CBSE Class 7 Mathematics Operations with Integers MCQs Set 10

Question. Value of (-2) × (-1) × (-5) × (-3) is
(a) 30
(b) –30
(c) 11
(d) –11

Answer: A

Question. Summary says product is negative if
(a) Both numbers are negative
(b) Both numbers are positive
(c) One is positive and one is negative
(d) One is zero

Answer: C

Question. Property a × (b + c) = a × b + a × c is called
(a) Associative
(b) Commutative
(c) Distributive
(d) Identity

Answer: C

Question. Value of 5 × (4 + (-2)) is
(a) 30
(b) 10
(c) 6
(d) –10

Answer: B

Question. Brahmagupta used the word "Dhana" for
(a) Negative numbers
(b) Zero
(c) Positive values
(d) Division

Answer: C

Question. Brahmagupta used the word "Rina" for
(a) Fortunes
(b) Debts
(c) Addition
(d) Positive values

Answer: B

Question. In test, +4 for correct and -2 for incorrect. Anita scored 40 marks with 15 correct answers. Incorrect answers were
(a) 5
(b) 10
(c) 15
(d) 20

Answer: B

Question. Temperature currently 8°C, drops 5°C each hour. Expression for temp after 4 hours is
(a) 8 – 5 × 4
(b) 8 + 5 × 4
(c) 4 × 5 – 8
(d) 8 – 5 – 4

Answer: A

Question. Sum is 27 and difference is 9, find the numbers
(a) 18, 9
(b) 20, 7
(c) 15, 12
(d) 10, 17

Answer: A

Question. Difference between two numbers means
(a) Adding them
(b) First number - second number
(c) Second number - first number
(d) Multiplying them

Answer: B

Question. In carrom coin game, rightward movement is taken as
(a) Negative
(b) Positive
(c) Zero
(d) No sign

Answer: B

Question. To find 7 minus 18 using tokens, we remove how many positives
(a) 7
(b) 11
(c) 18
(d) 25

Answer: C

Question. 7 - 18 value will be
(a) 11
(b) -11
(c) 25
(d) -25

Answer: B

Question. First strike moves coin 'a' units right and second strike moves 'b' units right, formula for final position P is
(a) P = a - b
(b) P = a + b
(c) P = a / b
(d) P = b - a

Answer: B

Question. Strike moves coin 5 units right and then 7 units left, final position will be
(a) 12
(b) 2
(c) -2
(d) -12

Answer: C

Question. Property a × (b × c) = (a × b) × c is called
(a) Commutative
(b) Distributive
(c) Associative
(d) Closure

Answer: C

Question. Value of (5 × -3) × 4 is
(a) 60
(b) –60
(c) 15
(d) –12

Answer: B

Question. Movement is -4 means the magnitude is
(a) -4
(b) 0
(c) 4
(d) 8

Answer: C

Question. Subtracting a number is same as adding its
(a) Multiplicative inverse
(b) Additive inverse
(c) Same number
(d) Zero

Answer: B

Question. Additive inverse of integer 'a' is represented as
(a) 1/a
(b) a
(c) -a
(d) 0

Answer: C

MATHS

INTEGERS

INTRODUCTION

Whole numbers with $+$ or $-$ signs are called integers.
Eg : $-17, -5, 0, 1, 3, \dots\dots\dots$

• Types of Integers
  • (1) Positive Integers : The numbers $1, 2, 3, 4, 5, \dots$ i.e., the natural numbers are called positive integers.
  • (2) Negative Integers : The numbers $-1, -2, -3, -4, -5, \dots$ are called negative integers.
  • (3) Zero Integers : The number $0$ is simply an integer. It is neither positive nor negative.

Question. Ex.1 Write the predecessor and successor of the following numbers $4, -4, 6, 1, b, n^2$
Answer:
For number $4$: Predecessor is $3$, Successor is $5$
For number $-4$: Predecessor is $-5$, Successor is $-3$
For number $6$: Predecessor is $5$, Successor is $7$
For number $1$: Predecessor is $0$, Successor is $2$
For number $b$: Predecessor is $b - 1$, Successor is $b + 1$
For number $n^2$: Predecessor is $n^2 - 1$, Successor is $n^2 + 1$

INTEGERS ON NUMBER LINE

Positive numbers are always on right side of zero & negative numbers are on left side of zero.
$-3 \quad -2 \quad -1 \quad 0 \quad 1 \quad 2 \quad 3 \dots$
-ve numbers $\leftarrow$ $0$ $\rightarrow$ +ve numbers
or we can say all integers are in ascending order from left to right.

ADDITION OF INTEGERS

In order to add two integers on a number line, we follow the following steps :

Question. Ex. Add the following integers : $6$ and $-9$
Answer: First we draw a number line and mark the integer $6$ on it.
To add $-9$ we move $9$ steps to the left from $6$. Thus, we reach at a point representing $-3$. Hence the sum of $6$ and $-9$ is $-3$. That is, $6 + (-9) = -3$. Note that if we represent the number $-9$ on the number line then to find $6 + (-9)$ we shall move $6$ units to the right of $-9$. Obviously, we reach at $-3$.

Question. Ex. Draw a number line and represent each of the following on it :
(i) $-2 + 8 + (-9)$ (ii) $-2 + (-3) + (-5)$
Answer:
(i) $-2 + 8 + (-9) = -3$
Start at $-2$, move $8$ steps right to reach $6$, then move $9$ steps left to reach $-3$.
(ii) $-2 + (-3) + (-5) = -10$
Start at $-2$, move $3$ steps left to reach $-5$, then move $5$ steps left to reach $-10$.

SUBTRACTION OF INTEGERS

We know that in the subtraction fact $7 - 2 = 5$, $7$ is the minuend, $2$ is the subtrahend and $5$ is the difference.

Step 1 : First we draw a number line and mark (label) the minuend on it.

Step 2 :
(i) To subtract a positive integer, we move to the left from the minuend as many steps as the second integer is.
(ii) To subtract a negative integer, we move to the right (not left) as many steps as the second integer is.

Step 3 : The point thus we reach represents the difference of two integers.

Question. Ex. Subtract the following integers : (i) $4 - 8$ (ii) $-5 - 4$
Answer:
(i) First we draw a number line and mark the number $4$ on it. To subtract $8$, we move $8$ steps to the left of $4$, thus we reach at the point representing $-4$. Hence, $4 - 8 = -4$.
(ii) Mark the integer $-5$ on a number line. To subtract $4$, we move $4$ steps to the left of $-5$, thus we reach at the point representing $-9$. Hence, $-5 - 4 = -9$.

That is smaller natural number $-$ Larger natural number $= - [\text{Larger natural number} - \text{Smaller natural number}]$. To add two negative numbers, we add the numbers without sign and then we put the negative sign (common sign) before the sum so obtained.

PROPERTIES OF ADDITION AND SUBTRACTION

• (1) Closure: Addition $\checkmark$, Subtraction $\checkmark$
• (2) Commutative: Addition $\checkmark$, Subtraction $\times$
• (3) Associative: Addition $\checkmark$, Subtraction $\times$
• (4) Additive Identity: Addition $\checkmark$, Subtraction $\times$
• (5) Additive Inverse: Addition $\checkmark$, Subtraction $\checkmark$

Eg.1 $5 + 3 = 8$ (integer), $-7 + 3 = -4$ (integer)

Eg.2 $3 + 7 = 10 = 7 + 3$, $4 - 5 = -1$ & $5 - 4 = 1$

Eg.3
$2 + (3 + 5) = 2 + 8 = 10$
$(2 + 3) + 5 = 5 + 5 = 10$
$1 - (7 - 9) = 1 - (-2) = 1 + 2 = 3$
$(1 - 7) - 9 = -6 - 9 = -15$

MULTIPLICATION OF INTEGERS

• (i) Two positive numbers.
• (ii) One positive and one negative number or negative to positive number.
• (iii) Two negative numbers.

Eg.
(i) $5 \times 6 = 30$
(ii) $7 \times 9 = 63$
(iii) $9 \times 10 = 90$
(iv) $-3 \times 1 = -3$
(v) $-7 \times 9 = -63$
(vi) $-11 \times 11 = -121$
(vii) $13 \times -5 = -65$
(viii) $10 \times -10 = -100$
(ix) $-40 \times -20 = 800$
(x) $-5 \times -1 = 5$

• Sign system for multiplication
  • $(+) \times (+) = +$ (Positive $\times$ Positive = Positive)
  • $(-) \times (+) = -$ (Negative $\times$ Positive = Negative)
  • $(+) \times (-) = -$ (Positive $\times$ Negative = Negative)
  • $(-) \times (-) = +$ (Negative $\times$ Negative = Positive)

PROPERTIES OF MULTIPLICATION

• (i) Closure $\checkmark$
• (ii) Commutative $\checkmark$
• (iii) Associative identity $\checkmark$
• (iv) Multiplicative identity $1$
• (v) Multiplicative inverse: reciprocal of given number

Eg.
(i) $16 \times 12 = 192$ (integer)
(ii) $17 \times 10 = 170 = 10 \times 17$ (commutative)

DISTRIBUTIVE PROPERTY

For any three integers $a, b, c$; $a \times (b + c) = a \times b + a \times c$

Let us observe the following products :
(i) $7 \times (2 + 5) = 49$ and $7 \times 2 + 7 \times 5 = 14 + 35 = 49$
Thus, $7 \times (2 + 5) = 7 \times 2 + 7 \times 5$
(ii) $-2 (-3 + 1) = -2 (-2) = 4$ and $-2 \times -3 + (-2) \times (1) = 6 - 2 = 4$
Thus $-2 \times (-3 + 1) = -2 \times (-3) + (-2) \times (1)$
This property of integers is known as the distributive property of multiplication over addition.

DIVISION OF INTEGERS

Division is the reverse process of multiplication.
For example, to divide $32$ by $-4$ means to find a number by which $-4$ should be multiplied such that it gives the product $32$. The answer is $-8$.

Eg : Observe the pattern and fill up the boxes.
(i) $6 \times 4 = 24 \therefore 24 \div 4 = 6$
(ii) $8 \times -5 = -40 \therefore -40 \div -5 = 8$
(iii) $-8 \times 3 = -24 \therefore \boxed{-24} \div 3 = -8$
(iv) $7 \times 5 = 35 \therefore 35 \div \boxed{5} = 7$
(v) $-6 \times 4 = -24 \therefore -24 \div \boxed{-6} = 4$
(vi) $-8 \times \boxed{-6} = -48 \therefore 48 \div \boxed{-6} = -8$

SIGN SYSTEM FOR DIVISION

(i) The quotient of two integers involving two like signs is positive or $(+) \div (+) = +$ and $(-) \div (-) = +$.
(ii) The quotient of two integers having opposite signs is negative or $(+) \div (-) = -$ and $(-) \div (+) = -$.

• Properties of division
  • (1) Closure: No (divisor should be non zero)
  • (2) Commutative: No
  • (3) Associative: No

Eg :
(i) $25 \div 5 = 5$ (integer)
(ii) $20 \div 10 = 2$ (integer)
(iii) $30 \div 7 \neq$ integer
(iv) $20 \div 5 = 4 \neq 5 \div 20$
(v) $(36 \div 9) \div 2 = 4 \div 2 = 2$
$36 \div (9 \div 2) = 36 \div \frac{9}{2} = 36 \times \frac{2}{9} = 4 \times 2 = 8$

EXERCISE - I (COMPETITIVE CORNER)

Question. 1. The additive identity of integers is
(a) $-1$
(b) $1$
(c) $0$
(d) none of these
Answer: (c)

Question. 2. The greatest positive integer is
(a) $0$
(b) $100$
(c) $999$
(d) none of these
Answer: (d)

Question. 3. The value of $5(10 – 9)$ is
(a) $5$
(b) $5 \times 10 – 5 \times 9$
(c) (a) and (b)
(d) none of these
Answer: (c)

Question. 4. The sum of two integers is also an integer, this property of integers is called
(a) Closure
(b) Commutative
(c) Associative
(d) None of these
Answer: (a)

Question. 5. Every integer is also a
(a) natural number
(b) whole number
(c) (a) and (b) both
(d) none of these
Answer: (d)

Question. 6. When $0$ is multiplied by any negative integer, their product will be
(a) a positive integer
(b) a negative integer
(c) zero
(d) none of these
Answer: (c)

Question. 7. The sum of two integers is always
(a) a natural number
(b) a whole number
(c) an integer
(d) none of these
Answer: (c)

Question. 8. The multiplicative identity of integers is
(a) $0$
(b) $+1$
(c) $-1$
(d) none of these
Answer: (b)

Question. 9. Every positive integer is greater than
(a) zero
(b) every negative integer
(c) both (a) and (b)
(d) none of these
Answer: (c)

Question. 10. The product of two integers is $12$, if one integer is $-3$ then the other one is:
(a) $+4$
(b) $-4$
(c) $3$
(d) $-3$
Answer: (b)

Question. 11. On subtracting $(-6)$ from $0$, we get:
(a) $-6$
(b) $6$
(c) $7$
(d) None of these
Answer: (b)

Question. 12. The additive inverse of $-6$ is:
(a) $6$
(b) $0$
(c) $-5$
(d) $-7$
Answer: (a)

Question. 13. $30 \times (-23) + 30 \times 14 = ?$
(a) $-270$
(b) $270$
(c) $1110$
(d) $-1110$
Answer: (a)

Question. 14. $(-8) \div 0 = ?$
(a) $-8$
(b) $0$
(c) $8$
(d) Not defined
Answer: (d)

Question. 15. By how much does $-3$ exceed $-5 ?$
(a) $-2$
(b) $2$
(c) $8$
(d) $-8$
Answer: (b)

Question. 16. What must be subtracted from $-3$ to get $-9 ?$
(a) $-6$
(b) $12$
(c) $6$
(d) $-12$
Answer: (c)

Question. 17. How much less than $-8$ is $-3 ?$
(a) $-5$
(b) $5$
(c) $11$
(d) $-11$
Answer: (a)

Question. 18. The sum of two integers is $93$. If one of them is $-59$, the other one is:
(a) $34$
(b) $-34$
(c) $152$
(d) $-152$
Answer: (c)

Question. 19. Resolve the brackets and simplify: $(28 \div 2) \div (56 \div 8).$
(a) $1$
(b) $4$
(c) $3$
(d) $2$
Answer: (d)

Question. 20. For integers:
(a) Addition is associative
(b) Addition is commutative
(c) Integer “0” is the identity under addition
(d) All of the above
Answer: (d)

Question. 21. Reciprocal of $\frac{1}{7}$ is:
(a) $7$
(b) $1$
(c) $-7$
(d) $1/7$
Answer: (a)

Question. 22. For any integer $x$ what is true:
(a) $x/0$ is not defined
(b) $x/1 = a$ (where $x \neq a$)
(c) option (a) and (b) both are wrong
(d) option (a) and (b) both are rigth
Answer: (a)

EXERCISE - II (CBSE CORNER)

Question. 1. Evaluate the following :
(i) $(-40) \div 10$
(ii) $60 \div (-6)$
(iii) $(-49) \div (-7)$
(iv) $(-79) \div 79$
(v) $13 \div [(-4) + 3]$
(vi) $0 \div (-14)$
(vii) $(-41) \div [(-40) + (-1)]$
(viii) [(-48) \div 12] \div 4$
(ix) Is $[(-7) + (6)] = [(-3) + 2]$ ?
Answer:
(i) $-4$
(ii) $-10$
(iii) $7$
(iv) $-1$
(v) $-13$
(vi) $0$
(vii) $1$
(viii) $-1$
(ix) yes

Question. 2. Write down a pair of integers whose :
(i) sum is $-7$
(ii) difference is $-10$
(iii) sum is $0$
Answer:
(i) $-1, -6$ or $-9, 2$
(ii) $-11, -1$ or $35, -45$
(iii) $-1, 1$ or $20, -20$

Question. 3. Write the value of
(i) $| +22 |$
(ii) $| -8 |$
(iii) $| 18 - 8 |$
(iv) $| - 5 - 4 |$
(v) $- | 3 - 2 |$
Answer:
(i) $22$
(ii) $8$
(iii) $10$
(iv) $9$
(v) $-1$

Question. 4. Arrange the following integers in ascending order
(i) $-20, 13, 4, 0, -5, +5$
(ii) $+30, -2, 0, -6, -20, 8$
Answer:
(i) $-20, -5, 0, 4, 5, 13$
(ii) $-20, -6, -2, 0, 8, 30$

Question. 5. Which temperature is higher ?
(i) $40^\circ\text{C}$ or $-40^\circ\text{C}$
(ii) $-18^\circ\text{C}$ or $12^\circ\text{C}$
(iii) $-2^\circ\text{C}$ or $-4^\circ\text{C}$
(iv) $17^\circ\text{C}$ or $27^\circ\text{C}$
Answer:
(i) $40^\circ\text{C}$
(ii) $12^\circ\text{C}$
(iii) $-2^\circ\text{C}$
(iv) $27^\circ\text{C}$

Question. 6. A water tank has steps inside it. A monkey is sitting on the toppest step (i.e., the first step). The water level is at the ninth step.
(i) He jumps $3$ steps down and then jumps $2$ steps up. If he continues in this way, in how many jumps will he reach the water level ?
(ii) After drinking water, he wants to go back, for this he jumps $4$ steps up and then jumps $2$ steps down in every move. In how many jumps will he reach back the top step ?
Answer:
(i) $11$ times
(ii) $5$ times

Question. 7. Verify and name the property used :
(i) $-110 \times (-237) = (-237) \times (-110)$
(ii) $(-35 \times 4) \times (-152) = -35 \times [4 \times (-152)]$
Answer:
(i) Commutative property of multiplication.
(ii) Associative property of multiplication.

Question. 8. Verify and name the property used :
(i) $-117 \times 251 + (-117) \times 249$
(ii) $156 \times 273 - 156 \times (-73)$
Answer:
(i) Distributive property of multiplication over addition
(ii) Distributive property of multiplication over subtraction

Question. 9. Verify that : $a \div (b + c) \neq (a \div b) + (a \div c)$, if $a = 12, b = -4, c = 2.$
Answer:
LHS $= 12 \div (-4 + 2) = 12 \div (-2) = -6$
RHS $= [12 \div (-4)] + [12 \div 2] = -3 + 6 = 3$
Since $-6 \neq 3$, hence verified.

Question. 10. The temperature at $12$ noon was $10^\circ\text{C}$ above zero. At what time the temperature will be $8^\circ\text{C}$ below $0^\circ\text{C}$, if it decreases at the rate of $2^\circ\text{C}$ per hour? If it decreases at the rate of $2^\circ\text{C}$ per hour till midnight, what would be the temperature at mid-night ?
Answer: $9$ pm, $-14^\circ\text{C}$

Question. 11. In a class test $(+3)$ marks are given for every correct answer and $(-2)$ marks are given for every incorrect answer and no marks for not attempting any questions.
(i) Ram scored $20$ marks. If he has got $12$ correct answers, how many questions has he attempted incorrectly ?
(ii) Mohan scores $-5$ marks in the test though he has written $7$ correct answers. How many questions has he attempted incorrectly ?
Answer:
(i) $8$
(ii) $13$

Question. 12. A boy has $₹ 350$ in his bank account. He deposits $₹ 40$ everyday for $10$ days. What will be the amount in his account at the end of $10$ days ?
Answer: $₹ 750$

Question. 13. In a class test containing $10$ questions, $5$ marks are answered for every correct answer and $(-2)$ marks are awarded for every incorrect answer and $0$ for questions not attempted.
(i) Mohan gets four correct and six incorrect answers. What is his score ?
(ii) Reshma gets five correct answer and five incorrect answers. What is her score ?
(iii) Heena gets two correct and five incorrect answers out of seven questions she attempts. What is her score ?
Answer:
(i) $8$ marks
(ii) $15$ marks
(iii) $0$ mark