Give an example to show that if two numbers are divisible by the given number, then the sum of the two
numbers is also exactly divisible by the same number.

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Solution

$21$ and $18$ are divisible by $3$ .
Therefore, if $21$ and $18$ are divisible by $3$ , then their sum i.e., $21 + 18 = 39$ is also divisible by $3$ .
Note: If two given numbers are divisible by a number, then their difference is also divisible by that number.

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Q. Which of the following statements are true?

(i) If a number is divisible by 3, it must be divisible by 9.
(ii) If a number is divisible by 9, it must be divisible by 3.
(iii) If a number is divisible by 4, it must be divisible by 8.
(iv) If a number is divisible by 8, it must be divisible by 4.
(v) A number is divisible by 18, if it is divisible by both 3 and 6.
(vi) If a number is divisible by both 9 and 10, it must be divisible by 90.
(vii) If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.
(viii) If a number divides three numbers exactly, it must divide their sum exactly.
(ix) If two numbers are co-prime, at least one of them must be a prime number
(x) The sum of two consecutive odd numbers is always divisible by 4.

Which of the following statements are true ?
(i) If a number is divisible by 3, it must be divisible by 9.
(ii) If a number is divisible by 9, it must be divisible by 3.
(iii) If a number is divisible by 4, it must be divisible by 8.
(iv) If a number is divisible by 8, it must be divisible by 4.
(v) A number is divisible by 18, if it is divisible by both 3 and 6.
(vi) If a number is bivisible by both 9 and 10, ut nyst be divisible by 90.
(vii) If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.
(viii) If a number divides three numbers exactly, it must divede their sum exactly.
(ix) If two numbers are co-prime , at least one of them must be a prime number.
(x) The sum of two consecutive odd numbers is always divisible by 4.

Which ofthe following statements are true?

(a) If anumber is divisible by 3, it must be divisible by 9.

(b) If anumber is divisible by 9, it must be divisible by 3.

(d) If anumber is divisible by 9 and 10 both, then it must be divisible by90.

(e) If twonumbers are co-primes, at least one of them must be prime.

(f) Allnumbers which are divisible by 4 must also be divisible by 8.

(g) Allnumbers which are divisible by 8 must also be divisible by 4.

(h) If a number exactly divides two numbers separately, it mustexactly divide their sum.

(i) If a number exactly divides the sum of two numbers, it mustexactly divide the two numbers separately.

Q. Choose the correct statements
S1: All the numbers divisible by 10 are also divisible by 5.
S2: A number divisible by 3 is also divisible by 6.
S3: A number is divisible by 7, if the last two digits are divisible by 7.
S4: If a number divides the product of two numbers exactly then it must exactly divide the numbers separately.
S5: If a number exactly divides two numbers separately, and after division, if its difference is taken then this difference will also be exactly divisible by that number.

Check if the given set of numbers is exactly divisible by $4$ . If yes , then find out whether the sum and difference of the two numbers are also exactly divisible by $4$ .

$64$ and $16$

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Give an example to show that if two numbers are divisible by the given number, then the sum of the twonumbers is also exactly divisible by the same number.

21 and 18 are divisible by 3. Therefore, if 21 and 18 are divisible by 3, then their sum i.e., 21+18=39 is also divisible by 3.Note: If two given numbers are divisible by a number, then their difference is also divisible by that number.

Give an example to show that if two numbers are divisible by the given number, then the sum of the two
numbers is also exactly divisible by the same number.

$21$ and $18$ are divisible by $3$ .
Therefore, if $21$ and $18$ are divisible by $3$ , then their sum i.e., $21 + 18 = 39$ is also divisible by $3$ .
Note: If two given numbers are divisible by a number, then their difference is also divisible by that number.