Worksheet on Knowing Our Numbers

Worksheet of Knowing Our Numbers for Grade 6

Solved Questions on Knowing Our Numbers

1. If p and q are two co-primes, what is their lowest common multiple?

a) q + p
b) q − p
c) q × p
d) q ÷ p

Answer: c) q × p

Explanation: The LCM of the co-prime numbers is the product of these two numbers.

Hence, LCM (p, q) = p × q = q × p

2. Which of the following numbers is divisible by 21?

a) 27604
b) 27804
c) 27894
d) 27904

Answer: b) 27804

Explanation: To divide the number by 21, it must be divisible by 3 and 7.

Divisibility by 3: To check divisibility by 3, find the sum of its digits to check divisibility.

a) Sum of digits of the number 27604
= 2 + 7 + 6 + 0 + 4 = 19, which is not divisible by 3

b) Sum of digits of the number 27804
= 2 + 7 + 8 + 0 + 4 = 21, which is divisible by 3

c) Sum of digits of the number 27894
= 2 + 7 + 8 + 9 + 4 = 30, which is divisible by 3

d) Sum of digits of the number 27904
= 2 + 7 + 9 + 0 + 4 = 22, which is not divisible by 3

Hence, the numbers 27804 and 27894 are divisible by 3.

Divisibility by 7: To check divisibility by 7, double the last digit and subtract the result from the remaining part of the number to check divisibility.

a) 27604: 2760 – (2 × 4) = 2752 which is not divisible by 7.
b) 27804: 2780 – (2 × 4) = 2772 which is divisible by 7.
c) 27894: 2789 – (2 × 4) = 2781 which is not divisible by 7.
d) 27904: 2790 – (2 × 4) = 2782 which is not divisible by 7.

Hence, the number 27804 is divisible by 7.

Therefore, 27804 is divisible by both 3 and 7. Hence, 27804 is divisible by 21.

3. Identify the suitable law for this identity:

5013 × 5031 − 5013 × 5103 = 5013 × (5031 − 5103)

a) Distributive Law of Addition over Multiplication.
b) Distributive Law of Subtraction over Multiplication.
c) Distributive Law of Multiplication over Addition.
d) Distributive Law of Multiplication over Subtraction.

Answer: d) Distributive Law of Multiplication over Subtraction.

Explanation: The distributive law of Multiplication over Subtraction states that:

If A, B and C are three whole numbers, then

A × (B − C) = (A × B) − (A × C)

Hence, the suitable law for this identity is the distributive law of Multiplication over Subtraction.

5013 × (5031 − 5103) = 5013 × 5031 − 5013 × 5103

5013 × 5031 − 5013 × 5103 = 5013 × (5031 − 5103)

4. The dimensions of a room are 12 m 60 cm, 9 m 45 cm and 11 m 55 cm, respectively. What is the longest rod that can measure precisely three dimensions of a room?

a) 1 m 5 cm
b) 1 m 50 cm
c) 10 m 5 cm
d) 10 m 50 cm

Answer: a) 1 m 5 cm

Explanation: The dimensions of the room are:

Length = 12 m 60 cm = 12 m + 60 cm = (12 × 100) cm + 60 cm = 1260 cm

Breadth = 9 m 45 cm = 9 m + 45 cm = (9 × 100) cm + 45 cm = 945 cm

Height = 11 m 55 cm = 11 m + 55 cm = (11 × 100) cm + 55 cm = 1155 cm

Thus, the longest rod that can measure precisely three dimensions of a room is HCF of 1260, 945 and 1155.

Using prime factorization,

1260 = 2 × 2 × 3 × 3 × 5 × 7

945 = 3 × 3 × 3 × 5 × 7

1155 = 3 × 5 × 7 × 11

HCF (1260, 945, 1155) = 3 × 5 × 7 = 105

Longest rod that can measure the dimensions of the room exactly
HCF (1260, 945, 1155) = 105 cm

= 100 cm + 5 cm

= 1 m 5 cm

5. Four bells will start tolling together at intervals of 15 minutes, 21 minutes, 5 minutes and 30 minutes, respectively. After how many seconds do they toll together?