Sure, let's solve each question step-by-step.
Problem 4:
From a rope of length [tex]\( 20 \frac{1}{2} \, m \)[/tex], a piece of length [tex]\( 3 \frac{5}{8} \, m \)[/tex] is cut off. To find the length of the remaining rope, follow these steps:
1. Convert the mixed numbers to improper fractions or decimals for easier calculation.
- [tex]\( 20 \frac{1}{2} \, m = 20 + 0.5 = 20.5 \, m \)[/tex]
- [tex]\( 3 \frac{5}{8} \, m = 3 + \frac{5}{8} = 3 + 0.625 = 3.625 \, m \)[/tex]
2. Subtract the length of the piece cut off from the initial length of the rope.
- Remaining length of the rope = [tex]\( 20.5 \, m - 3.625 \, m \)[/tex]
Therefore, the length of the remaining rope is [tex]\( 16.875 \, m \)[/tex].
Problem 5:
The weights of three packets are [tex]\( 2 \frac{3}{4} \, kg \)[/tex], [tex]\( 3 \frac{1}{3} \, kg \)[/tex], and [tex]\( 5 \frac{2}{5} \, kg \)[/tex]. Find the total weight.
1. Convert the mixed numbers to improper fractions or decimals.
- [tex]\( 2 \frac{3}{4} \, kg = 2 + 0.75 = 2.75 \, kg \)[/tex]
- [tex]\( 3 \frac{1}{3} \, kg = 3 + 0.33333 \approx 3.33333 \, kg \)[/tex]
- [tex]\( 5 \frac{2}{5} \, kg = 5 + 0.4 = 5.4 \, kg \)[/tex]
2. Add the weights of all three packets.
- Total weight = [tex]\( 2.75 \, kg + 3.33333 \, kg + 5.4 \, kg \)[/tex]
Therefore, the total weight of all the three packets is [tex]\( 11.48333 \, kg \)[/tex].
Problem 6:
Shivani read 25 pages of a book containing 100 pages. Nandni read [tex]\( \frac{2}{5} \)[/tex] of the same book. Determine who read less.
1. Calculate the number of pages Nandni read.
- Nandni read = [tex]\( \frac{2}{5} \times 100 = 40 \)[/tex] pages.
2. Compare the pages read by Shivani and Nandni.
- Shivani read 25 pages.
- Nandni read 40 pages.
Since 25 pages < 40 pages, Shivani read less.
Therefore, the answer is Shivani.
