If a number is divisible by 9, it must be divisible by 3. (True or False)
The given statement is True 9 = 3 × 3. Hence, if a number is divisible by 9, it will also... View Article
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If a number is divisible by 3, it must be divisible by 9. (True or False)
The given statement is False For example 12 is divisible by 3 but is not divisible by 9
Find the common factors of: (a) 20 and 28 (b) 15 and 25 (c) 35 and 50 (d) 56 and 120
(a) 20 and 28 Answer Factors of 20=1, 2, 4, 5, 10 and 20 Factors of 28= 1, 2, 4, 7,... View Article
Write the smallest digit and the greatest digit in the blank space of each of the following numbers so that the number formed is divisible by 3: (a) __ 6724 (b) 4765 __ 2
(a) __ 6724 Let us first add the digits of the given number 6+ 7+ 4+ 2=19 We know that The... View Article
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... 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... 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... 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... 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... 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... 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... 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... 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 +... 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.... 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
(a) 2 × 1768 × 50 On rearranging the given number we get, = 2 × 50 × 1768 = 100 × 1768 = 176800... 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... View Article
Write the predecessor of: (a) 94 (b) 10000 (c) 208090 (d) 7654321
Solution (a) 94 (a) The predecessors of 94 =94 – 1 = 93 (b) 10000 (b) The predecessors of 10000=10000 – 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... 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... 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 (b) After... View Article
