Important Questions: Integers


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QUESTION: 1

What do we call the set of negative numbers and whole numbers?

Solution:

The set of negative numbers and whole numbers is called integers. 

Z={,....−2,−1,,0,1,2,.....}

QUESTION: 2

Which of the following is the smallest positive integer?

Solution:

1 is the smallest positive integer.

QUESTION: 3

Where are the negative numbers located on a horizontal number line?

Solution:

All the other positive numbers to its right are greater than, the negative numbers are located on the left side of 0. 

QUESTION: 4

What is the opposite of earning Rs. 100?

Solution:

The required opposite is spending Rs. 100.

QUESTION: 5

How is the withdrawal of RS. 200 represented?

Solution:

Withdrawal of Rs. 200 means amount 200 is subtracted from our account. Option B is correct.

QUESTION: 6

Which of the following is true with respect to −28 and −32?

Solution:

Because -32 is on the left of -28 on the number line, so it is smaller.

QUESTION: 7

Where do we place the positive numbers on a vertical number line with respect to 0?

Solution:

Positive number are located above 0 and negative numbers are located below 0 on a vertical number line 

QUESTION: 8

What is the representation of 30 km towards the west?

Solution:

Since west is on the left side, and there are negative integers on the left, so it's -30 kms.

QUESTION: 9

What is the nature of the product of a negative integer by itself, odd number of times?

Solution:

(−1)×(−1)×(−1)........odd times 

= (−1)  which is negative.

QUESTION: 10

What is the nature of the product of a negative number by itself even number of times?

Solution:

(−1)×(−1)×(−1)....even times =1,which is positive.

QUESTION: 11

Calculate (−32)×(−4)×(−3)×0×(−6)

Solution:

(−32)×(−4)×(−3)×0×(−6)=0 as the product of any number and 0 is 0.

QUESTION: 12

If the dividend and the divisor have like signs, what is the sign of the quotient?

Solution:

If dividend and divisor have positive signs then the quotient will be positive. If dividend and divisor have negative signs , then the quotient will be positive because 2 negative signs becomes positive.

QUESTION: 13

If the dividend and divisor have unlike signs, what is the sign of the quotient?

Solution:

If the dividend and divisor have unlike signs then the quotient will be Negative.

Division of Integers is similar to the division of whole numbers (both positive) except the sign of the quotient needs to be determined.

If both the dividend and divisor are positive, the quotient will be positive.
(+16) ÷ (+4) = +4

If both the dividend and divisor are negative, the quotient will be positive.
(-16) ÷ (-4) = +4

If only one of the dividend or divisor is negative, the quotient will be negative.
(+16) ÷ (-4) = -4     or   (-16) ÷ (+4) = -4

In other words, if the signs are the same the quotient will be positive, if they are different, the quotient will be negative
Hence Option B

QUESTION: 14

Match the following.

Solution:

(132) / (-12) = -11

(-144) / (+16) = -9

(-32) / (-4) = 8

(196) / (4) = 49

QUESTION: 15

With respect to which of the following operations is closure property satisfied by the set of integers?

Solution:

The closure property states that when you perform an operation on any two numbers in a set, the result of the computation is another number in the same set .Since division can result in changing an integer in decimals. So its closed in addition, subtraction and multplication.

QUESTION: 16

What is the additive identity element for the set of integers?

Solution:

0 is identity element with respect to addition of integers, e.g.,(−5)+0 = +0+(−5) = (−5)

QUESTION: 17

Which of the following is the multiplicative identity in the set of integers?

Solution:

1 is the identity element with respect to multiplication.

QUESTION: 18

What is the value of 124×4−3+118÷2?

Solution:

Use BODMAS rule & simplify:

= 124×4  −3 + 118+2

= 496 − 3 + 59

= 552

QUESTION: 19

Which of the following order is used while evaluating an expression?

Solution:

(),{},[] is the correct order of evaluation of brackets.

QUESTION: 20

If a negative sign precedes a bracket, what happens to the terms inside it?

Solution:

If a negative sign precedes a bracket, the signs of the terms inside the bracket are changed.

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