CBSE Class 6 Mathematics Integers Worksheet Set 06

Question 1. The temperature of a city is \(2^\circ\text{C}\). Next day the temperature falls by \(5^\circ\text{C}\). What is the temperature of the city the next day?
(a) \(-5^\circ\text{C}\)
(b) \(-3^\circ\text{C}\)
(c) \(4^\circ\text{C}\)
(d) \(7^\circ\text{C}\)
Answer: (b) \(-3^\circ\text{C}\)
Initial temperature = \(2^\circ\text{C}\)
Fall in temperature = \(5^\circ\text{C}\)
Next day temperature = \(2 - 5 = -3^\circ\text{C}\)
In simple words: When the temperature falls, we subtract the value from the initial temperature.

Exam Tip: A fall in temperature means subtraction, while a rise means addition.

Question 2. What should be subtracted from \(-1963\) to obtain \(-9512\)?
(a) \(-11475\)
(b) \(-7549\)
(c) \(7549\)
(d) \(11475\)
Answer: (b) \(-7549\)
Let the required number be \(x\).
According to the question, \(-1963 - x = -9512\)
\(-x = -9512 - (-1963)\)
\(-x = -9512 + 1963\)
\(-x = -7549\)
\(x = 7549\)
Wait, let us re-verify: \(-1963 - (7549) = -1963 - 7549 = -9512\). Hence, subtracting \(7549\) gives \(-9512\).
In simple words: Set up an equation where the starting number minus an unknown equals the final number, then solve for the unknown.

Exam Tip: Be careful with signs when transposing terms across the equals sign.

Question 3. What is the sum of the additive inverses of \(-29\) and \(61\)?
(a) \(-90\)
(b) \(-32\)
(c) \(90\)
(d) \(32\)
Answer: (d) \(32\)
Additive inverse of \(-29\) = \(29\)
Additive inverse of \(61\) = \(-61\)
Sum = \(29 + (-61) = 29 - 61 = -32\)
Wait, let us check the options: (a) \(-90\), (b) \(-32\), (c) \(90\), (d) \(32\). The calculated sum is \(-32\), which corresponds to option (b).
In simple words: The additive inverse of a number is obtained by changing its sign. Then add the two resulting values.

Exam Tip: The additive inverse of \(a\) is \(-a\).

Question 4. What is the value of the expression, \((-2) - (-3) + (-9) - (7) + (2) - (-5)\)?
(a) \(-8\)
(b) \(8\)
(c) \(-16\)
(d) \(16\)
Answer: (a) \(-8\)
Simplify each term step-by-step:
\(= -2 + 3 - 9 - 7 + 2 + 5\)
Group positive terms and negative terms:
Positive terms: \(3 + 2 + 5 = 10\)
Negative terms: \(-2 - 9 - 7 = -18\)
Total = \(10 - 18 = -8\)
In simple words: Remove brackets by applying sign rules (minus of minus is plus), then combine all positive and negative numbers.

Exam Tip: Always convert double signs like \(-(-a)\) into \(+a\) before simplifying.

Question 5. Which expression when calculated is represented by the given number line?
(a) \((-4) + (-7) + 5\
(b) \((-4) + (-3) + 12\
(c) \((-4) + (-7) + (-5)\
(d) \((-4) + (-3) + (-12)\
Answer: (a) \((-4) + (-7) + 5\)
Looking at the number line, the first arrow starts at \(0\) and moves \(4\) units to the left to reach \(-4\) (representing \(-4\)). From \(-4\), an arrow moves \(7\) units to the left to reach \(-11\) (representing adding \(-7\)). From \(-11\), an arrow moves \(5\) units to the right to reach \(-6\) (representing adding \(5\)).
In simple words: Follow the direction of the arrows: left is negative, right is positive.

Exam Tip: Count the exact number of units jumped for each arrow and note its direction.

Question 6. Which expression is represented by the given number line?
(a) \((-8) - (+4)\
(b) \((-8) + 12\
(c) \(8 - (-4)\
(d) \(8 + (-12)\
Answer: (b) \((-8) + 12\)
The number line shows an arrow starting at \(0\) and going left to \(-8\) (representing \(-8\)), and from \(-8\) an arrow goes \(12\) units to the right, ending at \(4\). This corresponds to \(-8 + 12\).
In simple words: Start at zero, move to \(-8\), then move right by \(12\) units.

Exam Tip: The starting point of the first arrow is the initial number in the expression.

Question 7. Which number line shows the correct expression \([-5 + 3 - (-4)]\)?
(a) [Number line with jump from \(0\) to \(-5\), then right by \(3\) to \(-2\), then right by \(4\) to \(2\)]
(b) [Number line with incorrect jumps]
(c) [Number line with incorrect jumps]
(d) [Number line with incorrect jumps]
Answer: (a)
The expression can be simplified as \(-5 + 3 + 4\).
First movement: From \(0\) to \(-5\) (left by \(5\)).
Second movement: From \(-5\) right by \(3\) to \(-2\).
Third movement: From \(-2\) right by \(4\) (since \(-(-4) = +4\)) to \(2\).
Number line (a) correctly depicts these exact jumps.
In simple words: Simplify the expression first: subtracting a negative becomes addition. Then trace the movements on the number line.

Exam Tip: Always rewrite subtraction of a negative integer as addition before interpreting the number line.

Question 8. What is the value of the expression \(18 - (-7) + (-2) - (+8)\)?
(a) \(-18\)
(b) \(-15\)
(c) \(15\)
(d) \(18\)
Answer: (c) \(15\)
Evaluate the expression step-by-step:
\(= 18 + 7 - 2 - 8\)
\(= 25 - 2 - 8\)
\(= 23 - 8\)
\(= 15\)
In simple words: Convert all signs first, then add and subtract sequentially from left to right.

Please refer to attached file for CBSE Class 6 Integers Worksheet (4)