Answered

Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

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]

Sagot :

GinnyAnswer
Let’s address Q.4:

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

To solve this, we need to understand how many whole pieces of 4 meters can be cut from a 21-meter long rope, and if there are any leftovers.

1. Total length of the rope: 21 meters
2. Length of each piece: 4 meters

We can find the number of 4-meter pieces by performing the division:

- Number of pieces = Total length of the rope / Length of each piece
- Leftover length = Total length of the rope % Length of each piece

Performing the calculation:
1. Number of pieces: \(21 \div 4 = 5\) pieces (since \(4 \times 5 = 20\), which is the maximum whole pieces we can get from 21 meters)
2. Leftover length: \(21 \mod 4 = 1\) meter (since \(21 - 20 = 1\))

So, Ramesh got 5 pieces of 4 meters each from the 21-meter long rope, and there is 1 meter of rope left over.

Answer: Ramesh got 5 pieces of the rope and there was 1 meter left.
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.