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\ 06-Jan-2025 Bharat Arora Proof-7 Reader’s Sign _______________________ Date __________

In general,
p r u p  r u p r p u
if , and are three non-zero rational numbers, then ×  ±  = × ± ×
q s v q  s v q s q v

Practice Time 1D

1. Multiply the following.
3 5 −7 6 3 8 −5 6
(a) by (b) by (c) by (d) by
10 12 18 7 4 − 9 8 −5
2. Simplify the following and express the result in standard form.

1

(a) −19 × 26 (b) −12 ×( − 10) (c) 18 × − 3 1  (d) −5 × 3 1

36 15 35  6 4 7
3. Simplify the following.
27
−2
−1
(a)    9 × −16    +    2 ×  5   3 (b)    5 × − 16  −    − 35 × 1 × 21   
5 
2
7
3
4. Fill in the blanks.
−13 11 11  −  5 −5
(a) × = × ......... (b) −19 ×   = × .........
9 15 15  13  13
−17
3
8
(c)    11 × − 7   × − 8 3 = ......... ×    − 7 8 × − 8   (d) −17 ×  3 × −35    =    9 × 7  3   × .........

16
 7
9
9
5. Evaluate the following by using distributive property.
2 5 2 4 6 5 6 2 3  − 6  ( 6
(a) × + × (b) × − × (c) ×   11 +− 4) ×
7 3 7 3 11 9 11 9 8 11
6. Identify the property of multiplication in the following.
−2
−9
1  − 16 − 16 1  − ( ) 2 7  ( ) ( ) 7 − ( )9
(a) ×   = × (b)  ×  × = ×  × 
13  5  5 13  3 6  5 3  6 5 
−11  −13  −13  −11  − ( ) 3  − ( ) 7 7   3 −7 − ( ) 7 
− ( ) ( )  3
(c) ×   = ×   = 1 (d) ×  +  =  ×  +  × 
−13  −11  −11  −13  4  9 8   4 9   4 8 
7. Verify that x × (y × z) = (x × y) × z for each of the following.
1 2 2 2 −1 2
(a) x = , y = and z = (b) x = , y = and z = 1
7 3 7 9 3 3
8. Verify that x × (y + z) = (x × y) + (x × z) for each of the following.
−4 2 2 2 −1 8
(a) x = , y = and z = (b) x = , y = and z = 1
7 3 7 9 3 9
9. Verify the property a × (b – c) = (a × b) – (a × c) for each of the following.
−4 2 2 2 −1 8
(a) a = , b = and c = (b) a = , b = and c =
5 5 7 9 5 9
10. Evaluate and find the reciprocal of the result of the following.

 −  3 −2  1  1 2 3 2 2
(a) −+   5   (b) 3 ×  −   4 (c) 3 × 5 + 3 × 5
1
 2
25 Rational Numbers