Rational Numbers

The standard form of $\frac{-24}{-36}$ is:

If we multiply a rational number by its reciprocal, we get:

What is the additive inverse of $\frac{-11}{-15}$?

Which of the following properties is NOT applicable to the division of rational numbers?

Simplify using the distributive property: $\frac{8}{17} \times \frac{12}{5} - \frac{8}{17} \times \frac{7}{5}$.

Identify the multiplicative inverse of $-3 \frac{2}{5}$.

Calculate the result of $0 \div \frac{4}{5}$.

Let $p = \frac{3}{4}$ and $q = -\frac{1}{3}$. If $x$ is the multiplicative inverse of the sum $(p + q)$ and $y$ is the sum of the multiplicative inverses of $p$ and $q$, find the value of the product $x \times y$.

If $a$ is the multiplicative inverse of $b$, then $b$ is the multiplicative inverse of $a$. This implies:

Simplify: $(\frac{3}{7} \times \frac{-2}{5}) + (\frac{3}{7} \times \frac{-3}{5})$.

In which direction do the values of rational numbers increase on a number line?

The decimal $0.6$ is equivalent to which fraction for representation on the number line?

If you move one unit to the right of $-5$ on the number line, you reach:

The fraction $\frac{4}{4}$ represents the same point as which integer?

On a number line, a point $A$ is at $x$. If moving $2/3$ units to the right of $A$ brings you to $0$, what is $x$?

If a point $X$ represents $\frac{-5}{6}$ and point $Y$ is the additive inverse of $X$, what is the distance between $X$ and $Y$ on the number line?

Which point is the furthest to the left on the number line?

If point $A$ is at $-\frac{4}{9}$ and point $B$ is at $\frac{5}{6}$, find the coordinate of the point $P$ such that the distance $AP$ is exactly double the distance $PB$ and $P$ lies between $A$ and $B$.

On a number line, $x = -\frac{1}{2}$ and $y = -\frac{5}{6}$. Find the coordinate of a point $z$ such that $y < z < x$ and $z$ is exactly at one-third of the distance from $y$ to $x$.

A point $P$ is at $-\frac{5}{9}$. If point $Q$ is $1\frac{2}{3}$ units to the right of $P$ and point $R$ is the midpoint of $PQ$, what is the coordinate of $R$?

A water tank is $\frac{3}{5}$ full. What fraction of the tank is empty?

For which operation is the set of rational numbers NOT commutative?

What is the result of $2 \div \frac{1}{2}$?

Find the value of $| \frac{-1}{2} + \frac{1}{2} |$.

Solve: $\frac{3}{4} + \frac{1}{2} \div \frac{1}{4} - \frac{1}{8}$.

A bottle contains $750$ ml of water. If a boy drinks $\frac{2}{3}$ of the water, how many ml are left in the bottle?

Evaluate the following expression: $(-\frac{1}{2})^3 + (\frac{1}{2})^2$.

A man earns ₹$x$ per month. He spends $\frac{1}{5}$ on rent, $\frac{1}{4}$ of the remainder on food, and $\frac{1}{3}$ of the new remainder on travel. If he saves ₹$8,000$, find $x$.

If $x$ is a rational number such that $x + \frac{1}{2} = \frac{1}{x} + \frac{1}{2}$, then $x$ can be:

A container holds $32$ litres of a mixture of milk and water. $\frac{3}{8}$ of the mixture is milk. If $4$ litres of water are added, what fraction of the new mixture is milk?