RBSE Solutions Class 6 Maths Chapter 4 Negative Numbers and Integers Exercise 4.3

Question 1. Subtract the following.
(i) \( + 32 - (+12) \)
(ii) \( + 7 - (+15) \)
(iii) \( (-14) - (-20) \)
(iv) \( (-30) - (-15) \)
(v) \( 23 - (-10) \)
(vi) \( (-27) - 22 \)
Answer:
(i) \( + 32 - (+12) = 32 - 12 = 20 \)
(ii) \( + 7 - (+15) = 7 - 15 = -8 \)
(iii) \( (-14) - (-20) = -14 + 20 = 6 \)
(iv) \( (-30) - (-15) = -30 + 15 = -15 \)
(v) \( 23 - (-10) = 23 + 10 = 33 \)
(vi) \( (-27) - 22 = -27 - 22 = -49 \) When subtracting a negative number, it is the same as adding the positive version of that number.
In simple words: For each problem, change the subtraction of a positive number to adding a negative number, or change the subtraction of a negative number to adding a positive number, then do the math.

🎯 Exam Tip: Remember that subtracting a positive number is like moving left on the number line, while subtracting a negative number is like moving right.

Question 2. Fill in the blanks.
(i) \( -5 + \text{____} = 0 \)
(ii) \( 7 + \text{____} = 0 \)
(iii) \( 11 + (-11) = \text{____} \)
(iv) \( (-3) + \text{____} = -7 \)
(v) \( 14 - \text{____} = 16 \)
(vi) \( (-4) + \text{____} = -8 \)
Answer:
(i) \( -5 + 5 = 0 \) The number that makes an equation equal to zero when added is called the additive inverse.
(ii) \( 7 + (-7) = 0 \)
(iii) \( 11 + (-11) = 0 \)
(iv) \( (-3) + (-4) = -7 \)
(v) \( 14 - (-2) = 16 \)
(vi) \( (-4) + (-4) = -8 \)
In simple words: Find the number that completes each math sentence. For example, to get zero, you need to add the opposite number.

🎯 Exam Tip: For fill-in-the-blank questions involving integers, think about what number would balance the equation to make it true.

Question 3. Fill in the blanks with the sign >, < or =
(i) \( (-2) + (-9) \text{...............} (-2) + (-4) \)
(ii) \( (-21) + (-10) \text{...........} (-10) + (-21) \)
(iii) \( 45 - (-12) \text{...............} (-12) + 45 \)
(iv) \( (-14) + (14) \text{............} (-7) + (1) \)
Answer:
(i) First, calculate both sides:
\( (-2) + (-9) = -2 - 9 = -11 \)
\( (-2) + (-4) = -2 - 4 = -6 \)
Since \( -11 \) is less than \( -6 \) (it is further left on the number line), the sign is \( < \).
\( (-2) + (-9) < (-2) + (-4) \)
(ii) First, calculate both sides:
\( (-21) + (-10) = -21 - 10 = -31 \)
\( (-10) + (-21) = -10 - 21 = -31 \)
Since both sides are equal, the sign is \( = \).
\( (-21) + (-10) = (-10) + (-21) \)
(iii) First, calculate both sides:
\( 45 - (-12) = 45 + 12 = 57 \)
\( (-12) + 45 = 33 \)
Since \( 57 \) is greater than \( 33 \), the sign is \( > \).
\( 45 - (-12) > (-12) + 45 \)
(iv) First, calculate both sides:
\( (-14) + (14) = 0 \)
\( (-7) + (1) = -6 \) Comparing numbers is easier after performing the operations on both sides.
Since \( 0 \) is greater than \( -6 \) (it is further right on the number line), the sign is \( > \).
\( (-14) + (14) > (-7) + (1) \)
In simple words: Solve each side of the blank separately. Then, compare the two answers to see if the first is greater than, less than, or equal to the second.

🎯 Exam Tip: Always solve both sides of the expression completely before deciding which comparison sign (>, <, or =) to use.

Question 4. Find the value of the following.
(i) \( (-7) + (-4) + 11 \)
(ii) \( (-12) + (-3) - (-4) \)
(iii) \( 14 - 8 - (-2) \)
(iv) \( (-24) + (-12) - (-8) \)
Answer:
(i) We need to find the sum of \( (-7) \), \( (-4) \), and \( 11 \).
First, add the negative numbers:
\( (-7) + (-4) = -11 \)
Then add \( 11 \) to the result:
\( -11 + 11 = 0 \)
So the value is \( 0 \).
(ii) We need to find the value of \( (-12) + (-3) - (-4) \).
First, combine the additions and subtractions:
\( (-12) + (-3) - (-4) \)
\( = -12 - 3 + 4 \)
\( = -15 + 4 \)
\( = -11 \)
So the value is \( -11 \).
(iii) We need to find the value of \( 14 - 8 - (-2) \).
First, perform the subtraction from left to right:
\( 14 - 8 = 6 \)
Then subtract the negative number:
\( 6 - (-2) = 6 + 2 = 8 \)
So the value is \( 8 \).
(iv) We need to find the value of \( (-24) + (-12) - (-8) \).
First, add the negative numbers:
\( (-24) + (-12) = -36 \)
Then subtract the negative number: Remember that subtracting a negative number is the same as adding its positive counterpart.
\( -36 - (-8) = -36 + 8 = -28 \)
So the value is \( -28 \).
In simple words: Calculate each expression by following the rules for adding and subtracting positive and negative numbers. Remember that subtracting a negative number changes to adding a positive number.

🎯 Exam Tip: When solving expressions with multiple operations, combine numbers with the same sign first, then perform the remaining additions and subtractions carefully. Pay close attention to the rules of signs.