Operations on Rational Numbers

Which of the following sum is in the simplest form?

State 'T' for true and 'F' for false.

(i) Every rational number can be expressed with a positive numerator.

(ii) Rational numbers $\frac{-11}{5}$, $\frac{1}{6}$, $\frac{3}{10}$, $\frac{6}{15}$ are arranged in ascending order.

(iii) $\left(\frac{8}{5}\times \frac{-3}{2}\right)+$ $\left(\frac{3}{10}\times \frac{11}{8}\right)$can be expressed as $(-1\frac{79}{80})$.

(iv) $\frac{15}{10}$ and $\frac{12}{8}$ are equivalent rational numbers.

Study the following statements carefully and select the correct option.

Statement $1$: Rational numbers are always closed under division.

Statement $2$: Division by zero is not defined.

Match the following.

From his home, Rahul walks $\frac{6}{7}$ km towards school and then returns $\frac{5}{6}$ km on the same way towards his home to reach a landmark. At what distance will he be now from his home?

Three friends Neena, Asha and Mehak divided a packet of rice weighing $87\frac{1}{2} kg$ equally. How many kgs of rice did each get?

$\frac{3}{20}$ of a delegation are from India, $\frac{1}{4}$ are from Britain, $\frac{3}{10}$ are from Germany and the rest are Americans. If there are $1200$ members in the delegation, then calculate how many Americans are there?

A box is to be filled with mangoes, each weighing $\frac{1}{10}kg$. The weight of the box should not exceed $\frac{3}{5}kg.$ Find the maximum number of mangoes that can be put inside the box.

Divide the sum of $\frac{5}{12}$ and $\frac{-17}{24}$ by the product of $\frac{2}{5}$ and $\frac{7}{4}$. What is the result?

Simplify : $\frac{\left(-18\frac{1}{3}\times 2\frac{8}{11}\right)-\left(4\frac{5}{7}\times 2\frac{1}{3}\right)}{\left|\frac{3}{5}+\left(\frac{-9}{10}\right)\right|+\left|-\left(\frac{-3}{5}\right)\right|}$

if $\frac{x}{y}=\frac{9}{8}$, then the value of $\frac{6}{7}+\frac{\left(y-x\right)}{\left(y+x\right)}$ equals

The product of two rational numbers is $-\frac{9}{16}$. If one of the numbers is  $-\frac{4}{3}$, then the other number is _________.

Which of the following statements is true?