Which of the following statements is not true
a. When two positive integers are added, we always get a positive integer
b. When two negative integers are added we always get a negative integer
c. When a positive integer and a negative integer is added we always get a negative integer
d. Additive inverse of an integer 2 is (-2) and the additive inverse of (-2) is 2

Solution:

To determine which of the above given statements is NOT true let us individually analyze the statement.

1. When two positive integers are added, we always get a positive integer.

Let us take two positive integers 2 and 3 if we add them together we get 2 + 3 = 5 which is a positive integer. Hence this statement is true.

1. When two negative integers are added we always get a negative integer.

Let us take two negative integers -2 and -3 if we add them together we get -2 + (-3) = -5 which is a negative integer. Hence this statement is true.

1. When a positive integer and a negative integer is added we always get a negative integer.

Let us take two integers 2 and -3. If we add them together we get 2 + (-3) = -1 which is a negative integer. Hence this statement is true. But if in the same condition we take integers as -2 and 2 on adding them we get 2 + (-2) = 0. Hence this statement is false.

2. Additive inverse of an integer 2 is (-2) and the additive inverse of (-2) is 2. This statement is true as we can see the additive inverse of a number is the number itself with opposite sign.

✦ Try This: What will be your answer if the two positive integers are subtracted, we always get a positive integer. Try examining the problem using illustration

We can solve the given problem using the properties of integers and by subtracting two positive integers

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 1

NCERT Exemplar Class 7 Maths Chapter 1 Exercise Problem 6

Which of the following statements is not true: a. When two positive integers are added, we always get a positive integer, b. When two negative integers are added we always get a negative integer, c. When a positive integer and a negative integer is added we always get a negative integer, d. Additive inverse of an integer 2 is (-2) and the additive inverse of (-2) is 2

Summary:

According to the integer rules the statement ‘when a positive integer and a negative integer is added we always get a negative integer’ is false

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