Q1. Divide the sum of \( \frac{2}{5} \) and \( \frac{3}{4} \) by the product of \( \frac{1}{2} \) and \( \frac{3}{7} \).

Q2. By what rational number should \( \frac{7}{8} \) be multiplied to get the product as \( \frac{21}{32} \)?

Q3. Verify the commutative property of addition for the following pairs of rational numbers:
(i) \( \frac{2}{5} \) and \( \frac{3}{7} \)
(ii) \( -\frac{4}{9} \) and \( \frac{5}{12} \)

Q4. Ramesh cut a 21 m long rope into pieces of 4 m length each. How many pieces of the rope did he get?

Q5. A, B, C, D, and E went to a restaurant for dinner. A paid \( \frac{2}{5} \) of the bill, B paid \( \frac{1}{4} \) of the bill, and the rest of the bill was shared equally by C, D, and E. What fraction of the bill was paid by each?

Q6. Find the multiplicative inverse of \( \frac{2}{5} \).

Q7. Find the additive inverse of \( \frac{12}{11} \).

Q8. Solve the following equations and check the solutions:
(i) \( 5 - 3(5x + 2) = 4(7 - 3x) + 1 \)
(ii) \( \frac{6x + 1}{3} + 1 = x - 3 \)

Q9. The sum of two numbers is 90 and the greater number exceeds thrice the smaller by 14. Find the numbers.

Q10. Find two consecutive even integers such that two-fifths of the smaller exceeds two-elevenths of the larger by 4.

Q11. The denominator of a fraction exceeds its numerator by 4. If the numerator and denominator are both increased by 3, the new fraction becomes \( \frac{3}{4} \). Find the original fraction.

Q12. When four consecutive integers are added, the sum is 46. Find the integers.

Q13. HIKE is a parallelogram. Find \( x \) and \( y \):
[tex]\[
\begin{align*}
E & \\
H & 2x + 10 \\
& 5y + 9 \\
K & 4y + 12 \\
& 3x + 9 \\
\end{align*}
\][/tex]

Q14. RICE is a rhombus. Find \( x \) and \( y \):
[tex]\[
\begin{align*}
E & x + 4 \\
& 6y + 8 \\
C & 2y + 9 \\
& 2x + 3 \\
\end{align*}
\][/tex]