Tamil Nadu Board Solutions for Chapter: Numbers, Exercise 7: Exercise 1.3

Explain your answer with reason for the following statement.

A number is divisible by $9$, if it is divisible by $3$.

Explain your answer with reason for the following statement.

A number is divisible by $6,$ if it is divisible by $12$.

Find the length of the longest rope that can be used to measure exactly the ropes of length $1 \mathrm{m} 20 \mathrm{cm},3 \mathrm{m} 60 \mathrm{cm}$ and $4 \mathrm{m}$.

Find the smallest number which is exactly divisible by all the numbers from $1$ to $9$.

Malarvizhi, Karthiga and Anjali are friends and natives of the same village. They work at different places. Malarvizhi comes to her home once in $5$ days. Similarly,Karthiga and Anjali come to their homes once in $6$ days and $10$ days respectively. Assuming that they met each other on the $1^{\text{st }}$ of October, and met again on $k^{st}$ October. Find the value of $k$.

Find whether the number $564872$ is divisible by $88$ (use of the test of divisibility rule for $8$ and $11$ will help)

Wilson, Mathan and Guna can complete one round of a circular track in $10,15$ and $20$ minutes respectively. If they start together at $7 \mathrm{a}.\mathrm{m}.$ from the starting point, at what time will they meet together again at the starting point?

A book seller has $175$ English books, $245$ Science books and $385$ Mathematics books. He wants to sell the books in a box, subject-wise in equal numbers. What will be the greatest number of the boxes required? Also find the number of books for each subject in a box.