General Multiplication

Multiply by a single figure number

We have seen various methods of multiplication but they were all for special cases, where some special condition was satisfied, like both numbers being close to 100 for example. We come now to the general multiplication technique, by which any two numbers can be multiplied together in one line, by mere mental arithmetic. First let us briefly revise how we multiply by a single figure number
Find 74 × 8.
We multiply each of the figures in 74 by 8 starting at the left: 7 × 8 = 56 and 4 × 8 = 32.
56 and 32     in the last part 2 is as it is and 3 is carry over 6+3=9  and 5 as it is
These are combined by carrying the 3 in 32 over to the 6 in 56: 5 23,6 = 592. The inner figures are merged together.
So 74 × 8 = 592.
Find 827 × 3. The three products are 24, 6, 21.
1 as it is 6+2=8 ,4  ( no any carry ) ,  2 as it is
So 827 × 3 = 2481. 

Practice A Multiply the following mentally: a 73 × 3    b 63 × 7     c 424 × 4     d 777 × 3                                                                                             e 654 × 3 f 717 × 8 g 876 × 7 

TWO-FIGURE NUMBER

The Vertically and Crosswise formula gives us the pattern for multiplying any numbers. 

Find 21 × 23. Think of the numbers set out one below the other: 

         2    1

                                    2      3

         ----------------------                                 

                                                                                          483

There are 3 steps 

A. Multiply vertically in the right-hand column:1  × 3= 3 

 B. Multiply crosswise and add: 

 2 × 3 = 6, 

 1 × 2 = 2,

6 + 2 = 8,  so 8 is the middle figure of the answer. 4 8

 C. Multiply vertically in the left-hand 2 1 column: 2× 2 = 4, 4 is the last figure of the answer. 

  Practice B Multiply mentally: a  31×31   b 21×31 c 32×31 d 22×13 e 13×12