Page 125 - Start Up Mathematics_6

Inference: Sum of two positive integers is positive, sum of two negative integers is negative
and sum of one positive and one negative integer takes the sign of the integer having the
greater absolute value.

Can you find when is the sum of two integers 0? What are these integers known as?

Try finding the value of 4 + 1, –5 + 5, 7 – 3 by this method.

EXERCISE 6.2

1. Using a number line, write the integer which is:
(a) 5 more than 1 (b) 6 more than –6 (c) 4 less than –4 (d) 5 less than 0
2. Use a number line to add the following integers:

(a) 10 + (–6) (b) (–2) + (–9) (c) 0 + (–6) (d) (–2) + (–5) + 4
3. Add without using a number line:
(a) (–138) + (–122) (b) (–269) + 169 (c) (–965) + 400

(d) (–139) + (–456) (e) (–278) + 278
4. Find the sum of:
(a) 567 and –897 (b) –764 and 674 (c) –458 and 765

(d) –56, –78 and –98 (e) 200, –56 and –240
5. Find the sum of:
(a) (–6) + (–9) + (–12) + (–24) (b) 87 + 0 + (–9) + (–48) + (–23)

(c) (–56) + 65 + (–34) + (–23) + 34 (d) (–23) + (–45) + (–39) + 25

Subtraction of Integers on a Number Line

Case I: Subtraction of two positive integers say +4 from +3, i.e., 3 – 4

Step 1: On the number line, let’s move 3 steps to the right from 0 to reach 3.

–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 4 steps to the left of 3 to reach –1.

–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, (+3) – (+4) = 3 – 4 = –1.
Case II: Subtraction of a positive integer from a negative integer say +4 from –3, i.e., –3 – 4
Step 1: On the number line, let’s move 3 steps to the left from 0 to reach –3.

–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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