GSEB Class 6 Maths Solutions Chapter 6 Integers InText Questions

Try These (NcErt Page 116)

Question 1. Write the following numbers with appropriate signs:
(a) 100 m below sea level.
(b) 25°C above 0°C temperature.
(c) 15°C below 0°C temperature.
(d) Any five numbers less than 0.
Answer:
(a) 100 m below sea level \( \implies -100 \) m
(b) 25°C above 0°C temperature \( \implies +25 \)° C
(c) 15°C below 0°C temperature \( \implies -15 \)° C
(d) Five numbers less than 0: { \( -1, -3, -10, -25, -105 \) }
Note:
(i) If profit is shown by a '+' sign, then loss may be shown using a '-' sign.
(ii) If moving up is shown by a '+' sign, then going down may be shown using a '-' sign.
(iii) If earnings are shown by a '+' sign, then spending may be shown using a '-' sign.
(iv) If temperature above 0° is a '+' sign, then temperature below 0° may be shown by a '-' sign.
(v) If depositing money in the bank is a '+' sign, then withdrawal is a '-' sign.
In simple words: When things go down or reduce, use a minus sign. When things go up or increase, use a plus sign. This helps you track changes in quantity or value.

Exam Tip: Remember that "below", "loss", "down", "spending", and "withdrawal" are usually associated with negative integers, while "above", "profit", "up", "earnings", and "deposit" are associated with positive integers.

Try These (NcErt Page 118)

Question 1. Mark 3, 7, -4, -8, -1 and -3 on the number line.
Answer:
The given numbers are marked on the number line as shown below:

The integer -8 is at A
The integer -3 is at C
The integer 3 is at E
The integer -4 is at B
The integer -1 is at D
The integer 7 is at F
Note: Look at the number line provided here. We observe that for every integer to the right of zero, there exists a corresponding integer to its left (at the same distance from zero but with a negative sign). Similarly, for every integer to the left of zero, there is a corresponding integer to its right (at the same distance from zero but with a positive sign).
In simple words: To mark numbers, draw a straight line with a zero in the middle. Positive numbers go to the right, and negative numbers go to the left. Just put a dot or a label at the correct spot for each number. Every number has a partner on the other side of zero with the opposite sign.

Exam Tip: When drawing a number line, ensure equal spacing between consecutive integers and clearly label the origin (0) and the direction of positive and negative numbers with arrows.

Try These (Page 119)

Question 1. Compare the following pairs of numbers using> or <.
(i) 0 ______ -8
(ii) -1 ______ -15
(iii) 5 ______ -5
(iv) 11 ______ 15
(v) 0 ______ 6
(vi) -20 ______ 2
Answer:
(i) \( 0 > -8 \)
(ii) \( -1 > -15 \)
(iii) \( 5 > -5 \)
(iv) \( 11 < 15 \)
(v) \( 0 < 6 \)
(vi) \( -20 < 2 \)
In simple words: For any two numbers, the one further to the right on a number line is always bigger. This means zero is larger than any negative number, and any positive number is larger than any negative number.

Exam Tip: Remember that positive numbers are always greater than negative numbers. For two negative numbers, the one closer to zero is greater.

Try These (Page 125)

Question 1. Draw a figure on the ground in the form of a horizontal number line as shown below. Frame questions as given in the said example and ask your friends.
Answer: Do it yourself.
In simple words: This question asks you to make your own number line and create questions based on it, then try them out with your friends.

Exam Tip: When doing practical activities, ensure your number line is clearly marked with equal intervals to represent integers accurately.

Try These (Page 125)

Question 1. Find the answers of the following additions:
(a) (-11) + (-12)
(b) (+10) +(+4)
(c) (-32) + (-25)
(d) (+23) + (+40)
Answer:
(a) \( (-11) + (-12) = -[11 + 12] = -23 \)
(b) \( (+10) + (+4) = +[10 + 4] = +14 \)
(c) \( (-32) + (-25) = -[32 + 25] = -57 \)
(d) \( (+23) + (+40) = +[23 + 40] = +63 \)
In simple words: When adding numbers with the same sign, you add their absolute values and keep the original sign. If both are negative, the answer is negative; if both are positive, the answer is positive.

Exam Tip: Always check the signs of the integers before adding. If signs are the same, sum the numbers and keep the sign. If signs are different, find the difference and use the sign of the larger absolute value.

Question 1. Find the solution of the following:
(a) (-7) + (+8)
(b) (-9) + (+13)
(c) (+7) + (-10)
(d) (+12) + (-7)
Answer:
(a) \( (-7) + (+8) \):
The opposite of \( (-7) \) is \( (+7) \). So, we can write \( (+8) \) as \( (+7) + (+1) \).
\( (-7) + (+8) = (-7) + (+7) + (+1) \)
\( = 0 + (+1) \) [because \( (-7) + (+7) = 0 \)]
\( = +1 \)
(b) \( (-9) + (+13) \):
We can write \( (+13) \) as \( (+9) + (+4) \).
\( (-9) + (+13) = (-9) + (+9) + (+4) \)
\( = 0 + (+4) \) [because \( (-9) + (+9) = 0 \)]
\( = +4 = 4 \)
(c) \( (+7) + (-10) \):
We can write \( (-10) \) as \( (-7) + (-3) \).
\( (+7) + (-10) = (+7) + (-7) + (-3) \)
\( = 0 + (-3) \) [because \( (+7) + (-7) = 0 \)]
\( = -3 \)
(d) \( (+12) + (-7) \):
We can write \( (+12) \) as \( (+7) + (+5) \).
\( (+12) + (-7) = (+7) + (+5) + (-7) \)
\( = (+7) + (-7) + (+5) \)
\( = 0 + (+5) \)
\( = +5 = 5 \)
In simple words: When adding numbers with different signs, you subtract the smaller number from the larger number. Then, you use the sign of the number that has the bigger absolute value. If the positive number is larger, the answer is positive; if the negative number is larger, the answer is negative.

Exam Tip: When adding integers with different signs, always determine which integer has the greater absolute value, as its sign will be the sign of the final sum.

Try These (Page 127)

Question 1. Find the solution of the following additions using a number line.
(a) (-2) + 6
(b) (-6) + 2
Answer:
(a) \( (-2) + 6 \):
First, move 2 steps to the left of 0 to reach -2. From there, move 6 steps to the right to reach 4.
\( (-2) + (+6) = +4 \)

(b) \( (-6) + 2 \):
On the number line, we first move 6 equal steps (each of 1 unit) to the left of 0, to reach -6. Then, move 2 steps to the right of -6 to reach -4.
\( (-6) + (+2) = -4 \)

In simple words: When using a number line to add, start at the first number. If you add a positive number, move right. If you add a negative number (or subtract), move left. The point where you finish is your answer.

Exam Tip: For number line additions, always begin at the first integer. Move right for positive additions and left for negative additions. Count steps carefully to avoid errors.

Question 2. Find the solution of the following without using number line:
(a) (+7) + (-11)
(b) (-13) + (+10)
(c) (-7) + (+9)
(d) (+10) + (-5)
Answer:
(a) \( (+7) + (-11) \):
We can write \( (-11) \) as \( (-7) + (-4) \).
\( (+7) + (-11) = (+7) + (-7) + (-4) = 0 + (-4) \)
\( [(+7) + (-7) = 0] = -4 \)
Thus, \( (+7) + (-11) = -4 \)
(b) \( (-13) + (+10) \):
We can write \( (-13) \) as \( (-10) + (-3) \).
\( (-13) + (+10) = (-10) + (-3) + (+10) \)
\( = (-10) + (+10) + (-3) \)
\( = 0 + (-3) = -3 \)
\( [(-10) + (+10) = 0] \)
Thus, \( (-13) + (+10) = -3 \)
(c) \( (-7) + (+9) \):
We can write \( (+9) \) as \( (+7) + (+2) \).
\( (-7) + (+9) = (-7) + (+7) + (+2) = 0 + (+2) \)
\( [(-7) + (+7) = 0] \)
\( = +2 \)
Thus, \( (-7) + (+9) = +2 \)
(d) \( (+10) + (-5) \):
We can write \( (+10) \) as \( (+5) + (+5) \).
\( (+10) + (-5) = (+5) + (+5) + (-5) = +5 + 0 \)
\( [(+5) + (-5) = 0] \)
Thus, \( (+10) + (-5) = (+5) \)
In simple words: When adding integers without a number line, use the rules of signs. If signs are different, subtract the smaller number from the larger one, then use the sign of the larger number. If signs are the same, just add them and keep that sign.

Exam Tip: To add integers without a number line, identify if the signs are the same or different. If different, find the absolute difference and use the sign of the number with the greater absolute value. If same, add the absolute values and keep the common sign.