CBSE Class 6 Mathematics Integers Assignment Set 05

VI - Mathematics Assignment No - 02 - Integers

Question 1. Replace * in each of the following by < or > so that the statement is true
(i) \(0 * 6\)
(ii) \(-8 * -15\)
(iii) \(-61 * 10\)
(iv) \(-12 * 12\)
(v) \(25 * -25\)
Answer:
(i) \(0 < 6\)
(ii) \(-8 > -15\)
(iii) \(-61 < 10\)
(iv) \(-12 < 12\)
(v) \(25 > -25\)
In simple words: On the number line, numbers to the right are always greater than numbers to the left.

Exam Tip: Every positive integer is always greater than any negative integer, and zero is greater than all negative integers.

Question 2. Write the absolute value of the following
(i) \(-15\)
(ii) \(25\)
(iii) \(0\)
(iv) \(-180\)
(v) \(-36\)
Answer:
(i) \(|-15| = 15\)
(ii) \(|25| = 25\)
(iii) \(|0| = 0\)
(iv) \(|-180| = 180\)
(v) \(|-36| = 36\)
In simple words: Absolute value means the numerical value without considering its positive or negative sign.

Exam Tip: The absolute value of any integer is always non-negative.

Question 3. Write the following integers in a decreasing order:
(i) \(0, 7, -3, -5, 15\)
(ii) \(3, -3, 5, -5, 7\)
(iii) \(15, -14, 13, 12, 0\)
(iv) \(19, -19, 15, 3, -3\)
(v) \(6, -7, -8, 9, -10\)
Answer:
(i) \(15, 7, 0, -3, -5\)
(ii) \(7, 5, 3, -3, -5\)
(iii) \(15, 13, 12, 0, -14\)
(iv) \(19, 15, 3, -3, -19\)
(v) \(9, 6, -7, -8, -10\)
In simple words: Decreasing order means arranging numbers from the largest to the smallest.

Exam Tip: When sorting negative numbers, remember that the number with the larger digits has a smaller value (e.g., -19 is smaller than -3).

Question 4. Using number line, write the integer which is
(i) 4 more than 6
(ii) 5 more than -6
(iii) 2 less than -5
(iv) 6 less than 4
Answer:
(i) Starting from 6 and moving 4 units to the right leads to 10.
(ii) Starting from -6 and moving 5 units to the right leads to -1.
(iii) Starting from -5 and moving 2 units to the left leads to -7.
(iv) Starting from 4 and moving 6 units to the left leads to -2.
In simple words: Move to the right for "more" (addition) and to the left for "less" (subtraction) on the number line.

Exam Tip: Always identify your starting point clearly before counting steps on the number line.

Question 5. Choose the largest and smallest integer among the following: \(32, -50, -75, 120, -365, 175\)
Answer:
Largest integer = 175
Smallest integer = -365
In simple words: The largest number is the one furthest to the right, and the smallest is the one furthest to the left on the number line.

Exam Tip: Large negative numbers carry a smaller value than any positive number or smaller negative numbers.

Question 6. Write the answer of the following
(i) Write the smallest integer
(ii) The opposite of -5
(iii) The third number greater than -6
(iv) The integer which divides the positive and negative integers on the number line.
(v) The value of \(3 * 4\) if \(a * b = a + b - 2\)
Answer:
(i) Not defined (NIL) as integers extend infinitely in the negative direction.
(ii) 5
(iii) -3 (Counting three units greater than -6: -5, -4, -3)
(iv) 0
(v) Substituting \(a = 3\) and \(b = 4\) into \(a + b - 2\):
\(3 + 4 - 2 = 7 - 2 = 5\)
In simple words: Follow each specific condition carefully to find the required integer value.

Exam Tip: Zero is neutral; it is neither positive nor negative, acting as the dividing center on the number line.

Question 7. Simplify
(i) \(10 - |-10| + 5\)
(ii) \(3 + |-3| + 2\)
(iii) \(|3 - 3| + 5\)
(iv) \(|5| + |7| - 12\)
Answer:
(i) \(10 - 10 + 5 = 0 + 5 = 5\)
(ii) \(3 + 3 + 2 = 6 + 2 = 8\)
(iii) \(0 + 5 = 5\)
(iv) \(5 + 7 - 12 = 12 - 12 = 0\)
In simple words: First convert absolute values into their positive numerical forms, then perform standard addition and subtraction.

Exam Tip: Always evaluate expressions inside absolute value bars completely before applying operations outside them.

Question 8. Write the next four integers in each of the following sequence:
(i) \(-15, -10, -5, \dots, \dots, \dots, \dots\)
(ii) \(13, 10, 7, 4, \dots, \dots, \dots, \dots\)
(iii) \(-3, -8, -13, -18, \dots, \dots, \dots, \dots\)
(iv) \(18, 14, 10, 6, \dots, \dots, \dots, \dots\)
(v) \(3, 6, 9, 12, 15, \dots, \dots, \dots, \dots\)
(vi) \(-6, -3, 0, 3, 6, \dots, \dots, \dots, \dots\)
Answer:
(i) 0, 5, 10, 15 (Pattern: add 5)
(ii) 1, -2, -5, -8 (Pattern: subtract 3)
(iii) -23, -28, -33, -38 (Pattern: subtract 5)
(iv) 2, -2, -6, -10 (Pattern: subtract 4)
(v) 18, 21, 24, 27 (Pattern: add 3)
(vi) 9, 12, 15, 18 (Pattern: add 3)
In simple words: Find the common difference between consecutive terms to determine the rule for the sequence.

Question 9. Use number line, add the following
(i) \(7 + 3 + (-5)\)
(ii) \(3 + (-3) + 5\)
(iii) \(5 + (-2) + 1\)
(iv) \(12 + (-7) + 5\)
(v) \(10 + (-3) + 2\)
Answer:
(i) \(7 + 3 - 5 = 10 - 5 = 5\)
(ii) \(3 - 3 + 5 = 0 + 5 = 5\)
(iii) \(5 - 2 + 1 = 3 + 1 = 4\)
(iv) \(12 - 7 + 5 = 5 + 5 = 10\)
(v) \(10 - 3 + 2 = 7 + 2 = 9\)
In simple words: Combine movements to the right for positive numbers and movements to the left for negative numbers.

Exam Tip: Perform additions and subtractions sequentially from left to right.

Question 10. Simplify without using number line.
(i) \(15 + 10 + (-7) + (-3)\)
(ii) \(3 + (-2) + 5 + (-3)\)
(iii) \(12 + (-10) + 6 + 9\)
(iv) \((-3) + (-2) + (-5) + 10\)
Answer:
(i) \(15 + 10 - 7 - 3\)
\(= 25 - 10 = 15\)
(ii) \(3 - 2 + 5 - 3\)
\(= 1 + 5 - 3 = 6 - 3 = 3\)
(iii) \(12 - 10 + 6 + 9\)
\(= 2 + 6 + 9 = 8 + 9 = 17\)
(iv) \(-3 - 2 - 5 + 10\)
\(= -10 + 10 = 0\)
In simple words: Group all positive numbers together and all negative numbers together before combining them.

Exam Tip: Adding numbers with the same sign keeps that sign, while adding opposite signs involves finding their difference.