Page 128 - Start Up Mathematics_6

At a Glance

1. The numbers ..., –4, –3, –2, –1, 0, 1, 2, 3, 4, ... are called integers.

2. The number zero is an integer but it is neither positive nor negative.
3. The number 0 is less than every positive integer and greater than every negative integer.
4. For every positive integer, there exists a negative integer having the same distance from the
origin but in opposite direction. These two integers are negative of each other and since their
sum is zero, they are also additive inverse of each other.

5. The absolute value of an integer a is the positive value of the integer. Absolute value of an
integer is also known as modulus and represents the distance of the integer from zero.
6. In order to add two integers having the same sign, we simply find the sum of their absolute
values and put the sign of the integers.
7. When one positive and one negative integers are to be added, we subtract the smaller number
from the bigger number after taking their absolute values and put the sign of the integer
whose absolute value is greater.

Review Exercises

Multiple ChoiCe Questions
1. The greatest negative integer lying between –7 and 4 is:

(a) 4 (b) 3 (c) –1 (d) –6
2. The sum of the integers obtained by taking successor and additive inverse of 452 is:
(a) 1 (b) 0 (c) –1 (d) 904
3. If x is a positive integer having a successor y, then value of y – x is:

(a) –1 (b) 0 (c) 1 (d) 2
4. The sum of 5 + (–5) + 5 + (–5) + 5 + (–5) + ... upto 50 terms is:

(a) 0 (b) –250 (c) 250 (d) 5
5. The value of the expression 1 – 2 + 3 – 4 + 5 – 6 + ... + 29 – 30 is:
(a) –14 (b) –15 (c) 0 (d) 15
6. The additive inverse of –3 is:

(a) 0 (b) 2 (c) 3 (d) –3

solve Mentally

True or False

1. On a number line, every positive integer lies to the right of every negative integer.
2. The sum of two negative integers is a positive integer.
3. The sum of three different integers can never be zero.

4. If b < a, then –a < –b.
5. When a negative integer is added to another negative integer its value decreases.

6. Absolute value of an integer is a whole number.

120