Multiplying by Two-Digit Numbers

Example : 8 x 17 = 136

Step 1: Set 8 on the unit rod E and 17 on AB.

Step 2: Multiplying the 8 by the 1 in 17, set the product 8 on G.

Step 3: Multiplying the 8 by the 7 in 17, set the product 56 on GH, and clear E of its 8. Since you already have 8 on G, you get, on FGH, a total of 136, which is the answer.

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

Example : 46 x 23 = 1,058

Step 1: Set 46 on EF, with E as the unit rod, and set 23 on AB.

Step 2: Multiplying the 6 in 46 by the 2 in 23, set the product 12 on GH.

Step 3: Multiplying the same 6 in 46 by the 3 in 23, set the product 18 on HI and clear F of its 6. Since you have 12 on GH, you get a total of 138 on GH.

Remember that each time the same digit in the multiplicand is multiplied by one digit after another in the multiplier, the value of the product is reduced by one rod or place.

Step 4: Multiplying the 4 in 46 by the 2 in 23, set the product 8 on G. This makes a total of 938 on GH.

Step 5: Multiplying the same 4 in 46 by the 3 in 23, set the product 12 on GH and clear E of its 4. This leaves the answer 1 058 on FGHI.

Note: In case both the multiplier and the multiplicand have two digits, (1) multiply the last digit of the multiplicand by the first digit of the multiplier; (2) multiply the same digit of the multiplicand by the last digit of the multiplier;

(3) multiply the first digit of the multiplicand by the first digit of the multiplier; and (4) multiply the same first digit of the multiplicand by the last digit of the multiplier. This is the fundamental rule of multiplication.

Example : 97 x 48 = 4 656

Step 1: Set 97 on EF, with F as the unit rod, and set 48 on AB.

Step 2: Multiplying the 7 in 97 by the 4 in 48, set the product 28 on GH.

Step 3: Multiplying the same 7 in 97 by the 8 in 48, set the product 56 on HI, and clear F of its 7. Since you have 28 on GH, you get a total of 336 on GHI.

Step 4: Multiplying the remaining 9 in 97 by the 4 in 48, set the product 36 on FG. This makes a total of 3 936 on FGHI.

Step 5: Multiplying the same 9 in 97 by the 8 in 48, set the product 72 on GH, and clear E of its 9. This gives you, on FGHI, a total of 4 656, which is the answer.

Note: The preceding examples will have indicated the desirability of clearing off each digit in the multiplicand after its multiplication by all the digits in the multiplier. If you did not do so, you would be greatly inconvenienced in operation. This is especially the case when the multiplicand is a large number. First, you would often find it hard to tell which of the digits in the multiplicand you had multiplied by all the digits in the multiplier. Second, this incorrect procedure would necessitate the removal of the multiplier further to the right beyond the product of the correct procedure by as many digits as there are in the multiplicand.