Multiplication and Division of Rational Numbers

Q. If Q is additive inverse of P, then the value of $1-\frac{P+2Q}{P-2Q}$ is
यदि Q, P का योज्य प्रतिलोम है, तब $1-\frac{P+2Q}{P-2Q}$ का मान है

1. 0
2. $-\frac{4}{3}$
3. $\frac{3}{4}$
4. $\frac{4}{3}$

Q.

Find the value of
$-\frac{16}{3}÷-\frac{4}{3}.$

1. 4

2. 2

3. 1

4. 3

Q.

Find the value of
$\frac{-16}{21}÷\frac{-4}{3}.$

1. $\frac{-3}{10}$

2. $\frac{4}{7}$

3. $\frac{-7}{21}$

4. $\frac{-7}{6}$

Q. For every non-zero rational number $\frac{a}{b}$ there exists a rational $\frac{c}{d}$ such that $\frac{a}{b}\times \frac{c}{d}=1$, then the rational number $\frac{c}{d}$ is known as ___.

1. Additive identity
2. Multiplicative identity
3. Additive inverse
4. Multiplicative inverse

Q. Which number is the multiplicative identity for rational numbers?

1. -1
2. 0
3. 1
4. 2

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. If $a=1\frac{5}{7},b=\frac{1}{4},c=\frac{1}{9}andd=(-1\frac{1}{4})$, then $a(b-c)÷d$= ___.

1. $\frac{-4}{21}$
   
   
2. $\frac{-6}{23}$
3. $\frac{-5}{27}$
4. $\frac{5}{21}$

Q. Express $[\frac{-1}{4}-\left(\frac{-1}{6}\right)]÷[\frac{1}{3}+\left(\frac{-1}{2}\right)]$

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

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

1. $\frac{36}{48}$
2. $\frac{25}{64}$
3. $\frac{27}{49}$
4. $\frac{27}{64}$

Q. How many pieces of equal size can be cut from a rope of 30 metres, each measuring $3\frac{3}{4}$ metres?

1. 8 m
2. 10 m
3. 6 m
4. 12 m