Samacheer Kalvi Class 6 Maths Solutions Term 3 Chapter 2 Integers Exercise 2.1

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 2 Integers Ex 2.1

Question 1. Fill in the blanks:
(i) The potable water available at 100 m below the ground level is denoted as ......... m.
(ii) A swimmer dives to a depth of 7 feet from the ground into the swimming pool. The integer that represents this, is ......... feet.
(iii) -46 is to the ........... of -35 on the number line.
(iv) There are ......... integers from -5 to +5 (both inclusive)
(v) ........ is an integer which is neither positive nor negative.
Answer:
(i) -100
(ii) -7
(iii) left
(iv) 11. These integers are -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5.
(v) 0
In simple words: When something is below ground or represents a loss, we use a negative number. When we count numbers on a line, numbers to the left are smaller. Zero is special because it is neither positive nor negative.

🎯 Exam Tip: Remember that "below" or "depth" implies a negative value. "Inclusive" means to count the starting and ending numbers too.

Question 2. Say True or False
(i) Each of the integers -18, 6, -12, 0 is greater than -20.
(ii) -1 is to the right of 0.
(iii) -10 and 10 are at equal distance from 1
(iv) All negative integers are greater than zero.
(v) All whole numbers are integers.
Answer:
(i) True. On a number line, numbers to the right are greater. All these numbers are to the right of -20.
(ii) False. On a number line, -1 is to the left of 0.
(iii) False. -10 is 11 units away from 1 (1 - (-10) = 11). 10 is 9 units away from 1 (10 - 1 = 9). They are not at an equal distance from 1.
(iv) False. All negative integers are smaller than zero.
(v) True. Whole numbers are 0, 1, 2, 3... and these are all part of the set of integers (..., -2, -1, 0, 1, 2,...).
In simple words: Think about a number line. Numbers get bigger as you move to the right. Negative numbers are always smaller than positive numbers and zero. Whole numbers are a type of integer.

🎯 Exam Tip: Visualizing a number line helps to quickly determine if one integer is greater than another or its position relative to zero.

Question 3. Mark the numbers 4, -3, 6, -1 and -5 on the number line.
Answer:
In simple words: Draw a straight line and mark zero in the middle. Put positive numbers to the right and negative numbers to the left. Make sure the space between each number is equal. Then, place a small dot on each number asked for.

🎯 Exam Tip: Use a ruler to ensure uniform spacing between the integers on the number line for accuracy.

Question 4. On the number line, which number is
(i) 4 units to the right of -7?
(ii) 5 units to the left of 3?
Answer:
(i) To find the number 4 units to the right of -7, we add 4 to -7: \( -7 + 4 = -3 \). So, the number is -3.
(ii) To find the number 5 units to the left of 3, we subtract 5 from 3: \( 3 - 5 = -2 \). So, the number is -2.
In simple words: Moving right on a number line means adding. Moving left means subtracting. Just count the steps in the correct direction.

🎯 Exam Tip: Always remember that "right" means addition and "left" means subtraction when working with number lines and integers.

Question 5. Find the opposite of the following numbers.
(i) 44
(ii) -19
(iii) 0
(iv) -312
(v) 789
Answer:
(i) The opposite of 44 is -44.
(ii) The opposite of -19 is +19 or simply 19.
(iii) The opposite of 0 is 0 itself, as it is neither positive nor negative.
(iv) The opposite of -312 is +312 or simply 312.
(v) The opposite of 789 is -789.
In simple words: The opposite of a number is the same distance from zero on the number line, but in the other direction. So, if a number is positive, its opposite is negative, and if it is negative, its opposite is positive. Zero is its own opposite.

🎯 Exam Tip: The opposite of a number always has the same absolute value but the reverse sign. Zero is unique as its opposite is zero.

Question 6. If 15 km east of a place is denoted as +15 km, What is the integer that represents 15 km west of it?
Answer: If east is represented by a positive value (+15 km), then west, being the opposite direction, is represented by a negative value. So, 15 km west will be -15 km.
In simple words: East and west are opposite directions. If east is plus, west is minus. So, 15 km west is -15 km.

🎯 Exam Tip: Understand that opposite directions or situations (like above/below, profit/loss) are typically represented by positive and negative integers.

Question 7. From the following number lines, identify the correct and the wrong representations with reason.
(i)
(ii)
(iii)
(iv)
(v)
Answer:
(i) Wrong. The integers are not continuously marked. For example, after 0, it jumps to 2, then 4, missing 1, 3, etc. All integers should be marked one after another.
(ii) Correct. The integers are correctly marked with equal spacing, showing consecutive numbers from -6 to 7.
(iii) Wrong. The integer -2 is marked incorrectly. It should be at the position for -2, not where -3 should be.
(iv) Correct. The integers are marked at equal distances, and the number line correctly represents even numbers with a consistent scale.
(v) Wrong. The negative integers are marked wrongly. For example, -1 is marked where -6 should be. The order of negative numbers is incorrect as they increase from left to right (-6, -5, -4, ...).
In simple words: A correct number line needs to have all numbers marked in order and with the same space between them. If numbers are skipped, mixed up, or marked in the wrong spot, the number line is wrong. Negative numbers get bigger as you move towards zero.

🎯 Exam Tip: When checking a number line, ensure consecutive numbers are present, the spacing is even, and numbers increase from left to right.

Question 8. Write all the integers between the given numbers.
(i) 7 and 10
(ii) -5 and 4
(iii) -3 and 3
(iv) -5 and 0
Answer:
(i) The integers between 7 and 10 are 8, 9.
(ii) The integers between -5 and 4 are -4, -3, -2, -1, 0, 1, 2, 3.
(iii) The integers between -3 and 3 are -2, -1, 0, 1, 2.
(iv) The integers between -5 and 0 are -4, -3, -2, -1.
In simple words: "Between" means the numbers that are larger than the first number and smaller than the second number, not including the first and last numbers themselves. Just count the integers in order.

🎯 Exam Tip: Remember to list all integers between the given numbers, but do not include the starting and ending numbers themselves unless "inclusive" is specified.

Question 9. Put the appropriate signs as <, > or = in the blank.
(i) -7 ___ 8
(ii) -8 ___ -7
(iii) -999 ___ -1000
(iv) 0 ___ -200
Answer:
(i) \( -7 < 8 \). A negative number is always smaller than a positive number.
(ii) \( -8 < -7 \). On the number line, -8 is to the left of -7, making it smaller.
(iii) \( -999 > -1000 \). For negative numbers, the number closer to zero is greater.
(iv) \( 0 > -200 \). Zero is always greater than any negative number.
In simple words: Think of a number line. Numbers on the right are always bigger (>). Numbers on the left are always smaller (<). Zero is bigger than any negative number.

🎯 Exam Tip: For negative numbers, the number that looks 'smaller' (closer to zero) is actually larger. Always compare their positions on the number line.

Question 10. Arrange the following integers in ascending order.
(i) -11, 12, -13, 14, -15, 16, -17, 18, -19, -20
(ii) -28, 6, -5, -40, 8, 0, 12, -1, 4, 22
(iii) -100, 10, -1000, 100, 0, -1, 1000, 1, -10
Answer:
(i) First, separate positive and negative integers:
Positive: 12, 14, 16, 18
Negative: -11, -13, -15, -17, -19, -20
Arranging positive integers in ascending order: 12, 14, 16, 18
Arranging negative integers in ascending order (most negative first): -20, -19, -17, -15, -13, -11
So, the full ascending order is: -20, -19, -17, -15, -13, -11, 12, 14, 16, 18.
(ii) Separating positive, negative integers and zero:
Positive: 6, 8, 12, 4, 22
Negative: -28, -5, -40, -1
Zero: 0
Arranging positive integers: 4, 6, 8, 12, 22
Arranging negative integers: -40, -28, -5, -1
The final ascending order is: -40, -28, -5, -1, 0, 4, 6, 8, 12, 22.
(iii) Separating positive, negative integers and zero:
Positive: 10, 100, 1000, 1
Negative: -100, -1000, -1, -10
Zero: 0
Arranging positive integers: 1, 10, 100, 1000
Arranging negative integers: -1000, -100, -10, -1
The final ascending order is: -1000, -100, -10, -1, 0, 1, 10, 100, 1000.
In simple words: To arrange numbers from smallest to biggest (ascending order), first list all negative numbers from largest absolute value to smallest (e.g., -100 before -10). Then, place zero, and finally list all positive numbers from smallest to biggest.

🎯 Exam Tip: Always place the most negative number first in ascending order, followed by less negative numbers, then zero, and finally positive numbers in increasing order.

Objective Type Questions

Question 12. There are ......... positive integers from -5 to 6.
(a) 5
(b) 6
(c) 7
(d) 11
Answer: (b) 6
In simple words: Positive integers are numbers greater than zero. From -5 to 6, the positive integers are 1, 2, 3, 4, 5, and 6. If you count them, there are 6 such numbers.

🎯 Exam Tip: Be careful to only count positive integers when asked, ignoring zero and negative numbers.

Question 13. The opposite of 20 units to the left of 0 is
(a) 20
(b) 0
(c) -20
(d) 40
Answer: (a) 20
In simple words: "20 units to the left of 0" means -20. The opposite of -20 is +20, or simply 20.

🎯 Exam Tip: Break the question into two steps: first find the number, then find its opposite.

Question 14. One unit to the right of -7 is
(a) +1
(b) -8
(c) -7
(d) -6
Answer: (d) -6
In simple words: Moving "one unit to the right" on a number line means adding 1. So, -7 + 1 = -6.

🎯 Exam Tip: Always add 1 for "one unit to the right" and subtract 1 for "one unit to the left".

Question 15. 3 units to the left of 1 is
(a) -4
(b) -3
(c) -2
(d) 3
Answer: (c) -2
In simple words: Moving "3 units to the left" on a number line means subtracting 3. So, 1 - 3 = -2.

🎯 Exam Tip: Visualizing this on a number line can prevent simple errors. Start at 1 and count 3 steps left.

Question 16. The number which determines marking the position of any number to its opposite on a number line is
(a) -1
(b) 0
(c) 1
(d) 10
Answer: (b) 0
In simple words: Zero is the central point on a number line. The opposite of any number is found at the same distance from zero, but on the other side. This makes zero the key reference point for opposites.

🎯 Exam Tip: Remember that zero acts as the origin or the point of symmetry for finding opposites on a number line.

Question 17. Arrange the following integers in descending order.
(i) 14, 27, 15, -14, -9, 0, 11, -17
(ii) -99, -120, 65, -46, 78, 400, -600
(iii) 111, -222, 333, -444, 555, -666, 777, -888
Answer:
(i) First, separate positive, negative integers and zero:
Positive: 14, 27, 15, 11
Negative: -14, -9, -17
Zero: 0
Arranging positive integers in descending order: 27, 15, 14, 11
Arranging negative integers in descending order (closest to zero first): -9, -14, -17
So, the full descending order is: 27, 15, 14, 11, 0, -9, -14, -17.
(ii) Separating positive and negative integers:
Positive: 65, 78, 400
Negative: -99, -120, -46, -600
Arranging positive integers in descending order: 400, 78, 65
Arranging negative integers in descending order: -46, -99, -120, -600
The final descending order is: 400, 78, 65, -46, -99, -120, -600.
(iii) Separating positive and negative integers:
Positive: 111, 333, 555, 777
Negative: -222, -444, -666, -888
Arranging positive integers in descending order: 777, 555, 333, 111
Arranging negative integers in descending order: -222, -444, -666, -888
The final descending order is: 777, 555, 333, 111, -222, -444, -666, -888.
In simple words: To arrange numbers from biggest to smallest (descending order), start with the largest positive numbers. Then, if present, include zero. Finally, list all negative numbers from the one closest to zero (the 'least negative') to the one furthest from zero (the 'most negative').

🎯 Exam Tip: For descending order, always start with the largest positive number, then smaller positive numbers, then zero, and finally negative numbers, with the negative number closest to zero coming first.