Page 122 - Start Up Mathematics_6

Addition of Integers on a Number Line

Case I: Addition of two negative integers say –4 and –3

Step 1: On the number line; let’s move 4 steps to the left of 0 to reach –4.

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10
Step 2: Now move 3 steps further to the left of –4 to reach –7.

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10
Thus, we observe that (–4) + (–3) = –7.
Case II: Addition of a positive and a negative integer say +6 and –2

Step 1: On the number line; let’s move 6 steps to the right of 0 to reach 6.

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10

Step 2: Now move 2 steps to the left of 6 to reach 4.

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10
Thus, we observe that (+6) + (–2) = +4.

• When a positive integer is added to an integer, the resulting integer becomes greater than the given
integer.
• When a negative integer is added to an integer, the resulting integer becomes less than the given integer.

Example 12: Using a number line, write the integer which is:
(a) 2 more than 7 (b) 3 more than –7

Solution: (a) 2 more than 7

Represent 7 on a number line. Now move 2 steps to the right of 7 to reach 9.

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10
(b) 3 more than –7

Represent –7 on a number line. Now move 3 steps to the right of –7 to

reach –4.

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10

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