NCERT Class 7 Solutions: Integers (Chapter 1) Exercise 1.2

Q-1 Write down a pair of integers whose:

  1. Sum is -7

  2. Difference is -10

  3. Sum is 0

Solution:

Integers on number line positve, negative and zero.

Integers on Number Line (+Ve and -Ve)

Integers on number line positve, negative and zero.

  1. Sum is -7

    10+3=7 or (7)+(0)=7

  2. Difference is -10

    (2)(12)=10

  3. Sum is zero

    5(5)=0

Q-2

  1. Write a pair of negative integers whose difference gives 8.

  2. Write a negative integer and a positive integer whose is sum -5.

  3. Write a negative integer and a positive integer whose difference is -3.

Solution:

  1. =(3)(11)

    =2+11

    =8

  2. =(11)+(6)

    =5

  3. =(7)(4)

    =3

Q-3 In a quiz, term A scored 40,10,0 and team B scores 10,0,40 in three successive rounds. Which term scored more? Can we say that we can add integers in any order?

Solution:

Commutative Property: The commutative property says that X + Y = Y + X. In words, you can swap the order of the two inputs of the plus operation and it won't matter.

Associative Property: The associative property says that (X + Y) + Z = X + (Y + Z), where the parentheses tell you what you should be doing first. This is quite different: it is no longer about changing the order of the operands in an operation, but rather the order of the operations themselves.

Additive Identity Property: The sum of any number and zero is the original number. For example 10 + 0 = 10. 0 is the identity for addition operation, it is known as additive identity.

Distributive property: The sum of two numbers times a third number is equal to the sum of each addend times the third number. We say that multiplication is distributive over addition. For example 4×(6+3)=4×6+4×3 .

Additive Inverse: The additive inverse of a number ‘a’ is the number that, when added to ‘a’, yields zero. This number is also known as the opposite (number), sign change, and negation. For a real number (including integers), additive inverse reverses its sign: the opposite of a positive number is negative, and the opposite of a negative number is positive

Given the commutative property apply in this example

Given the Commutative Property

Given the commutative property apply in this example

Team A scored 40,10,0

Total Score of Team A =40+10+0=30

Team B scored 10,0,40

Total Score of Team B =10+0+(40)=30

The scores of both teams are therefore equal

  • Yes, we can add integers in any order. This is the result of commutative property of addition.

  • We just observed that the scores obtained by both teams in successive rounds were numerically equal but were added different in order. Yet, the total score of both terms came out equal

Q-4 Fill in the blanks to make the following statements true:

  1. (5)+(8)=(8)+()

  2. (53)+=(53)

  3. 17+=0

  4. [13+(12)]+(..)=13+[(12)+(7)]

  5. (4)+[15+(3)]=[(4)+15]+()

Solution:

  1. (5)+(8)=(8)+()

    Here apply commutative property of addition

    (5)+(8)=(8)+(5)

  2. (53)+=(53)

    Any value added to zero remains unchanged. Zero is known as additive identity.

    (53)+0=(53)

  3. 17+=0

    Any positive value when added to the same negative value results in zero. The two numbers which when added yield zero are additive inverses of each other.

    So, 17+(17)=0

  4. [13+(12)]+(..)=13+[(12)+(7)]

    By the associative property of addition, we can change the order in which we do the additions without changing the result.

    [13+(12)]+(7)=13+[(12)+(7)]

  5. (4)+[15+(3)]=[(4)+15]+()

    Again by the associative property,

    (4)+[15+(3)]=[(4)+15]+(3)

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