Division of Rational Numbers

Q. By what number should $\frac{-33}{8}$ be divided to get $\frac{-11}{2}$?

1. $\frac{-4}{3}$
2. $\frac{4}{3}$
3. $\frac{3}{4}$
4. $\frac{-3}{4}$

Q.

The product of two rational numbers is $\frac{14}{5}$. If one of them is $\frac{-7}{6},$ find the other.

1. $\frac{12}{5}$

2. $\frac{-12}{5}$

3. $\frac{-6}{5}$

4. $\frac{-8}{5}$

Q.

Division of the reciprocal of $\frac{5}{11}$ by $\frac{-55}{18}$ results in $\frac{-18}{25}$.

1. True

2. False

Q.

What should be added to $-\frac{21}{36}$ to get $-\frac{1}{9}$ ?

1. $\frac{-17}{36}$

2. $\frac{17}{36}$

3. $\frac{-25}{36}$

4. $\frac{25}{36}$

Q. If the product of any two rational numbers is 3 and one of them is $\frac{1}{4}$, then find the other number.

1. 2
2. 12
3. 7
4. 14

Q. The product of two rational numbers is $\frac{-25}{36}$ . If one of the numbers is $\frac{-5}{6}$, find the other number.

1. $\frac{5}{6}$
2. $\frac{6}{5}$
3. $\frac{6}{5}$
4. $\frac{-5}{6}$

Q.

Divide $\frac{-48}{11}$ by $\frac{12}{33}$.

1. $\frac{-3}{4}$

2. $\frac{-4}{3}$

3. 12

4. -12

Q.

If 7 identical articles cost $₹5\frac{2}{21},$ then find the cost of 1 article.

1. $₹\frac{147}{107}$

2. $₹\frac{107}{147}$

3. $₹\frac{7}{20}$

4. $₹1\frac{2}{21}$

Q. Given that $\frac{-6p-9}{3}=\frac{2p+9}{5}$, what is the value of p?

1. 5
2. -2
3. -4
4. 3

Q. Evaluate:
$\frac{-8}{9}+\frac{4}{9}+\frac{-2}{9}$

Q.

A car covers a distance of $30\frac{5}{8}$ km in $2\frac{1}{2}$ hours. How much distance will it cover in 1 hour?

1. $11\frac{1}{4}$ km

2. $12\frac{1}{4}$ km

3. $21\frac{1}{4}$ km

4. $9\frac{1}{4}$ km

Q. A car covers a distance of $30\frac{5}{8}$ km in $2\frac{1}{2}$ hours. How much distance will it cover in 1 hour?

Q.

If the area of a room is $\frac{226}{4}$ m² and its breadth is $\frac{57}{16}$ meters, then what is its length?

1. $\frac{409}{57}$ m

2. $\frac{904}{57}$ m

3. 15$\frac{49}{57}$ m

4. 15$\frac{94}{57}$ m

Q. Using the appropriate properties of operations of rational numbers, evaluate the following:
$\frac{3}{13}\times \frac{4}{5}\times \frac{7}{5}\times \frac{4}{13}\times \frac{5}{13}$

Q. If the area of a room is $\frac{226}{4}$ m² and its breadth is $\frac{57}{16}$ meters, then what is its length?

Q. A car runs $16km$ using $1$ litre of petrol. How much distance will it cover using $2\frac{3}{4}litres$ of petrol?

Q.

A car covers a distance of $30\frac{5}{8}$ km in $2\frac{1}{2}$ hours. How much distance will it cover in 1 hour?

1. $11\frac{1}{4}$

2. $12\frac{1}{4}$

3. $21\frac{1}{4}$

4. $9\frac{1}{4}$

Q. Simplify : $\frac{3}{8}\times [5+\{\frac{3}{4}-(\frac{1}{2}-\frac{1}{3})\}]÷6\frac{7}{10}$

Q. Match the following.

1. $\frac{23}{9}$
2. $-4$
3. $-\frac{25}{4}$
4. $\frac{5}{7}$

Q. A car covers a distance of $30\frac{5}{8}$ km in $2\frac{1}{2}$ hours. How much distance will it cover in 1 hour?
[2 Marks]

Q.

Division of the reciprocal of $\frac{5}{11}$ by $\frac{-55}{18}$ results in $\frac{-18}{25}$.

1. False

2. True

Q.

The reciprocal of ____________ does not exist.

Q. $(-37)+6=?$

1. $31$
2. $-43$
3. $-31$
4. None of these

Q. Match the correct answers.

1. $\frac{7}{3}$
2. -1
3. 1
4. $\frac{-3}{7}$

Q.

Choose the rational numbers whose numerator is $(-5)\times 6$, and the denominator is $(34-23)\times (7-5)$.

1. $\frac{20}{11}$

2. $\frac{40}{22}$

3. $\frac{-15}{11}$

4. $\frac{-30}{22}$

Q.

Divide $\frac{-48}{11}$ by $\frac{12}{33}$.

1. $\frac{-3}{4}$

2. $\frac{-4}{3}$

3. $\frac{-2}{3}$

4. $\frac{3}{4}$

Q.

If 7 identical articles cost $₹5\frac{2}{21},$ then find the cost of 1 article.

1. $₹\frac{147}{107}$

2. $₹\frac{107}{147}$

3. $₹\frac{7}{20}$

4. $₹1\frac{2}{21}$

Q.

The product of two rational numbers is $\frac{-36}{49}$ . If one the numbers is $\frac{-4}{7}$, find the other number.

1. - 8

2. 9

3. - 10

4. 10

Q. A vehicle covers a distance of $43.2$ km in $2.4$ litres of petrol. How much distance will it cover in one litre of petrol ?