GSEB Class 6 Maths Solutions Chapter 6 Integers Exercise 6.1

Gujarat Board Textbook Solutions Class 6 Maths Chapter 6 Integers Ex 6.1

 

Question 1. Write opposites of the following:
(a) Increase in weight
(b) 30 km north
(c) 326 BC
(d) Loss of 700
(e) 100 m above sea level.
Answer:
(a) Decrease in weight
(b) 30 km south
(c) 326 AD
(d) Gain of 700
(e) 100 m below sea level
In simple words: To find the opposite, think about the reverse action or state. For example, the opposite of "increase" is "decrease," and the opposite of "above" is "below."

Exam Tip: Always consider the context when finding opposites, especially for directional or financial terms. An increase is countered by a decrease, and moving north is countered by moving south.

 

Question 2. Represent the following numbers as integers with appropriate signs.
(a) An aeroplane is flying at a height two thousand metre above the ground.
(b) A submarine is moving at a depth, eight hundred metre below the sea level.
(c) A deposit of rupees two hundred.
(d) A withdrawal of rupees seven hundred.
Answer:
(a) \( + 2000 \) m
(b) \( - 800 \) m
(c) \( + 200 \)
(d) \( - 700 \)
In simple words: When things go up, like height above ground or money deposited, we use a plus sign. When things go down, like depth below sea level or money withdrawn, we use a minus sign.

Exam Tip: Remember that 'above', 'gain', 'deposit' indicate positive integers, while 'below', 'loss', 'withdrawal' indicate negative integers. Always include the sign for clarity.

 

Question 3. Represent the following numbers on a number line:
(a) \( + 5 \)
(b) \( - 10 \)
(c) \( + 8 \)
(d) \( - 1 \)
(e) \( - 6 \)
Answer:
(a) Representation of \( + 5 \): Point A on the number line represents \( + 5 \).
(b) Representation of \( - 10 \): Point B on the number line represents \( - 10 \).
(c) Representation of \( + 8 \): Point C on the number line represents \( + 8 \).
(d) Representation of \( - 1 \): Point D on the number line represents \( - 1 \).
(e) Representation of \( - 6 \): Point E on the number line represents \( - 6 \).
In simple words: To show a number on a number line, you draw a line with zero in the middle. Positive numbers go to the right, and negative numbers go to the left. Mark the number with a point.

Exam Tip: When drawing a number line, ensure equal spacing between consecutive integers. Clearly label the point representing the integer with a capital letter.

 

Question 4. Adjacent figure is a vertical number line, representing integers. Observe it and locate the following points:
(a) If point D is \( + 8 \), then which point is \( - 8 \)?
(b) Is point G a negative integer or a positive integer?
(c) Write integers for points B and E.
(d) Which point marked on this number line has the least value?
(e) Arrange all the points in decreasing order of value.
Answer:
(a) The point F represents \( - 8 \).
(b) The point G is a negative integer.
(c) The integer at B is \( + 4 \). The integer at E is \( - 10 \).
(d) The point E corresponds to the least number.
(e) The decreasing order is: D, C, B, A, O, H, G, F, E.
In simple words: On a vertical number line, numbers get bigger as you go up and smaller as you go down. Zero is usually in the middle.

Exam Tip: For vertical number lines, understand that values increase upwards and decrease downwards. Identifying the position of zero and the unit scale is crucial for correctly locating other points.

 

Question 5. Following is the list of temperatures of five places in India on a particular day of the year.

(a) Write the temperatures of these places in the form of integers in the blank column.
(b) Following is the number line representing the temperature in degree Celsius. Plot the name of the city against its temperature.
(c) Which is the coolest place?
(d) Write the names of the places where temperatures are above \( 10^{\circ}\text{C} \).
Answer:
(a)(b) The cities are plotted on the number line at their respective integer temperatures: Siachin at \( -10^{\circ}\text{C} \), Shimla at \( -2^{\circ}\text{C} \), Srinagar at \( -5^{\circ}\text{C} \), Delhi at \( +20^{\circ}\text{C} \), and Ahmedabad at \( +30^{\circ}\text{C} \).
(c) Siachin (\( -10^{\circ}\text{C} \)) is the coolest place.
(d) Delhi (\( +20^{\circ}\text{C} \)) and Ahmedabad (\( +30^{\circ}\text{C} \)) are the places where temperatures are above \( 10^{\circ}\text{C} \).
In simple words: "Below \( 0^{\circ}\text{C} \)" means negative temperatures, and "above \( 0^{\circ}\text{C} \)" means positive temperatures. Cooler places have lower (more negative) numbers. You can mark each city on a temperature line at its correct spot.

Exam Tip: When working with temperatures, remember that 'below zero' translates to negative integers, and 'above zero' translates to positive integers. The lowest number represents the coolest temperature.

 

Question 6. In each of the following pairs, which number is to the right of the other on the number line?
(a) 2, 9
(b) -3, -8
(c) 0, -1
(d) -11, 10
(e) -6, 6
Answer: The greater integer is on the right of the smaller.
(a) 2, 9: The integer 9 is to the right of integer 2.
(b) -3, -8: The integer -3 is to the right of integer -8.
(c) 0, -1: The integer 0 is to the right of integer -1.
(d) -11, 10: The integer 10 is to the right of integer -11.
(e) -6, 6: The integer 6 is to the right of integer -6.
(f) 1, -100: The integer 1 is to the right of integer -100.
In simple words: On a number line, numbers increase as you move to the right. So, the bigger number in any pair will always be on the right side.

Exam Tip: Visualize the number line; positive numbers are to the right of zero, and negative numbers are to the left. Any positive number is always to the right of any negative number.

 

Question 7. Write all the integers between the given pairs (write them in the increasing order).
(a) 0 and -7
(b) -4 and 4
(c) -8 and -15
(d) -30 and -23
Answer:
(a) 0 and -7: The integers between 0 and -7 (in increasing order) are: -6, -5, -4, -3, -2 and -1.
(b) -4 and 4: The integers between -4 and 4 (in increasing order) are: -3, -2, -1, 0, 1, 2 and 3.
(c) -8 and -15: The integers between -8 and -15 (in increasing order) are: -14, -13, -12, -11, -10, -9.
(d) -30 and -23: The integers between -30 and -23 (in increasing order) are: -29, -28, -27, -26, -25, and -24.
In simple words: To find integers between two numbers, list all the whole numbers that are larger than the first number and smaller than the second number. Always put them in order from smallest to largest.

Exam Tip: Remember to list integers in *increasing* order. Carefully check the inclusive/exclusive nature of 'between' to ensure you don't include the boundary numbers themselves.

 

Question 8.
(a) Write four negative integers greater than -20.
(b) Write four negative integers less than -10.
Answer:
(a) -19, -18, -17 and -16 are greater than -20. (Any negative integer closer to zero than -20 is greater than -20).
(b) -11, -12, -13 and -14 are less than -10. (Any negative integer further from zero than -10 is less than -10).
In simple words: For negative numbers, "greater than" means closer to zero, and "less than" means further away from zero.

Exam Tip: On a number line, numbers increase as you move to the right. So, "greater than" means to the right, and "less than" means to the left, regardless of whether the numbers are positive or negative.

 

Question 9. For the following statements, write True (T) or False (F). If the statement is false, correct the statement.
(a) -8 is to the right of -10 on a number line.
(b) -100 is to the right of -50 on a number line.
(c) Smallest negative integer is -1.
(d) -26 is greater than -25.
Answer:
(a) True.
(b) False; correct statement: -100 is to the left of -50 on a number line.
(c) False; correct statement: 'Greatest negative integer is -1.'
(d) False; correct statement: '-26 is smaller than -25.'
In simple words: Remember, numbers get bigger as you go right on a number line. If a number is on the right, it's bigger. If it's on the left, it's smaller.

Exam Tip: Pay close attention to negative numbers. For negatives, a smaller absolute value means a greater number (e.g., -5 is greater than -100 because -5 is closer to 0).

 

Question 10. Draw a number line and answer the following:
(a) Which number will we reach if we move 4 numbers to the right of -2.
(b) Which number will we reach if we move 5 numbers to the left of 1.
(c) If we are at -8 on the number line, in which direction should we move to reach -13?
(d) If we are at -6 on the number line, in which direction should we move to reach -1?
Answer:
(a) Starting from -2 and moving 4 steps towards right (each step being equal to 1 unit) we will reach at 2.
(b) Starting from 1 and moving 5 steps, each of 1 unit, towards left, we will reach at number -4.
(c) To reach -13 from -8, we have to move towards the left of -8 on the number line. This is because -13 is smaller than -8.
(d) To reach -1 from -6, we have to move towards the right of -6 on the number line. This is because -1 is greater than -6.
In simple words: Moving right on a number line means adding, and moving left means subtracting. To decide the direction, compare the start and end numbers.

Exam Tip: Remember that moving to the right on a number line represents addition (increasing value), and moving to the left represents subtraction (decreasing value). Always draw a small sketch if you find it confusing.

 

Addition of integers:
Like whole numbers, the integers can also be added. We obey the following rules

Rule I: Adding integers with like signs:
For adding integers with like signs (both positive or both negative), we add their numerical values, and place the common sign before the sum.
Examples:
(i) \( (+ 2) + (+ 10) = (+ 12) \)
(ii) \( (-3) + (- 7) = (- 10) \)

Rule II: Adding integers of unlike signs:
For adding integers of unlike signs, we find the difference of their numerical values and give the result of the sign of the integer with the greater numerical value.
(i) \( (+13) + (-8) = (+ 5) \)
(ii) \( (+ 5) + (- 18) = (- 13) \)