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P Pankaj Sanodiya
123456 8 + 6 = 987648 + 6 = 987654 1234567 8 + 7 = 9876536 + 7 = 9876543 Yes, the pattern works. As 123456 = 111111 + 11111 + 1111 + 111 + 11 + 1, 123456  8 = (111111 + 11111 + 1111 + 111 + 11 + 1) 8                    = 111111 8 + 11111 8 + 1111  8 + 111 8 + 11 8 + 1  8                    = 888888 + 88888 + 8888 + 888 + 88 + 8                    = 987648 And, 123456 8 + 6 = 987648 + 6 = 987648

P Pankaj Sanodiya
(a) 728 101= 728 (100 + 1)                      = 728 100 + 728 1                      = 72800 + 728                      = 73528 (b) 5437 1001 = 5437 (1000 + 1)                           = 5437  1000 + 5437  1                           = 5437000 + 5437                           = 5442437 (c) 824 25 (800 + 24) 25 = (800 + 25 - 1) 25                                              =800 ...

P Pankaj Sanodiya
If the product of 2 numbers is 1, then both the numbers have to equal to 1. For example, 1 x 1 = 1 However, 1 x 6 = 6 Clearly, the product of two whole numbers will be 1 in the situation when both numbers to be multiplied are 1.

P Pankaj Sanodiya
If the product of 2 whole numbers is zero, then one of them is definitely zero. For example, 0 x 2 = 0 and 17 x 0 = 0 If the product of 2 whole numbers is zero, then both of them may be zero. 0 x 0 = 0 However, 2 x 3 = 6 (Since numbers to be multiplied are not equal to zero, the result of the product will also be non-zero.)

P Pankaj Sanodiya
(a) 1 + 0 It does not represent zero.   (b) 0 × 0 It represents zero.   (c) It represents zero.   (d) It represents zero.

P Pankaj Sanodiya
We can represent a number by two rectangles. for example 12 = 3 x 4 or 2 x 6 five other such examples are : 24 = 12 x 2  or 24 = 6 x 4  18 = 9 x 2 or 18 = 3 x 6 15 = 15 x 1 or 15 = 3 x 5 30 = 10 x 3 or 30 = 5 x 6  40 = 10 x 4 or 40 = 5 x 8.

P Pankaj Sanodiya
3, 6, 10, 15, 21, 28, 36.

H Harsh Kankaria
can be shown as rectangles.  (Note: We are not counting squares as recatangles here)

H Harsh Kankaria
and  can be shown as squares. 4: 2 rows and 2 columns. 9: 3 rows and 3 columns

H Harsh Kankaria
can be shown only as a line. They cannot be shown as rectangle or square or triangle.

H Harsh Kankaria
(a) Zero is the smallest natural number. - False. 0 is not a natural number. (b) 400 is the predecessor of 399. - False. 400 is the successor of 399. (c) Zero is the smallest whole number. - True. (d) 600 is the successor of 599. - True (e) All natural numbers are the whole numbers.- True. (f) All whole numbers are natural numbers.-False. 0 is a whole number but not a natural number. (g)...

H Harsh Kankaria
(i) (c) Distributivity of multiplication over addition. (ii) (a) Commutativity under multiplication. (iii)   (b) Commutativity under addition.

H Harsh Kankaria
Amount of milk supplied in the morning =  Amount of milk supplied in the evening =  Total amount of petrol =  Cost of 1 litre of milk =   Cost of  of milk =

H Harsh Kankaria
Amount of petrol filled on Monday =  Amount of petrol filled on Tuesday =  Total amount of petrol =  Cost of 1 litre of petrol =   Cost of  of petrol =

H Harsh Kankaria
The product of the folllowing using suitable properties are: (a) Using distributive law.                  (b) Using distributive law. (c) Using Distributive law. (d) Using Distributive law.

H Harsh Kankaria
(a) Using Distributive law.                       (b) Using Commutative under multiplication Using Distributive law.   (c)  Using Distributive law.       (d) Using distributive law.

H Harsh Kankaria
The product of the following by suitable rearrangement are: (a)   (b) (c)                (d)   (e)                     (f)

H Harsh Kankaria
Sum by suitable rearrangement: (a) 837 + 208 + 363   (b) 1962 + 453 + 1538 + 647