Multiplying by One-Digit Numbers

Before start the example, i would let you know the rod will set the notation for easily explaination as below:

Example : 4 x 2 = 8

Step 1: Set the multiplicand 4 on the unit rod D and the multiplier 2 on rod A,

thus leaving two vacant rods between

the numbers.

Step 2: Multiply the multiplicand 4 by the mu1tiplier 2. Set the product 8 on F, the second rod to the right of the multiplicand, and clear rod D of its 4.

Note: The accompanying diagram shows another way to illustrate the same problem.

Here the two figures in the row designated Step 1 indicate that the multiplier 2 and the multiplicand 4 have been set on A and D respectively. The two figures in the row designated Result show the multiplier 2 remaining on A and the product 8 which has been set on F as the result of the multiplication.

Example : 8 x 6 = 48

Step 1: Set 8 on the unit rod D and 6 on A, leaving two vacant rods.

tep 2: Multiplying 8 by 6, set the product 48 on EF, and clear D of its 8. In this step, the first rod to the right of the multiplicand, designated E, is the tens’ rod of the product 48.

Note: Some experts say it is desirable to clear away the multiplicand before setting the product. For instance, in the above example, they say that the product 48 should be set on EF after clearing D of its 8. This method has the merit of saving the time of shifting the hand back to the left to clear off the multiplicand after setting the product.  

Example : 24 x 7 = 168

Step 1: Set 24 on DE, with E as the unit rod, and set 7 on A.

Step 2: Multiplying the 4 in 24 by 7, set the product 28 on FG, and clear E of its 4.

Step 3: Multiplying the remaining 2 in 24 by 7, set the product 14 on EF, thereby adding this new product to the 28 on FG, and clear E of its 2.

This makes a total of 168 on EFG, which is the answer.

Note 1: The reason for setting the product 14 on the rods EF, which are one place higher than FG, is obvious. When adding 14, do not take the trouble of thinking that this product is 140 in actual value and that therefore this must be set on EF. Instead just mechanically set the 1 in 14 on E and add the 4 in 14 to the previous 2 on F, and let the result form itself automatically.

Note 2: In Step 2, F is the tens’ rod of the product 28, while in Step 3, E is the tens’ rod of the product 14. In each step of multiplication, the first rod to the right of that figure in the multiplicand which is multiplied is the tens’ rod of the product.

Note 3: When there are two digits in the multiplicand, first multiply the last digit by the multiplier and then the first digit.