Class 6 Maths Integers Worksheet - Free Printable

Solution to the Problems

#### Q.1. Write 'True' or 'False' for the following:

(i) $-20^\circ \text{C}$ represent temperature "above $20^\circ \text{C}$"
- False: $-20^\circ \text{C}$ is a temperature below $0^\circ \text{C}$, not above $20^\circ \text{C}$.

(ii) $8 > (-10)$
- True: $8$ is greater than $-10$ because positive numbers are always greater than negative numbers.

(iii) $|-2| = 2$
- True: The absolute value of $-2$ is $2$, as the absolute value function removes the sign.

(iv) $|-4 - 2| = -6$
- False: First, calculate $-4 - 2 = -6$. Then, the absolute value of $-6$ is $6$, not $-6$.

(v) $(-3) > (-5)$
- True: On the number line, $-3$ is to the right of $-5$, so $-3$ is greater than $-5$.

Answers:
(i) False
(ii) True
(iii) True
(iv) False
(v) True

---

#### Q.2. Fill up the blanks:

(i) Integer which is neither positive nor negative is _______
- 0: The integer $0$ is neither positive nor negative.

(ii) Predecessor of $(-99)$ is _______
- $-100$: The predecessor of $-99$ is $-99 - 1 = -100$.

(iii) $|-26 - 14| = $ _______
- $40$: First, calculate $-26 - 14 = -40$. Then, the absolute value of $-40$ is $40$.

(iv) Successor of $(-100)$ is _______
- $-99$: The successor of $-100$ is $-100 + 1 = -99$.

(v) Largest 3-digit negative integer is _______
- $-100$: The largest 3-digit negative integer is $-100$.

Answers:
(i) $0$
(ii) $-100$
(iii) $40$
(iv) $-99$
(v) $-100$

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#### Q.3. Subtract $(-25)$ from the sum of $15$ and $35$.

First, find the sum of $15$ and $35$:
$$
15 + 35 = 50
$$
Next, subtract $(-25)$ from $50$. Subtracting a negative is the same as adding:
$$
50 - (-25) = 50 + 25 = 75
$$

Answer:
$$
\boxed{75}
$$

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#### Q.4. Add the sum of $(-2063)$ and $562$ to $(-2063)$.

First, find the sum of $(-2063)$ and $562$:
$$
-2063 + 562 = -1501
$$
Next, add this result to $(-2063)$:
$$
-1501 + (-2063) = -1501 - 2063 = -3564
$$

Answer:
$$
\boxed{-3564}
$$

---

#### Q.5. Simplify:

(i) $(-50) + (-200) - (-500)$
- Simplify step by step:
$$
(-50) + (-200) - (-500) = -50 - 200 + 500 = -250 + 500 = 250
$$

(ii) $23 - (-15) + 12$
- Simplify step by step:
$$
23 - (-15) + 12 = 23 + 15 + 12 = 38 + 12 = 50
$$

(iii) $(24 + 6) \div (-3)$
- Simplify step by step:
$$
(24 + 6) \div (-3) = 30 \div (-3) = -10
$$

(iv) $19 + [10 \times (7 - 9)]$
- Simplify step by step:
$$
19 + [10 \times (7 - 9)] = 19 + [10 \times (-2)] = 19 + (-20) = 19 - 20 = -1
$$

(v) $12 \div [16 - (6 + 2 - 6 + 3)]$
- Simplify step by step:
$$
16 - (6 + 2 - 6 + 3) = 16 - (6 + 2 - 6 + 3) = 16 - (5) = 11
$$
$$
12 \div 11 = \frac{12}{11}
$$

Answers:
(i) $250$
(ii) $50$
(iii) $-10$
(iv) $-1$
(v) $\frac{12}{11}$

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#### Q.6. Write additive inverse of:

(i) $(-5347)$
- The additive inverse of $-5347$ is $5347$.

(ii) $0$
- The additive inverse of $0$ is $0$.

(iii) $4231$
- The additive inverse of $4231$ is $-4231$.

(iv) $2132 - 132$
- First, simplify $2132 - 132 = 2000$. The additive inverse of $2000$ is $-2000$.

(v) $-10 - 5$
- First, simplify $-10 - 5 = -15$. The additive inverse of $-15$ is $15$.

Answers:
(i) $5347$
(ii) $0$
(iii) $-4231$
(iv) $-2000$
(v) $15$

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#### Q.7. Observe the number line given above and answer the following:

(i) What is the position of Reeta on the number line?
- Reeta is positioned at $-3$ on the number line.

(ii) What is the position of Seema?
- Seema is positioned at $5$ on the number line.

(iii) What is the distance between Reeta and Seema?
- The distance between two points on the number line is the absolute value of their difference:
$$
\text{Distance} = |5 - (-3)| = |5 + 3| = |8| = 8
$$

Answers:
(i) $-3$
(ii) $5$
(iii) $8$

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Final Answers:

Q.1:
(i) False
(ii) True
(iii) True
(iv) False
(v) True

Q.2:
(i) $0$
(ii) $-100$
(iii) $40$
(iv) $-99$
(v) $-100$

Q.3:
$$
\boxed{75}
$$

Q.4:
$$
\boxed{-3564}
$$

Q.5:
(i) $250$
(ii) $50$
(iii) $-10$
(iv) $-1$
(v) $\frac{12}{11}$

Q.6:
(i) $5347$
(ii) $0$
(iii) $-4231$
(iv) $-2000$
(v) $15$

Q.7:
(i) $-3$
(ii) $5$
(iii) $8$

Boxed Final Answer:
$$
\boxed{75, -3564, 250, 50, -10, -1, \frac{12}{11}, 5347, 0, -4231, -2000, 15, -3, 5, 8}
$$