Rational and Irrational Numbers on Number Line

$\frac{x}{20}=\frac{54}{x}, x=?$

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.

Solve:

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

How many times do we use $9$ to write the numbers between $1$ to $100$?

Represent $\frac{-7}{4}$ on the number line.

Represent on the number line: $\frac{11}{2}$.

Represent  on the number line: $\frac{9}{4}$

Every natural number is a rational number. 

Every integer is a natural number

In the number line below, D is the midpoint between B and C and the length of AC is half the length of CD.

Point A represents the rational number, _____.

(Note: Enter the simplest form of the rational number.)

In the number line below, M represents 0 and N represents $ \frac{1}{5}$.

Which of the following points could be representing $ -0.5$?

Look at the number line below.

The rational number that $\text{'}p\text{'}$ is representing on the number line is _____.

In the number line shown below $C$ is the mid point of $AB$.

$C$ represents the rational number _____.

(Note: Expects the answer in $\frac{p}{q}$ form simplified to the lowest form.)

Write five rational numbers which are less than $-2$.

The rational number that does not have a reciprocal is $0$.

Write any $6$ rational numbers of your choice.