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Under which property multiplication used in $\frac{- 19}{29} \times \frac{29}{- 19} = 1$ ?

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Commutative Property

Multiplicative inverse

Associative Property

Identity Property

answer is B.

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Detailed Solution

It is given the expression is

\frac{- 19}{29} \times \frac{29}{- 19}

.
We know that multiplicative inverse for any number

n

\frac{1}{n}

where

n \neq 0 .

The product of a number and its multiplicative inverse is

1

.
Let us take a number

n = \frac{- 19}{29}

.
From definition the multiplicative inverse of

n

is,

\frac{1}{n} = \frac{29}{- 19}

Now consider the product of

n

and

\frac{1}{n}

as follows,

\frac{- 19}{29} \times \frac{29}{- 19} = 1

Hence, multiplicative inverse property is used in

\frac{- 19}{29} \times \frac{29}{- 19} = 1

.
Therefore, the correct option is 2.

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