Properties of Rational Numbers

Write the rational number for each point labelled with letters, on the number line:

Write the rational number for each point labelled with letters, on the number line:

Find using distributivity: $\left\{\frac{9}{16}\times \frac{4}{12}\right\}+\left\{\frac{9}{16}\times \left(\frac{-3}{9}\right)\right\}$

Find using distributivity: $\left\{\frac{7}{5}\times \left(\frac{-3}{12}\right)\right\}+\left\{\frac{7}{5}\times \frac{5}{12}\right\}$

Write:
The rational numbers that are equal to their reciprocals.

Tell what property allows you to compute $\frac{1}{3}\times \left(6\times \frac{4}{3}\right)$ as $\left(\frac{1}{3}\times 6\right)\times \frac{4}{3}$.

Name the property under multiplication used in the following:

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

Name the property under multiplication used in the following:
$\frac{-13}{17}\times \frac{-2}{7}=\frac{-2}{7}\times \frac{-13}{17}$

The reciprocal of a positive rational number is _____. (positive/negative)

The product of two rational numbers is always a _____ number.

Reciprocal of $\frac{1}{x}$, where $x\ne 0$ is _____.

The reciprocal of $–5$ is $k$, then $-5k=$ _____.

Zero has _____ reciprocal.

Write the rational number that is equal to its negative.

Write the rational number that does not have a reciprocal.

Multiply $\frac{6}{13}$ by the reciprocal of $\frac{-7}{16}$. [Give the answer in $\frac{p}{q}$ form]

Name the property under multiplication used in the following.

$\frac{-4}{5}\times 1=1\times \frac{-4}{5}=\frac{-4}{5}$

Find the multiplicative inverse of $-1$.

Find the multiplicative inverse of the following.
$-1\times \frac{-2}{5}$

Find the multiplicative inverse of the following.
$\frac{-5}{8}\times \frac{-3}{7}$