An Old Mental Math Trick

16-year-old Helena Muffly wrote exactly 100 years ago today: 

Thursday, September 28, 1911: With just about the same languor as last year, I pursue my studies. It is almost a review, nothing hardly new. Tomorrow we commence with mental arithmetic. Certainly is baby stuff, but we haven’t had it for two years and he thinks we need it. I am eager to take up something I haven’t yet had.

Her middle-aged granddaughter’s comments 100 years later:

Grandma sounds bored. She must have been good at mental arithmetic and found it easy.

In the days before calculators it was important to know how to quickly do various math operations in your head—and students learned many math “tricks” and practiced mental math strategies.

Here is an example of a math trick that enables you to easily multiply certain two digit numbers together in your head:

To multiply together two numbers whose tens are alike, and the sum of whose units is ten.

RULE: Multiply the units together for the two right-hand figures of the product, and the remaining part of the multiplicand by the remaining part of the multiplier increased by 1.

Example: 64 X 66 =  ?




Solution: The 6 units X 4 units = 24 units which we write for the two right-hand figures of the product. Then 6 tens multiplied by 1 more than itself for the remaining figures. Thus, 6 X (6+1) = 42.

 Kimball’s Commercial Arithmetic (1911 )

Now you can try doing some mental math. Here are some oral exercises that were in the book:

Oral Exercises

1.  Multiply 25 by 25

2.  Multiply 35 by 35

3.  Multiply 75  by 75

4.  Multiply 17 by 13

5.  Multiply 43 by 47

6;  Multiply 56 by 54

7;  Multiply 15 by 15

8.  Multiply 22 by 28

9.  Multiply 65 by 65

4 Responses

    • The 1911 arithmetic book is just filled with various mental math tricks. People must have developed huge working memories in the process of becoming good at doing mental math.

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