Question

Find the value of the following using multiplication pattern
 $ 29 \times 31 $
(A) $ 866 $
(B) $ 799 $
(C) $ 699 $
(D) $ 899 $

Answer 1

Hint: The identity property of multiplication states that for all numbers $ a,a \times 1 = 1 \times a $ . Use of this property leaves $ 45 $ facts to be memorized.

Complete step-by-step answer:
Multiplication pattern $ 29 \times 31 $
 $ = 29 \times 31 $ . . . . (By using $ \left( {{x^2} - {y^2}} \right) = \left( {x - y} \right)\left( {x + y} \right) $ )
 $ = (30 - 1)(30 + 1) $
 $ = 900 - 1 $
 $ = 899 $
Therefore, from the above explanation, the correct option is [D] 899.
The repeated addition of the same number is expressed by multiplication in short. Hence repeated addition of \[2\] five times is equal to $ 2 $ multiply by \[5\]. Thus $ 3 \times 6 = 18 $ that \[3\] multiplied by $ 6 $ is equal to $ 18 $ or product of \[3\] and \[6\] is \[18,\]or \[3\] into \[6\] is equal to\[18\], or\[\;3\] into \[6\] is equal to \[18\], or product of\[\;3\] and \[6\] is \[18\]. $ 3 \times 6 = 18 $ is called a multiplication fact.

Note: The zero property of multiplication states that any number multiplied by zero is zero. That is for any number $ a,a \times 0 = 0 \times a = 0 $ . This post can be used to reduce the number of posts requiring memorization by $ 11, $ having only $ 55 $ posts.