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Using appropriate properties find:

(i)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:

(a) $\frac {2}{8}$

(b) $ \frac {-5}{9}$

(c) $\frac {-6}{-5}$

(d) $\frac {2}{-9}$

(e) $\frac {19}{-6}$

(i) $\frac {2}{8}$

Additive inverse of $\frac {2}{8}$= $\frac {-2}{8}$

(ii) $ \frac {-5}{9}$

Additive inverse of $ \frac {-5}{9}$ = $ \frac {5}{9}$

(iii) $\frac {-6}{-5} =\frac {6}{5}$

Additive inverse of $\frac {-6}{-5}$= $\frac {-6}{5}$

(iv)$\frac {2}{-9}=\frac {-2}{9}$

Additive inverse of $\frac {2}{-9}$ =$\frac {2}{9}$

(v) $\frac {19}{-6}= \frac {-19}{6}$

Additive inverse of $\frac {19}{-6}$ =$\frac {19}{6}$

Verify that - ( -

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

(i) 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)

(ii) x=-13/17

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.

(a)$-13$

(b)$ \frac {-13}{19}$

(c) $\frac {1}{5}$

(d) $\frac {-5}{8} \times \frac {-3}{7}$

(e) $-1 \times \frac {-2}{5}$

(f) $-1$

(a) $-13$

Multiplicative inverse of $-13$=$\frac {-1}{13}$

(b)$ \frac {-13}{19}$

Multiplicative inverse of $ \frac {-13}{19}$ =$ \frac {-19}{13}$

(c)$\frac {1}{5}$

Multiplicative inverse of $\frac {1}{5}$=$5$

(d) $\frac {-5}{8} \times \frac {-3}{7}=\frac {15}{56}$

Multiplicative inverse of $\frac {-5}{8} \times \frac {-3}{7}$ =$\frac {56}{15}$

(e) $-1 \times \frac {-2}{5}= \frac {2}{5}$

Multiplicative inverse of $-1 \times \frac {-2}{5}$ =$ \frac {5}{2}$

(f) $-1$<

Multiplicative inverse of $-1$=-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 $ \frac {6}{13} \times (- \frac {16}{7}) =- \frac {96}{91}$

Associativity

Is 8/9 the multiplicative inverse of $-1 \frac {1}{8}$

Why or why not?

$-1 \frac {1}{8}$

$=\frac {-9}{8}$

Now

$ \frac {8}{9} \times (-\frac {9}{8}) = -1$

So it is not the multiplicative inverse

Why or why not?

$3 \frac {1}{3}$

=10/3

Now

$ \frac {3}{10} \times \frac {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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