# Ex.1.1 Q5 Rational Numbers Solution - NCERT Maths Class 8

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## Question

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

(i) \begin{align}\;\frac{{ - 4}}{5} \times 1 = 1 \times \frac{{ - 4}}{5} = \frac{{ - 4}}{5}\end{align}

(ii) \begin{align}\;\frac{{ - 13}}{{17}} \times \frac{{ - 2}}{7} = \frac{{ - 2}}{7} \times \frac{{ - 13}}{{17}}\end{align}

(iii) \begin{align}\;\frac{{ - 19}}{{29}} \times \frac{{29}}{{ - 19}} = 1\end{align}

Video Solution
Rational Numbers
Ex 1.1 | Question 5

## Text Solution

What is known?

Rational number.

What is unknown?

Name of the property.

(i) \begin{align}\;\frac{{ - 4}}{5} \times 1 = 1 \times \frac{{ - 4}}{5} = \frac{{ - 4}}{5}\end{align}

Reasoning:

So, $$1$$ is the multiplicative identity.

Steps:

\begin{align}\;\frac{{ - 4}}{5} \times 1 = 1 \times \frac{{ - 4}}{5} = \frac{{ - 4}}{5}\end{align}

$$\therefore 1$$ is the multiplicative identity and here, property of multiplicative identity is used.

(ii) \begin{align}\;\frac{{ - 13}}{{17}} \times \frac{{ - 2}}{7} = \frac{{ - 2}}{7} \times \frac{{ - 13}}{{17}}\end{align}

Reasoning:

In general, $$a \times b = b \times a$$ for any two rational numbers. This is called commutativity of multiplication.

Steps:

\begin{align}\frac{{ - 13}}{{17}} \times \frac{{ - 2}}{7} &= \frac{{ - 2}}{7} \times \frac{{ - 13}}{{17}}\\ [a \times b] &= [b \times a]\end{align}

Commutativity of multiplication of rational numbers is used here.

(iii) \begin{align}\;\frac{{ - 19}}{{29}} \times \frac{{29}}{{ - 19}} = 1\end{align}

Reasoning:

For a rational number \begin{align}\frac{a}{b}\end{align} the multiplicative inverse is the reciprocal of that number that is \begin{align}\frac{b}{a}\end{align} . So that the product of the rational number and its multiplicative inverse is $$1.$$

Steps:

\begin{align}\frac{{ - 19}}{{29}} \times \frac{{29}}{{ - 19}} &= 1\\\left[ {\left( {\frac{a}{b}} \right) \times \left( {\frac{b}{a}} \right)} \right] &= 1\end{align}

Multiplicative Inverse.

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