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Using appropriate properties find:

- Using commutativity property of rational number

Now using Distributivity property

(ii) Using commutativity property of rational numbers

Now using Distributivity property

Write the additive inverse of each of the following:

- 2/8
- -5/9
- -6/-5
- 2/-9
- 19/-6

(i) 2/8

Additive inverse = -2/8

(ii) -5/9

Additive inverse = 5/9

(iii) -6/-5 =6/5

Additive inverse = -6/5

(iv) 2/-9=-2/9

Additive inverse =2/9

(v) 19/-6= -19/6

Additive inverse =19/6

Verify that - ( -

(i) x =11/15 (ii) x=-13/17

- x=11/15
Additive inverse

-x=-11/15 As (11/15) + (-11/15) =0

The above also represent that additive inverse of (-11/15) is (11/15) or we can say that

- (-11/15)=11/15

Or x=-(-x)

Additive inverse

-x=-13/17 As (-13/17) + (13/17) =0

The above also represent that additive inverse of (13/17) is (-13/17)) or we can say that

- (13/17) = -13/17

Or x=-(-x)

Find the multiplicative inverse of the following.

- -13
- -13/19
- 1/5
- -5/8 X -3/7
- -1 X -2/5
- - 1

- -13
Multiplicative inverse =-1/13

- -13/19
Multiplicative inverse =-19/13

- 1/5
Multiplicative inverse =5

- -5/8 X -3/7 =15/56
Multiplicative inverse =56/15

- -1 X -2/5 =2/5
Multiplicative inverse =5/2

Multiplicative inverse =-1

Name the property under multiplication used in each of the following:

- 1 is the multiplicative identity
- Commutatively
- Multiplicative inverse

Multiply 6/13 by the reciprocal of -7/16

Reciprocal of -7/16= -16/7

So (6/13) X ( -16/7) =-96/91

Associativity

Is 8/9 the multiplicative inverse of

Why or why not?

=-9/8

Now

(8/9) X (-9/8) = -1

Why or why not?

=10/3

Now

(3/10) X (10/3) =1

So it is the multiplicative inverse

Write:

(i) The rational number that does not have a reciprocal.

(ii) The rational numbers that are equal to their reciprocals.

(iii) The rational number that is equal to its negative.

- 0
- 1 and -1
- 0

Fill in the blanks.

(i) Zero has __________ reciprocal.

(ii) The numbers __________ and __________ are their own reciprocals

(iii) The reciprocal of - 5 is __________.

(iv) Reciprocal of (1/x) where is x ≠ 0 __________.

(v) The product of two rational numbers is always a __________.

(vi) The reciprocal of a positive rational number is __________.

- No
- 1 and -1
- -1/5
- X
- Rational Number
- Positive rational number

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