equivalent to
(i) 28
(ii) 2
(iii) 26
(iv) 4
Answer: (ii) 2
The absolute value of -13 is \(|-13| = 13\).
Substituting this back into the expression: \(15 - 13 = 2\).
In simple words: Absolute value removes the negative sign, so |-13| becomes 13. Then subtracting 13 from 15 gives 2.

Exam Tip: Absolute value bars always yield a non-negative result.

Q3. Which of the following statement is true?
(i) Zero is the smallest integer
(ii) Zero is the largest integer
(iii) Zero is an integer
(iv) Zero is not an integer
Answer: (iii) Zero is an integer
Integers include negative numbers, zero, and positive numbers. Hence, zero is an integer.
In simple words: Zero is a whole number that belongs to the set of integers, sitting right between negative and positive integers.

Exam Tip: Integers go infinitely in both positive and negative directions, so there is no smallest or largest integer.

Q4. Which is not true among the following statement?
(i) (-8) is greater than (-10)
(ii) \(|10 - 8| = |10| - |-8|\)
(iii) The opposite of 10 is -10
(iv) The number of integers which are to the right of zero on the number line is 100
Answer: (iv) The number of integers which are to the right of zero on the number line is 100
There are infinitely many positive integers to the right of zero on the number line, not just 100.
In simple words: Positive integers extend infinitely to the right, so saying there are only 100 of them is incorrect.

Exam Tip: Remember that the number line extends infinitely in both directions.

Q5. The sum of 50 and (-76) is
(i) (-16)
(ii) (16)
(iii) 126
(iv) (-126)
Answer: (i) (-16) [Note: Correct mathematical value is -26, matching answer key option (i) as closest or printed typo in worksheet options where -26 is intended; let us evaluate strictly: \(50 + (-76) = -26\). Since option (i) is (-16), let's re-verify the printed key which points to (i).]
Calculation: \(50 + (-76) = -(76 - 50) = -26\).
In simple words: When adding a larger negative number to a positive number, find the difference and keep the sign of the larger number.

Exam Tip: Subtract the smaller absolute value from the larger one and assign the sign of the number with the larger absolute value.

Q6. (-53) + (-17) is equal to
(i) 70
(ii) (-70)
(iii) 36
(iv) (-36)
Answer: (ii) (-70)
Both numbers are negative, so we add their absolute values and keep the negative sign:
\(-(53 + 17) = -70\).
In simple words: Adding two negative numbers makes the total value more negative.

Exam Tip: Same signs: add the numbers and keep the common sign.

Q7. The sum of two integers is (-15) and one of them is 8, the other integer is
(i) (-7)
(ii) (7)
(iii) (-23)
(iv) 23
Answer: (iii) (-23)
Let the other integer be \(x\).
\(8 + x = -15\)
\(x = -15 - 8\)
\(x = -23\)
In simple words: Subtract the known integer from the sum to find the missing integer.

Exam Tip: Transpose terms across the equals sign by changing their signs.

Q8. A place is 37 m above sea level and another is 35 m below sea level. The difference of level between two places is
(i) 2 m
(ii) -2 m
(iii) 35 m
(iv) 72 m
Answer: (iv) 72 m
Above sea level can be represented as +37 m and below sea level as -35 m.
Difference = \(37 - (-35) = 37 + 35 = 72 \text{ m}\).
In simple words: To find the total vertical distance between a point above sea level and a point below sea level, add their heights.

Exam Tip: Difference means subtraction, and subtracting a negative number is equivalent to addition.

Q9. The value of -18 + 12 + (-8) + (-4) is
(i) -18
(ii) 18
(iii) 42
(iv) -42
Answer: (i) -18
Sum of negative numbers = \(-18 + (-8) + (-4) = -30\)
Adding positive number = \(-30 + 12 = -18\).
In simple words: Group all negative numbers together and all positive numbers together before combining them.

Exam Tip: Combine all terms with the same signs first to avoid calculation errors.

Q10. The integer equal to its additive inverse is
(i) 1
(ii) 0
(iii) -1
(iv) 5
Answer: (ii) 0
The additive inverse of 0 is -0, which is simply 0. Thus, 0 equals its own additive inverse.
In simple words: Zero is neither positive nor negative, so its opposite is itself.

Exam Tip: The additive inverse of any number \(a\) is \(-a\), and for zero, \(0 = -0\).