Introduction to Rational Numbers

A girl is $18$years younger than her mother. In $6$years' time, the sum of their ages will be $54$. Find the age of girl.

Direction: What will come in place of the question mark(?) in the following questions?

If Bhanu spends $\frac{1}{5}$ of her pocket money on bags, $\frac{1}{8}$ on accessories, $\frac{1}{4}$ on food, $\frac{1}{10}$ on conveyance and $\frac{1}{20}\mathrm{th}$ on music CDS. If at the end of the month she saved $₹ 1210$ , find her expenditure on food and conveyance.

Direction: What will come in place of the question mark(?) in the following questions?

In a firm, $\frac{1}{3}$ of the total employees work in the production department, $\frac{1}{12}$ of the total employees are in an HR department, $\frac{1}{4}$ in the marketing department and $\frac{1}{12}$ of the total employees are in the accounts department. If the rest of the $120$ employees are from the miscellaneous department, find the total employees in the HR and marketing departments.

Direction: What will come in place of the question mark(?) in the following questions?

Sugandha spent $\frac{1}{3}$ of her profit on electricity bill and $\frac{1}{2}$ on the purchase of new furniture $\frac{1}{6}$ of the profit she left with after incurring all the office expenses is $₹ 12,000$. What will the expenditure on electricity be?

Direction: What will come in place of the question mark(?) in the following questions?

A man spends $\frac{2}{5}$ of his salary on house rent. $\frac{3}{10}$ of his salary spend on food and $\frac{1}{8}\mathrm{th}$ of his salary spend on conveyance. If he has $₹ 21,000$ left with him, find his expenditure on house rent and food.

State True or False
$2\times \left(6+3\right)=2\times 6+2\times 3$

State True or False
$15+8=8+$_____

Additive inverse of integer $7$ is _____

State True or False
The solution of the equation $5x+7=0$ is a whole number.

State True or False
When we add two whole numbers, the result will always be a whole number.

The solution of the equation $x+2=3$ is _____

State True or False
The solution of the equation $x+5=5$ is a whole number.

State True or False
When we subtract two whole numbers, the result will always be a whole number.

If the value the given rational number in the simplest form $\frac{18}{45}$ is $\frac{a}{5}$, then find the value of $a$

Convert the following rational numbers to decimal form: $\frac{-16}{5}$

Express the following rational numbers in decimal form: $\frac{3 }{8 }$

Express the following rational numbers in decimal form: $\frac{19}{6}$

If $\mathrm{x}=\frac{5}{9}, \mathrm{y}=\frac{2}{3}$, then show that $|x\times y|=\left|x\right|\times \left|y\right|$

Solve:

$\frac{13}{15}\times \left(\frac{-25}{26}\right)$

Solve:

$\left(\frac{-36}{5}\right)\times \left(\frac{20}{-3}\right)$