(-5/9+2/-5)+-11/18 = -5/9+ (2/-5+-11/18) plz answer me fast and with steps
Answers
Answer:
5. Write the smallest 5-digit number and express it in the form of its prime factors.
Solutions:
The smallest five digit number = 10000
NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.5 - 6
10000 = 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5
6. Find all the prime factors of 1729 and arrange them in ascending order. Now state the relation, if any; between two consecutive prime factors.
Solutions:
NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.5 - 7
1729 = 7 × 13 × 19
13 – 7 = 6
19 – 13 = 6
Hence, the difference between two consecutive prime factors is 6.
7. The product of three consecutive numbers is always divisible by 6. Verify this statement with the help of some examples.
Solutions:
(i) 2 × 3 × 4 = 24 which is divisible by 6
(ii) 5 × 6 × 7 = 210 which is divisible by 6
8. The sum of two consecutive odd numbers is divisible by 4. Verify this statement with the help of some examples.
Solutions:
(i) 5 + 3 = 8 which is divisible by 4
(ii) 7 + 9 = 16 which is divisible by 4
(iii) 13 + 15 = 28 which is divisible by 4
9. In which of the following expressions, prime factorisation has been done?
(a) 24 = 2 × 3 × 4
(b) 56 = 7 × 2 × 2 × 2
(c) 70 = 2 × 5 × 7
(d) 54 = 2 × 3 × 9
Solutions:
(a) 24 = 2 × 3 × 4
Since, 4 is composite. Hence, prime factorisation has not been done
(b) 56 = 7 × 2 × 2 × 2
Since, all the factors are prime. Hence, prime factorisation has been done
(c) 70 = 2 × 5 × 7
Since, all the factors are prime. Hence, prime factorisation has been done
(d) 54 = 2 × 3 × 9
Since, 9 is composite. Hence prime factorisation has not been done
10. Determine if 25110 is divisible by 45. [Hint: 5 and 9 are co-prime numbers. Test the divisibility of the number by 5 and 9].
Solutions:
45 = 5 × 9
1, 5 are factors of 5
1, 3, 9 are factors of 9
Hence, 5 and 9 are co-prime numbers
The last digit of 25110 is 0. Hence, it is divisible by 5
Sum of digits 25110
2 + 5 + 1 + 1 + 0
= 9
Since, the sum of digits of 25110 is divisible by 9. Hence, 25110 is divisible by 9
Since the number is divisible by both 5 and 9
Therefore 25110 is divisible by 45
11. 18 is divisible by both 2 and 3. It is also divisible by 2 × 3 = 6. Similarly, a number is divisible by both 4 and 6. Can we say that the number must also be divisible by 4 × 6 = 24? If not, give an example to justify your answer.
Solutions:
No, since, 12 and 36 are both divisible by 4 and 6. But 12 and 36 are not divisible by 24
12. I am the smallest number, having four different prime factors. Can you find me?
Solutions:
Since, it is the smallest number. Therefore it will be the product of 4 smallest prime numbers
2 × 3 × 5 × 7 = 210