NCERT Solutions for Class 6 Maths Chapter 6: Integers Exercise 6.3

Understanding Subtraction of Integers & Additive Inverse

To subtract an integer from another integer, we add its additive inverse. This is the gold standard rule of integer subtraction. The additive inverse of any integer is simply that same number with the opposite sign. For instance, the additive inverse of $+5$ is $-5$, and the additive inverse of $-8$ is $+8$. When we subtract a number, we change the subtraction sign to an addition sign and change the number being subtracted to its additive inverse.

Let's visualize this with a simple rule:
$a - b = a + (-b)$
$a - (-b) = a + b$

For example, if you are asked to find $10 - (-5)$, you convert the subtraction of $-5$ into the addition of its additive inverse, $+5$. The expression becomes $10 + 5$, which is $15$. This clear concept eliminates confusion about double negative signs and helps you solve problems flawlessly on your sketchpad or notebooks.

How to Subtract Integers Step-by-Step

1. Identify the Problem — Write down the given subtraction expression clearly. For example, $(-15) - (-18)$.
2. Find the Additive Inverse — Look at the second integer (the one being subtracted). Identify its additive inverse. Here, the second integer is $-18$, so its additive inverse is $+18$.
3. Convert Subtraction to Addition — Replace the subtraction sign with an addition sign, and replace the second integer with its additive inverse. The expression changes from $(-15) - (-18)$ to $(-15) + 18$.
4. Apply Addition Rules to Solve — Since we have one negative integer $(-15)$ and one positive integer $(18)$, we find the difference between their absolute values ($18 - 15 = 3$) and apply the sign of the larger absolute value (which is positive). The final answer is $3$.

NCERT Exercise 6.3 Core Solved Examples

• Example 1: Find $35 - (20)$ To find the solution, rewrite the subtraction of $+20$ as the addition of its additive inverse $-20$. $35 - 20 = 35 + (-20)$ Since the numbers have opposite signs, subtract the smaller absolute value from the larger absolute value ($35 - 20 = 15$). Because 35 is positive and has the larger absolute value, the result is $+15$.
• Example 2: Find $(-20) - (13)$ Write the expression by adding the additive inverse of $13$, which is $-13$. $(-20) - 13 = (-20) + (-13)$ Since both integers are negative, we add their absolute values ($20 + 13 = 33$) and keep the common negative sign. Result: $-33$.
• Example 3: Fill in the blank with >, < or =: $(-3) + (-6)$ ___ $(-3) - (-6)$ Step 1: Solve the Left-Hand Side (LHS): $(-3) + (-6) = -9$ Step 2: Solve the Right-Hand Side (RHS): $(-3) - (-6) = (-3) + 6 = 3$ Step 3: Compare LHS and RHS: Since $-9 < 3$, the blank must be filled with '<'. Therefore, $(-3) + (-6) < (-3) - (-6)$.

Exam Tip: Avoiding Sign Errors

Many Class 6 students make mistakes with the negative sign. A common error is writing $- (-x)$ as $-x$. Remember: Subtracting a negative number is exactly the same as adding a positive number. Think of it as 'taking away a debt', which makes you richer! Always use brackets to separate signs, e.g., write $12 - (-4)$ instead of $12 -- 4$, and convert it to $12 + 4 = 16$ before doing any arithmetic.

Practice Questions with Solutions

• Q: Find the value of: $(-7) - 8 - (-25)$ A: Step 1: Write down the expression: $(-7) - 8 - (-25)$ Step 2: Change the subtraction of $8$ to addition of $-8$, and subtraction of $-25$ to addition of $+25$. Expression: $(-7) + (-8) + 25$ Step 3: Add the negative integers first: $(-7) + (-8) = -15$ Step 4: Now solve the remaining addition: $(-15) + 25$ Since the signs are different, subtract $15$ from $25$ which gives $10$. Final answer: 10
• Q: Fill in the blank: $(-21) - (-10)$ ____ $(-31) + (-11)$ A: Step 1: Solve LHS: $(-21) - (-10) = (-21) + 10 = -11$ Step 2: Solve RHS: $(-31) + (-11) = -42$ Step 3: Compare LHS and RHS values: Since $-11$ is greater than $-42$ (it is closer to zero on the number line), LHS > RHS. Final answer: >
• Q: Find the value of: $50 - (-40) - (-2)$ A: Step 1: Write down the expression: $50 - (-40) - (-2)$ Step 2: Convert subtractions to addition of opposites: $50 + 40 + 2$ Step 3: Add the positive integers together: $50 + 40 = 90$, then $90 + 2 = 92$ Final answer: 92
• Q: Find the value of: $(-13) + 32 - 8 - 1$ A: Step 1: Write the expression: $(-13) + 32 - 8 - 1$ Step 2: Group positive and negative terms together: $32 + (-13) + (-8) + (-1)$ Step 3: Add all negative integers: $(-13) + (-8) + (-1) = -22$ Step 4: Simplify the final expression: $32 + (-22) = 10$ Final answer: 10

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