Page 53 - classs 6 a_Neat

OPERATIONS ON INTEGERS
From the above examples, we obtain the rules for addition of integers, which are gtven below.
ADDITION OF INTEGERS We have learnt how to add two whole numbers on the number line. We shall
extend the same method for addition of integers, using the number line.
RULES FOR ADDITION OF INTEGERS
Adding -3 to a number means moving 3 steps to the left of the number.
Adding -2 to a number means moving 2 steps to the left of the number, and so on. RULE: If two positive integers or two negative integers are added, we add their values regardless
of their signs and give the sum their common sign.
SOLVED EXAMPLES

EXAMPLE 1: Add +7 and -4 on the number line.
SOLUTION: On the number line we start from O and move 7 steps to the right to reach a point A. EXAMPLE 4: Add the following integers:
Now, starting from A, we move 4 steps to the left to reach a point B, as shown below. (i) +27 and +19 (ii) -42 and -35

B A SOLUTION: Using the rule for addition of integers having like signs, we get:
(i) + 27 (ii) - 42
0 1 2 3 4 5 6 7 8 +19 -35
+ 46 - 77
27 + 19 = 46. (-42) + (-35) = - 77.
And, B represents the integer 3.
:. 7 + (-4) = 3. EXAMPLE5: Add the integers -5928 and -965.

EXAMPLE 2. Add +3 and -8 on the number line. SOLUTION: Using the rule for addition of integers with like signs, we get:
SOLUTION: On the number line we start from O and move 3 steps to the right to reach a point A.
Now, starting from A, we move 8 steps to the left to reach a point B, as shown below. - 5928
- 965
- 6893
3 Steps
(-5928) + (-965) = - 6893.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
A
B
RULE: To add a positive and a negative integer, we find the difference between their numerical
values regard less of their signs and give the sign of the integer with the greater value to it.

REMARK: In order to add two integers of unlike signs, we see which is more and by how much.
8 Steps
Clearly, B represents the integer -5. EXAPMLE 6. Add: (i) -36 + 19 (ii) 49 + (-27)
:. 3 + (-8) = - 5.
SOLUTION: (i) - 36 (ii) + 49
+ 19 - 27
EXAMPLE 3. Add -3 and -6 on the number line. - 27 + 22
SOLUTION: On the number line, we start from O and move 3 steps to the left to reach a point A.
Now, starting from A, we move 6 steps to the left to reach a pointB, as shown below. (-36) +19 = - 17. 49 + (-27) = 22.

6 Steps 3 Steps EXAMPLE 7: Add: (-2056) + 679.

SOLUTION: We subtract 679 from 2056 and give a minus sign to the result.
B A
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 - 2056

+ 573
Clearly, B represents -9. + 337
:. (-3) + (-6) = - 9. (-236) + 573 = 337.