Lincoln practiced arithmetic problems in a sum book made of folded paper and stitched in the middle. Historians believe that Lincoln practiced these problems in 1824 when he was 15 years old.
Note the verse in the lower left corner:
Questions for Illustrations 1 & 2
In Illustration 2, Lincoln assigned himself the problem of multiplying 342,435 by 342. Attempt to solve this problem. Once you have your answer, you can check it just like Abraham checked his. He used a technique called the "Rules of Nines." Follow the directions below.
1. First draw a sizeable X on your paper and put an "A" on the right side of the X, a "B" on the left side, a "C" on top, and a "D" on bottom.
2. What do you get when you add together all the numerals in the multiplicand? Add the numerals in 342,435 or: 3 + 4 + 2 + 4 + 3 + 5.
3. Add together the numerals that make up the multiplier of 342 (3 + 4 + 2).
4. Finally, add up the numerals in your product (the answer you got when you multiplied 342,435 by 342. That's ___ + ___ + ___ + ___ + ___ + ___ + ___ + ____ + ___.
5. What was the number you got when you added up the numerals in the multiplicand? (Your answer for #1) Divide this number by 9. Put your remainder in the big "X" below, right next to the letter A.
6. What did you get when you added up the numerals in the multiplier? (Your answer for #2) Divide that number by 9 and put the remainder in the "X" by the letter B.
7. Now do the same thing with the number you got once you added the numerals in the product. Put the remainder in the top of the "X", next to the letter C.
8. Here are the last three steps. Multiply together the number you put next to A with the number you put next to B. Divide by 9 one last time and put your remainder next to D, in the bottom of the "X."
9. Is the number you put in the top of the "X" (near the C) the same as the number in the bottom of the "X" (near D)? Then your multiplication is correct! Did you get an X that looks like the one by Lincoln?
* The images on this screen have a resolution of 72 dots per inch (dpi), and therefore will print poorly. You can obtain a larger version of Illustration 1 and Illustration 2, but be aware that each file will take as much as 60 seconds to load with a 28.8K modem.