1Mark (√) if true and (×) if false: (a) Any number, however large, can be written using the ten digits 0 to 9. (b) The smallest natural number is zero (0). (c) The first and smallest whole number is zero (0). (d) The natural numbers start at 1 and go on for ever. (e) The smallest number that 2, 1 and 0 can make is 102.
2Write the three digit numbers that can be made from 2, 1 and 7.
3Write the largest and the smallest three digit number that 7, 9 and 0 can make, then find their sum and their difference.
4Simplify: (a) \( 20 + 5 \times 3 \) (b) \( 400 - (50 \times 2) \) (c) \( 80 + (20 \div 4) \) (d) \( 50 \times (4 \div 2) \) (e) \( 44 - \{4 + (5 - 2)\} \)
5Write each of these as a mathematical statement and simplify: (a) Sima had 400 rupees and bought a book for 185 rupees. Her uncle then gave her 200 rupees. How much money does she have now? (b) Rachana gave the shopkeeper a 500 rupee note for 5 exercise books costing 45 rupees each. How much change does she get back?
6Write each statement in mathematical form and simplify: (a) What do you get when the sum of 182 and 8 is divided by the difference of 75 and 65? (b) What do you get when 15 is taken from five times 18 and the result is divided by 5?
7Use the divisibility tests: (a) Which of 1644, 113, 843 and 1056 are exactly divisible by 2? (b) Which of 111, 7542, 9437 and 1464 are exactly divisible by 3?
8Use the divisibility tests: (a) Which of 1434, 1250, 1965 and 2100 are exactly divisible by 5? (b) Which of 9240, 16800, 18480 and 13680 are exactly divisible by 11?
9Write the set of factors of each number: (a) 12 (b) 13 (c) 18 (d) 32 (e) 9
10(a) Write the set of multiples of 4 that are less than 20. (b) Write the set of multiples of 2 that are less than 20. (c) Is every multiple of 4 also a multiple of 2?
11A school bell rings every 45 minutes. How many times does it ring in 3 hours?
12Find the prime factorization of each number by the division method: (a) 275 (b) 729 (c) 625 (d) 288 (e) 720
13Find the prime factors of 450 and 240, and write the prime factors they share.
14(a) Find the square of 1, 6, 4 and 10. (b) Find the square root of 4, 49, 36 and 64. (c) Pick out the square numbers from 21, 25, 63, 36, 4, 49, 99 and 1.
15(a) Students are arranged in a square with 9 in each line and 3 students are left over. How many students are there in all? (b) Students are arranged in a square with 8 in each line and 5 students are short. How many students were there to begin with?
16Find the H.C.F. by making the set of factors: (a) 14 and 21 (b) 16 and 24 (c) 48 and 72
17Find the H.C.F. by the prime factorization method: (a) 60 and 75 (b) 54 and 90 (c) 18, 24 and 36
18At most how many people can 25 oranges and 30 amala be shared between so that everyone gets an equal number of each?
19Find the L.C.M. by making the set of multiples: (a) 10 and 15 (b) 11 and 22 (c) 12 and 16 (d) 15 and 18
20Find the L.C.M. by the prime factorization method: (a) 20 and 25 (b) 32 and 36 (c) 24 and 30
21Show that the product of 12 and 16 equals the product of their H.C.F. and their L.C.M.
22Two measuring tapes are 20 cm and 30 cm long. What is the shortest length that both tapes can measure out exactly?
23Simplify: \( [\,40 \div \{2 + (5 - 3)\}\,] + 7 \)
24Use the divisibility test to show whether 637 is exactly divisible by 7.
25Use the tree method to write the prime factorization of 180.
26When 144 plants are set out in a square with equal numbers in every row and column, how many plants stand in one row?
27Two numbers have H.C.F. 6 and L.C.M. 72. If the first number is 24, what is the second number?