RBSE Solutions Class 6 Maths Chapter 4 Negative Numbers and Integers Exercise 4.2

Question 1. Using the number line find the integer which is:
(i) 4 more than 5
(ii) + 4 more than (- 4)
(iii) 6 less than 3
(iv) + 4 less than (-1)
Answer:
(i) To find 4 more than 5, start at 5 on the number line and move 4 units to the right. This brings you to 9. So, \( 5 + 4 = 9 \). Moving right on the number line means adding a positive value.
(ii) To find + 4 more than -4, start at -4 on the number line and move 4 units to the right. This brings you to 0. So, \( -4 + 4 = 0 \). Adding a number and its opposite always results in zero.
(iii) To find 6 less than 3, start at 3 on the number line and move 6 units to the left. This brings you to -2. So, \( 3 - 6 = -2 \). Moving left on the number line means subtracting a positive value.
(iv) To find + 4 less than -1, start at -1 on the number line and move 4 units to the left. This brings you to -5. So, \( -1 - 4 = -5 \). Subtracting a positive number from a negative number makes the result even more negative.
In simple words: When finding numbers on a line, move right for "more than" and left for "less than". Add for right moves, subtract for left moves.

🎯 Exam Tip: Always pay attention to the direction of movement on the number line; "more than" means moving right (positive direction), and "less than" means moving left (negative direction).

Question 2. Find the value of the following using the number line.
(i) 9 +(-3)
(ii) (-4) + (-3)
Answer:
(i) For \( 9 + (-3) \): Start at 0, move 9 units to the right to reach 9. Then, because you are adding -3 (a negative number), move 3 units to the left from 9. You will land on 6. So, \( 9 + (-3) = 9 - 3 = 6 \). Adding a negative number is the same as subtracting a positive number.
(ii) For \( (-4) + (-3) \): Start at 0, move 4 units to the left to reach -4. Then, because you are adding another negative number (-3), move 3 more units to the left from -4. You will land on -7. So, \( (-4) + (-3) = -4 - 3 = -7 \). When adding two negative numbers, the result is a larger negative number.
In simple words: To add on a number line, start at the first number. If you add a positive number, move right. If you add a negative number, move left.

🎯 Exam Tip: Remember that adding a negative number is equivalent to subtracting its positive counterpart. Visualize this movement on the number line to avoid mistakes.

Question 3. Without using the number line find the sum of the following.
(i) 11 + (-2)
(ii) (-4) + (-6)
(iii) (-250) + 150
(iv) (- 380) + (- 270)
(v) (-14) + 4
(vi) (- 180) + (-80)
Answer:
(i) \( 11 + (-2) = 11 - 2 = 9 \). When adding a negative number to a positive number, subtract the smaller absolute value from the larger one and keep the sign of the number with the larger absolute value.
(ii) \( (- 4) + (- 6) = - 4 - 6 = - 10 \). When adding two negative numbers, sum their absolute values and keep the negative sign.
(iii) \( (-250) + 150 = - 250 + 150 = - 100 \). The absolute value of -250 is larger than 150, so the result is negative.
(iv) \( (- 380) + (- 270) = - 380 - 270 = - 650 \). Both numbers are negative, so we add their values and keep the negative sign.
(v) \( (-14) + 4 = -10 \). Here, 14 is larger than 4, and since 14 is negative, the answer will also be negative.
(vi) \( (- 180) + (-80) = - 180 - 80 = - 260 \). Adding two negative numbers always results in a larger negative sum.
In simple words: When signs are different, subtract the numbers and use the sign of the bigger number. When signs are the same, add the numbers and use that sign.

🎯 Exam Tip: Always remember the rules for adding integers: same signs mean add and keep the sign; different signs mean subtract the smaller absolute value from the larger and keep the sign of the number with the larger absolute value.

Question 4. Find the sum of the following:
(i) 137 + (-354) +125
(ii) (- 312) + 39 + 192
(iii) 37 +(-3)+ 24 +(-8)
(iv) 102 + (-24) + (24) + (-11)
Answer:
(i) \( 137 + (-354) + 125 \)
\( = 137 - 354 + 125 \)
\( = (137 + 125) - 354 \) (Group positive numbers together first)
\( = 262 - 354 \)
\( = -92 \). Adding numbers with different signs means subtracting their absolute values.
(ii) \( (- 312) + 39 + 192 \)
\( = - 312 + (39 + 192) \) (Group positive numbers together)
\( = - 312 + 231 \)
\( = -81 \). The negative number has a larger absolute value, so the result is negative.
(iii) \( 37 + (-3) + 24 + (-8) \)
\( = 37 - 3 + 24 - 8 \)
\( = (37 + 24) - (3 + 8) \) (Group positive numbers and negative numbers separately)
\( = 61 - 11 \)
\( = 50 \). This method simplifies the calculation by combining like-signed numbers first.
(iv) \( 102 + (- 24) + (24) + (-11) \)
\( = 102 - 24 + 24 - 11 \)
\( = 102 + (-24 + 24) - 11 \) (Notice that -24 and +24 cancel each other out)
\( = 102 + 0 - 11 \)
\( = 102 - 11 \)
\( = 91 \). Identifying pairs of opposite numbers simplifies calculations greatly.
In simple words: To add several numbers, combine all the positive numbers first, then combine all the negative numbers. After that, find the total by subtracting the smaller sum from the larger sum.

🎯 Exam Tip: When dealing with multiple integers, group positive numbers together and negative numbers together before performing the final addition or subtraction. Also, look for any numbers that are opposites (like -24 and +24) as they will cancel each other out to zero.