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

3. Find the reciprocal of the following.
3 ( − 4)  512   32
−×
−× 
(a) ÷ (b)   ÷  
13 65  15   9 
4. Fill in the blanks.
−4 −6
(a) .......... ÷ (–3) = (b) (–12) ÷ .......... =
15 5
−13 12 −31 −1
5. Divide the sum of and by the product of and .
5 7 7 2
6. Verify that x ÷ y ≠ y ÷ x for each of the following.

−4 2 2 −1
(a) x = , y = (b) x = , y =
5 5 9 5
7. Verify that x ÷ (y ÷ z) ≠ (x ÷ y) ÷ z for each of the following.

1 2 1 2 −1 2
(a) x = , y = and z = (b) x = , y = and z = 1
8 3 4 9 3 3
Problems Based on Real Life Situations

Rational numbers are used in our daily life to represent quantity, cost, etc. Let us now solve some
real life problems involving rational numbers.
1 2 1
Example 19: Jaya bought a pen for `15 , a book for `24 and an ice cream for `15 . How much
money did she spend on everything? 2 3 4
1 2 1
Solution: The cost of a pen = `15 , the cost of a book = `24 , and the cost of an ice cream = `15
2 3 4
1 2 1
\ Total money spent by Jaya = `15 + `24 + `15
2 3 4

+
+
 31 74 61  186 296 183  665 5
= `  2 + 3 + 4   = `  12  = `  12   = `55 12




Hence, the total money spent by Jaya is `55 5 .
12
1
Example 20: A person spends 2 part of his salary on house rent, 3 part on food and part on
5 10 8
transportation. If he is left with `7000, find his expenditure on food and transportation.
Solution: Let the salary of a person be `x.
According to the question,

 2 3 1   16x + 12x + 5x
x –  5 x + 10 x + 8  ⇒ x –   40   = `7000
x = `7000


⇒ 40x − 33x = `7000 ⇒ 7x = `7000 × 40
40
7000 × 40
⇒ x = ` = `40000
7

 3 
\ The expenditure on food = `   10 × 40000 = `12000


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