Page 10 - SM inner class 8.cdr

4. Verify the follow ing and name the prop erty also :
3 æ - 2ö - 7 3 æ - 2 - 7ö æ -7 2 ö -13 -7 æ 2 -13 ö
(i) ç + ÷ + = + ç + ÷ (ii) ç + ÷ + = + ç + ÷
4 è 5 ø 10 4 è 5 10 ø è 11 - ø 5 22 11 è -5 22 ø
3
æ -2 - ö æ - ö 2 -3
1
(iii) - + ç + ÷ = - +1 ÷ +
ç
è 3 4 ø è 3 ø 4
5. Subtract the following rational numbers:
3 1 -5 1 -8 -3 -9
(i) from (ii) from (iii) from (iv) from -1
4 3 6 3 9 5 7
18 13 32 6 4
(v) - from 1 (vi) - from 0 (vii) - from - (viii) -7 from -
11 9 13 5 7

6. Simplify the follow ing:
4 3 - 2 - 11 5 - 8 - 13 17
(i) + + + (ii) + + 0 + +
3 5 3 5 8 9 3 24
-13 11 -5 7 4 - 8 - 5 1
(iii) + + + (iv) + + +
20 14 7 10 7 9 21 3
-14
7. The sum of two rational numbers is -2. If one of the numbers is , find the other.
5
-1 5
8. The sum of two rational numbers is . If one of the numbers is find the other.
2 6
-5 -3
9. What number should be added to so as to get ?
8 2
5
10. What number should be added to -1 so as to get ?
7

Multiplication of Rational Number Properties of Multiplication of Rational
Numbers
We already know that product of two given
fractions = product of their numerators 1. Closure property
¸ product of their denominators
The product of two rational numbers is always
Similarly, we will follow the same rule for the a rational number. Hence Rational numbers
product of rational numbers. are closed under multiplication.
a c
Therefore, product of two rational numbers = If and are any two rational numbers,
product of their numerators ¸ product of their b a c d ac
denominators. then ´ = is also a rational number.
b d bd
a c
Thus, if and are any two rational numbers, For example:
b d
a c a ´ c 1 7 1
then ´ = (i) ´ 7 = = 2 is a rational number.
b d b ´ d 3 3 3
4 5 20
2 3 (ii) ´ = is a rational number.
Example 11. Multiply by . 3 9 27
7 5
2 3 2 ´ 3 6 2. Commutative property
Solution: ´ = =
7 5 7 ´ 5 35 Multiplication of rational numbers is
commutative.
5 æ 3 a c
- ö
Example 12. Multiply by ç ÷ If and are any two rational numbers, then
9 è 4 ø b d
a
5 æ - 3ö 5 ´ -3 -15 -5 a ´ c = c ´ .
Solution: ´ ç ÷ = = = b d d b
9 è 4 ø 9 ´ 4 36 12
10
Mathematics In Focus - 8