Page 9 - SM inner class 8.cdr

3 7 - 11 - 5 -5
Example 7. Evaluate: + + + . Example 9. What should be added to to get
5 3 5 3 8
æ 3 - 11ö æ 7 - 5ö 7 ?
Solution: ç + ÷ + ç + ÷
è 5 5 ø è 3 3 ø 9
æ3 + -11) ö æ7 ( - ö Solution: Let the required number be x then,
(
5)
= ç ÷ + ç + ÷ According to the questions,
è 5 ø è3 3 ø
-5 7 7 5
5
æ3 -11 ö æ7 - ö + x = Þ x = +
= ç ÷ + ç ÷ 8 9 9 8
è 5 ø è 3 ø 56 + 45 101
-8 2 -24 + 10 Þ x = =
= + = 72 72
5 3 15 101
-14 Hence, the required number is .
= 72
15
Example 10. Verify the equation given below,
Example 8. What should be subtracted from and name the property also.
-3
7
to get -6? æ 3 - 2ö - 7 3 æ -2 - ö
7 ç + ÷ + = + ç + ÷
è 4 5 ø 10 4 è 5 10 ø
Solution: Let the required number be x then,
7
2
æ3 - ö -7 3 æ -2 - ö
According to the questions, L.H.S. = ç + ÷ + R.H.S = + ç + ÷
è4 5 ø 10 4 è 5 10 ø
-3
- x = -6 æ15 - ö -7 3 æ 4 7
8
- - ö
7 = ç ÷ + = + ç ÷
-3 è 20 ø 10 4 è 10 ø
Þ = x - 6
æ
7 = 7 + -7 = 3 + ç -11 ö
÷
-3 20 10 4 è 10 ø
Þ + 6 = x
7 = 7 -14 = 15 - 22
- + 42 20 20
3
Þ x =
7 = -7 = -7
39 20 20
=
7 L.H.S = R.H.S
39
Hence, the required number is . Thus, rational numbers are associative under
7 addition.
E xercise 1.1

1. Write the follow ing ratio nal numbers in the stan dard form:
44 34 -28 -105
(i) (ii) (iii) (iv)
77 - 20 -15 98
2. Deter mine which ratio nal number is greater in each case:
5 -3 -5 4 -7 -5
(i) , (ii) , (iii) ,
8 7 7 -9 11 8

3. Add the following rational numbers:
-5 3 -15 7
(i) and (ii) and
7 7 4 4
-8 -4 6 -9
(iii) and (iv) and
11 11 13 13

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Mathematics In Focus - 8