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Using divisibility tests, determine which of the following numbers are divisible by 11: (a) 5445 (b) 10824 (c) 7138965 (d) 70169308 (e) 10000001 (f) 901153

Solution (a) 5445 Let us carry out the sum of the digits at odd places = 5 + 4 = 9 Let us carry out the sum of the digits at even places... View Article

Using divisibility tests, determine which of following numbers are divisible by 6: (a) 297144 (b) 1258 (c) 4335 (d) 61233 (e) 901352 (f) 438750 (g) 1790184 (h) 12583 (i) 639210 (j) 17852

(a) 297144 As the given number ends with 4. Hence, the last digit is divisible by 2 On adding all the digits of the given number, we... View Article

Using divisibility tests, determine which of the following numbers are divisible by 2; by 3; by 4; by 5; by 6; by 8; by 9; by 10; by 11 (say, yes or no):

Numbers Divisible By 2 3 4 5 6 8 9 10 11 128 Yes No Yes No No Yes No No No 990 ------ ------ ------ ------ ------ ------ ------... View Article

Fill in the blanks: (a) A number which has only two factors is called a . (b) A number which has more than two factors is called a . (c) 1 is neither nor . (d) The smallest prime number is . (e) The smallest composite number is _. (f) The smallest even number is ____.

Solutions: (a)A number which has only two factors is called a prime number. A prime number is the one that has exactly two factors,... View Article

Write seven consecutive composite numbers less than 100 so that there is no prime number between them.

Solution Seven consecutive composite numbers that are less than 100 so that there is no prime number in between lie between numbers 89... View Article

Express the following as the sum of two odd primes. (a) 44 (b) 36 (c) 24 (d) 18

A prime number is a positive integer having exactly two factors. If p is a prime, then its only factors are necessarily 1 and p itself. Except... View Article

What is the greatest prime number between 1 and 10?

A prime number is a number that has exactly two factors, i.e. ‘1’ and the number itself. The prime numbers between 1 and 10 are 2,... View Article

State whether the following statements are True or False: (a) The sum of three odd numbers is even. (b) The sum of two odd numbers and one even number is even. (c) The product of three odd numbers is odd. (d) If an even number is divided by 2, the quotient is always odd. (e) All prime numbers are odd. (f) Prime numbers do not have any factors. (g) Sum of two prime numbers is always even. (h) 2 is the only even prime number. (i) All even numbers are composite numbers. (j) The product of two even numbers is always even.

(a) The sum of three odd numbers is even. The given statement is False. The sum of three odd numbers is odd. Example: 3 + 5 + 7 = 15, which is... View Article

Study the pattern: 1 × 8 + 1 = 9 1234 × 8 + 4 = 9876 12 × 8 + 2 = 98 12345 × 8 + 5 = 98765 123 × 8 + 3 = 987 Write the next two steps. Can you say how the pattern works? (Hint: 12345 = 11111 + 1111 + 111 + 11 + 1)

123456 × 8 + 6 = 987654 1234567 × 8 + 7 = 9876543 Given that 123456 = (111111 + 11111 + 1111 + 111 + 11 + 1) 123456 × 8 =... View Article

Match the following: (i) 425 × 136 = 425 × (6 + 30 + 100) (a) Commutativity under multiplication. (ii) 2 × 49 × 50 = 2 × 50 × 49 (b) Commutativity under addition. (iii) 80 + 2005 + 20 = 80 + 20 + 2005 (c) Distributivity of multiplication over addition.

Column A Column B (i) 425 × 136 = 425 × (6 + 30 + 100) (a) Commutativity under multiplication. (ii) 2 × 49... View Article

Find the product by suitable rearrangement: (a) 2 × 1768 × 50 (b) 4 × 166 × 25 (c) 8 × 291 × 125 (d) 625 × 279 × 16 (e) 285 × 5 × 60 (f) 125 × 40 × 8 × 25

On rearranging the given number we get, = 2 × 50 × 1768 = 100 × 1768 = 176800 On rearranging the given number we get, = 4 × 25 × 166 = 100... View Article

Find the sum by suitable rearrangement: (a) 837 + 208 + 363 (b) 1962 + 453 + 1538 + 647

(a) Given 837 + 208 + 363 On arranging them we get = (837 + 363) + 208 = 1200 + 208 = 1408 837 + 208 + 363=1408 (b) Given 1962 + 453 +... View Article

Write the predecessor of: (a) 94 (b) 10000 (c) 208090 (d) 7654321

Solution (a) The predecessors of 94 =94 – 1 = 93 (b) The predecessors of 10000=10000 – 1 = 9999 (c)The predecessors of 208090= 208090 – 1 =... View Article

Estimate the following products using general rule: (a) 578 × 161 (b) 5281 × 3491 (c) 1291 × 592 (d) 9250 × 29 Make four more such examples.

(a) 578 × 161 On rounding off by general rule 578 rounded off to 600 161 rounded off to 200 respectively 600 × 200... View Article

Estimate each of the following using general rule: (a) 730 + 998 (b) 796 – 314 (c) 12904 + 2888 (d) 28292 – 21496 Make ten more such examples of addition, subtraction and estimation of their outcome.

Solution (a) 730 + 998 On rounding off the numbers to hundreds we get 730 rounds off to 700 998 rounds off to 1000 Hence, 730 + 998 = 700 +... View Article

Place commas correctly and write the numerals: (a) Seventy three lakh seventy five thousand three hundred seven. (b) Nine crore five lakh forty one. (c) Seven crore fifty two lakh twenty one thousand three hundred two. (d) Fifty eight million four hundred twenty three thousand two hundred two. (e) Twenty three lakh thirty thousand ten.

(a) After placing the commas the numeral of the given number seventy-three lakh seventy-five thousand three hundred seven is 73,75,307... View Article

Express the number appearing in the following statement in standard form: The population of India was about 1,027,000,000 in March, 2001.

The population of India was about 1,027,000,000 in March 2001. Answer The given number can be expressed in standard form as 1.027 × 109.... View Article

Express the number appearing in the following statement in standard form: The earth has 1,353,000,000 cubic km of sea water.

The earth has 1,353,000,000 cubic km of seawater. Answer The given number can be expressed in standard form as 1.353 × 109 cubic km.... View Article

Express the number appearing in the following statement in standard form: 60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm.

60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm. Answer The given number can be expressed in standard... View Article

Express the number appearing in the following statement in standard form: The distance of the Sun from the centre of the Milky Way Galaxy is estimated to be 300,000,000,000,000,000,000 m.

The distance of the Sun from the centre of the Milky Way Galaxy is estimated to be 300,000,000,000,000,000,000 m. Answer The given number can be... View Article