Rupesh Pathak and Vaishali Bhatia Solutions for Chapter: Rational Numbers, Exercise 7: Worksheet

State whether the following is true or false.

$\frac{4}{5}-\left(\frac{-1}{6}\right)\ne \frac{1}{6}-\left(\frac{-4}{5}\right).$

Name the property used in each of the following $\frac{-2}{5}\times \left(\frac{1}{3}-\frac{4}{7}\right)=\frac{-2}{5}\times \frac{1}{3}-\frac{2}{5}\times \frac{-4}{7}.$

Name the property used: $7+\frac{1}{3}=\frac{1}{3}+7.$
 

Name the property used in each of the following $\left(\frac{-6}{7}\right)\times \left(\frac{1}{3}\times \frac{-4}{5}\right)=\left(\frac{-6}{7}\times \frac{1}{3}\right)\times \left(\frac{-4}{5}\right).$

Name the property used in each of the following $\left(\frac{-11}{15}\right)\times \left(\frac{-5}{44}\right)=\left(\frac{-5}{44}\right)\times \left(\frac{-11}{15}\right).$

Write any six rational number between $\frac{-1}{7} \mathrm{and} \frac{1}{7}.$

Represent $\frac{-3}{5}÷\left(\frac{-2}{5}\right) \mathrm{and} \left[\frac{1}{4}\times \left(\frac{-1}{3}\right)\right]+\frac{1}{3}$ on the same number line.

Find any $10$ rational number between $\left(\frac{2}{5}÷\frac{1}{3}-\frac{4}{15}\right) \mathrm{and} \left(\frac{4}{3}\times \frac{5}{4}÷\frac{25}{2}\right).$