Jharne De and Ranjana Kumar Solutions for Chapter: Rational Numbers, Exercise 6: Test Paper 2

A motorboat covers $13\frac{4}{5} \mathrm{m}$ in $1$ second. If the distance covered by the motorboat in $15$ seconds is $k \mathrm{m}$, find $k$.

Verify $\left|x\right|\times \left|y\right|=|x\times y|$ for $x=-\frac{5}{9}$ and $y=-\frac{3}{5}$.

Find the missing number using the properties of the rational number in the following:
$-\frac{4}{7}\times 2\frac{3}{4}=2\frac{3}{4}\times$ _____.

Find the missing number using the properties of the rational number in the following:
$\frac{7}{9}\times \left(\frac{4}{13}-\frac{1}{2}\right)=\frac{7}{9}\times \frac{4}{13}-$ _____ $\times \frac{7}{9}$.

Find the sum and difference of any two rational numbers smaller than $2$.

Use distributive property to solve the following:
$\frac{3}{5}\times \frac{-7}{8}+\frac{9}{15}\times \frac{7}{8}$

Verify and name the property of the following:
$\frac{2}{7}\times \left(\frac{3}{4}-\frac{7}{8}\right)=\frac{2}{7}\times \frac{3}{4}-\frac{2}{7}\times \frac{7}{8}$

Find $6$ rational numbers between $-\frac{5}{7}$ and $-\frac{2}{3}$.