CBSE Class 6 Mathematics Integers Assignment Set 06

VI - Mathematics Assignment No - 01 - Integers

Question 1. Write in the form of integer
(i) \(10^\circ\text{C}\) below normal temperature.
(ii) \(5\text{ cm}\) more than the actual length.
(iii) Earning Rs 500 from some source.
(iv) A loss of Rs 200 in the shop.
(v) Rahul received 24 marks more in comparison of his previous marks.
Answer:
(i) -10
(ii) +5
(iii) +500
(iv) -200
(v) +24
In simple words: Negative signs represent values below or losses, while positive signs represent gains or values above.

Exam Tip: Always use a minus sign for reduction, loss, or below, and a plus sign for increase, gain, or above.

Question 2. Write the opposite of each of the following statements
(i) Earning of Rs 1000
(ii) Gaining a weight of \(5\text{ kg}\)
(iii) A deposit of Rs 500 in the bank
(iv) Going \(10\text{ m}\) towards west
(v) \(5\text{ km}\) above the sea - level
Answer:
(i) Loss of Rs 1000
(ii) Losing a weight of \(5\text{ kg}\)
(iii) Withdrawal of Rs 500 from the bank
(iv) Going \(10\text{ m}\) towards east
(v) \(5\text{ km}\) below the sea level
In simple words: The opposite of a statement replaces terms like earning with losing, above with below, and west with east.

Exam Tip: Look for directional or financial counterpart words to find the exact opposite statement.

Question 3. Mark the following integers on the number line
(i) 5
(ii) -5
(iii) -2
(iv) 7
(v) 10
Answer:
To represent these integers, draw a horizontal line with zero in the middle. Mark positive integers 5, 7, and 10 to the right of zero, and negative integers -2 and -5 to the left of zero at equal intervals.
In simple words: Positive numbers go to the right of zero, and negative numbers go to the left.

Exam Tip: Ensure equal spacing between consecutive integer points on the number line.

Question 4. Which number is larger in each of the following pairs.
(i) \(0, -2\)
(ii) \(5, -5\)
(iii) \(2, -7\)
(iv) \(-113, 365\)
(v) \(-10, -12\)
Answer:
(i) 0
(ii) 5
(iii) 2
(iv) 365
(v) -10
In simple words: Every positive number is larger than any negative number, and closer numbers to zero on the right are larger.

Exam Tip: Between two negative numbers, the one with the smaller absolute value is always greater.

Question 5. Mark the smaller number on the number line
(i) \(0, -2\)
(ii) \(15, -15\)
(iii) \(4, -7\)
(iv) \(13, -15\)
(v) \(7, 9\)
Answer:
(i) -2
(ii) -15
(iii) -7
(iv) -15
(v) 7
In simple words: The smaller number always lies to the left of the other number on the number line.

Exam Tip: Negative numbers are always smaller than positive numbers or zero.

Question 6. Write all integers between:
(i) 0 and 5
(ii) 3 and -3
(iii) 12 and 15
(iv) -5 and 7
(v) -3 and 0
Answer:
(i) 1, 2, 3, 4
(ii) -2, -1, 0, 1, 2
(iii) 13, 14
(iv) -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6
(v) -2, -1
In simple words: List all whole integer steps strictly lying between the two given numbers without including the endpoints.

Question 7. Using the number line with the integer, what is:
(i) 5 more than 2
(ii) 5 more than -5
(iii) 3 more than -4
(iv) 3 less than -1
(v) 7 less than 4
Answer:
(i) Starting from 2, move 5 steps to the right to reach 7.
(ii) Starting from -5, move 5 steps to the right to reach 0.
(iii) Starting from -4, move 3 steps to the right to reach -1.
(iv) Starting from -1, move 3 steps to the left to reach -4.
(v) Starting from 4, move 7 steps to the left to reach -3.
In simple words: "More than" means moving right on the number line, and "less than" means moving left.

Exam Tip: Translate "more than" as addition (+) and "less than" as subtraction (-) to verify mentally.

Question 8. Fill the blanks by using appropriate symbol > or <
(i) \(-3 \dots \dots 3\)
(ii) \(5 \dots \dots 7\)
(iii) \(13 \dots \dots -3\)
(iv) \(-15 \dots \dots 7\)
(v) \(12 \dots \dots -15\)
Answer:
(i) \(-3 < 3\)
(ii) \(5 < 7\)
(iii) \(13 > -3\)
(iv) \(-15 < 7\)
(v) \(12 > -15\)
In simple words: The open mouth of the symbol points towards the larger number.

Exam Tip: Remember that positive integers are always greater than negative integers.

Question 9. Write the following integers in an increasing order
(i) \(5, -7, -2, 0, 9\)
(ii) \(-23, 13, 0, -6, 7\)
(iii) \(12, 0, -3, -5, 7\)
(iv) \(5, 7, -5, -7, 0\)
(v) \(13, 25, -27, 56, 100\)
Answer:
(i) \(-7, -2, 0, 5, 9\)
(ii) \(-23, -6, 0, 7, 13\)
(iii) \(-5, -3, 0, 7, 12\)
(iv) \(-7, -5, 0, 5, 7\)
(v) \(-27, 13, 25, 56, 100\)
In simple words: Arrange numbers from smallest (most negative) to largest (most positive).

Exam Tip: Write down all negative numbers first in descending order of their absolute values, followed by zero and positive numbers.

Question 10. Write (i) 5 negative integers greater than -5
(ii) 5 negative integers less than -15.
Answer:
(i) -4, -3, -2, -1, 0 (Note: 0 is neither positive nor negative, so strictly negative integers greater than -5 are -4, -3, -2, -1)
Let's list the standard textbook sequence: -4, -3, -2, -1, 0.
(ii) -16, -17, -18, -19, -20
In simple words: Greater negative integers are closer to zero, while lesser negative integers are further away from zero.

Exam Tip: Pay close attention to the direction of inequalities when dealing with negative numbers.