Two Old Mental Math Tricks for Adding Fractions

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

Tuesday, September 24, 1912:  It is raining now. I guess or was. Had an exam in Geometry. Took up Arithmetic today. Didn’t have to but I chose to do so.

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

High school courses apparently were only a month of so long a hundred years ago.

I wonder why Grandma decided to take Arithmetic if it wasn’t required. Maybe she enjoyed doing mental math.

Here are two mental math tricks for adding fractions that I found in a hundred year old textbook:

Example 1: Add two fractions whose numerators are 1.

Solution: Add the denominators, and place the sum over the product of the denominators.

Example 2: Add two fractions whose numerators are alike and greater than 1.

Solution: Add the denominators and multiply the sum by the numerator of either of the fractions, and write the product over the product of the denominators.

Source: Kimball’s Commercial Arithmetic (1911)

If you like  math, you might also enjoy these previous posts:

An Old Mental Math Trick

Odd, Unusual, and Strange Math Problems

More Odd, Unusual, and Strange Math Problems

Cube Root Word Problems

1911 Algebra Problems: The Lusitania and Molasses

Old Math Problems

7 Responses

  1. Your ready for algebra.

  2. That’s an interesting approach Sheryl. I’d have approached it quite differently….

  3. I have to admit I couldn’t even read the whole thing. I am sharing it with my husband who does tutoring in math and I think he was working with fractions recently.

    • Even when using the tricks recommended in the book, the math seems difficult. I don’t know how people were able to do so much in their heads back then .

      • I don’t even know if I would think it quite difficult, my mind just wanders when I see a whole lot of numbers. I did well in math. mostly, except for algebra 3. My youngest son never understood why he was supposed to put his work down. He could do it in his head and just didn’t see any reason to write it out.

  4. [...] started on August 26, 1912. On September 24, 1912, Grandma [...]

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