Page 20 - Math_Genius_V1.0_C8_Flipbook

E:\Working\Focus_Learning\Math_Genius-8\Open_Files\01_Chapter_1\Chapter_1
\ 06-Jan-2025 Bharat Arora Proof-7 Reader’s Sign _______________________ Date __________

Example 10: Find the additive inverse of rational number −1 .
5

Solution: For the rational number −1 , we have
5 Quick Check
−
1  1 = 11 = 0 = 0 Find the additive identity and
+−

5   5 5 5 additive inverse of the following
rational numbers:
 −  1 1 −+11 0 2 −3
Also,   5  + 5 = 5 = 5 = 0 1. 2. 7

3
1  1  − 1 1 4 −3
Thus, +−  =   + = 0 3. 4.

5  5  5  5 − 7 −7
Hence, 1 is the additive inverse of the rational number −1 .
5 5
Practice Time 1B

1. Add the following rational numbers.

3 −5 −3 −5 1 3 −3 5
(a) and (b) and (c) and (d) and
8 8 7 14 − 3 4 4 18
(e) −3 , 1 and 1 (f) −2 , 1 and 1 (g) −3 , 1 and 2
7 4 8 3 5 8 11 11 11
2. State the property used in each of the following.

2

 2  − 3  − 3  2   −  1      1  −  1    2  1 
+
(a)   +   5   =   5  +   (b)     3  +      =   3  +     +    

 

 7 

5

5

7
  5
  5

14 14 4  − 4
(c) += (d) +   = 0
0
17 17 7  7 
3. Fill in the blanks.
−4 7 7 6 6
(a) + = + ..... (b) + .... =
7 8 8 7 7
−2  7  3  −2 7  4
(c) +  +  =  +  + ..... (d) + .... = 0
3  8  5  3  8 9
4. Verify the closure property of addition for the following pairs of rational numbers.
3 − 5 −2 −5 −11 5 1 7
(a) and (b) and (c) and (d) and
7 7 5 7 12 18 4 9
5. Verify the associative property of addition for the following rational numbers.
2 2 1 −3 1 1 2 − 4 7 4 1 − 1
(a) , and (b) , and (c) , and (d) , and
3 5 7 7 5 8 9 5 9 7 14 21
5 −3
6. If a = and b = , then verify that a + b = b + a.
8 7
5 −3 8
7. If x = , y = and z = , then verify that x + (y + z) = (x + y) + z.
8 7 11
8. Find a rational number which is the additive inverse of its own.
Mathematics-8 18