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

How Does Catechize Differ From Catechism?

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

Sunday, September 22, 1912: Went to S.S. this afternoon and attended Catechize.

Recent photo of the site where the McEwensville Baptist Church once stood.

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

When I read this diary entry, I got stuck on a simple vocabulary question. I remember going to “catechism” class when I was in middle school. How does “catechize” differ from “catechism”? Is it a different part of speech?

The Free Online Dictionary defines catechize as “to teach the principles of Christian dogma, discipline, and ethics by means of questions and answers.”

While catechism is “a book giving a brief summary of the basic principles of Christianity in question-and-answer form.”

Grandma was 17-years-old when she wrote this entry. I’m surprised that she hadn’t completed catechize and joined the church when she was in her early teens.

Mother Remodeled Skirt

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

Saturday, September 21, 1912: Ma made over a skirt for me. Got a pair of rubbers today.

wils36346.i — From Bedell Company advertisement in November, 1912 issue of Ladies Home Journal.

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

I guess that Grandma’s mother was trying to save about $1.98 by making over the skirt. I can’t remember the last time I remodeled a skirt . . . or dress. (Actually, I don’t think that I’ve ever remodeled one.) Yet, Grandma and her mother did it regularly.

On June 3, 1912, Grandma wrote:

I am trying to remodel a skirt which was once the property of the benevolent Ruthie. I’ll know whether I’ll wear it or not after it’s finished.

And, on February 24, 1912 she wrote:

I fixed over a dress for myself this afternoon. It was one of my Aunt Annie’s cast-offs. I had one trying time a getting the waist and skirt together. I have it fixed now and tried it on to see the result. I’m not so much pleased with my sewing. It seems rather short in the back.

Grandma sounded like she wasn’t very satisfied with either of her remodeling efforts, but she didn’t express any similar qualms about the skirt her mother remodeled. Apparently her mother was more proficient at sewing than she was.

—-

On September 18, Grandma mentioned walking to school through the rain and mud—hopefully her new rubber overshoes made the trek slightly less arduous the next time it rained.

Trying to Select a Class Pin

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

Wednesday, September 17, 1912: Had to walk to school through the rain. Also through the mud. Our class is deciding upon a class pin, but we’re making such slow progress in making up our minds as to which pin to take, that I doubt we’ll ever get them at all.

DSC04607.crop — Recent photo of the building that once housed McEwensville High School.

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

Yuck—a mile and a half walk to school in the rain on muddy dirt roads. It sure doesn’t sound like fun. Did Grandma wear galoshes to school?

Did Grandma and her classmates have a catalog that they were going to order the class pin out of? . . . or were they planning to order it from a sales representative or at a nearby jewelry shop?

Grandma’s class was small. Only six students graduated in Spring 1913 from McEwensville High School. It’s amazing how much effort they put into creating a class identity. A few days previous to this diary entry, Grandma wrote about the differences in opinion about class colors and now they can’t seem to agree on a class pin.

All Mortals Have to Suffer for Their Errors

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

Monday, September 16, 1912: I don’t feel very good these last few days. I don’t know but I really think that it is likening to be near a grape vine. Alas all mortals have to suffer for their errors.

concord grapes on vine — Concord Grapes (Source: Wikipedia)

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

If I could have a conversation with Grandma, this is what I’d say:

Grandma, what were you thinking!

Of course, you couldn’t have known we’d be reading it a hundred years later; but what kind of role model is that for your children, grandchildren, and great-grandchildren?

. . . Actually, given your later strong stance against alcohol, my sense is that some are smiling.

An Afternoon with A Friend

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

Sunday, September 15, 1912: Went to Sunday School this morning. Was over to see Carrie this afternoon.

corn field at edge of town — A recent late summer photo of a corn field at the edge of McEwensville.

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

Carrie refers to Grandma’s friend Carrie Stout. She lived on a nearby farm that was located about half way between Grandma’s house and McEwewnsville.

Carrie is the most frequently mentioned friend in the diary—and she seemed to be Grandma’s closest confidant. I think she was a couple of years younger than Grandma.

What did the teens do on a nice September afternoon? . . . chat about the latest happenings? . . . gossip about other friends?. . . giggle about cute buys? . . . go for a walk? . .. explore new things? . . .

Harvest Home Sunday

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

Sunday, September 8, 1912: Went to Sunday School this afternoon. Had Harvest Home services at church.

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

Harvest Home was one of my favorite Sundays when I was a child. Do any churches still have Harvest Home services?

I loved to gather fruits and vegetables for the beautiful display in the front of the church—and then during the service I enjoyed looking at the interesting squash, pumpkins and other vegetables. And, it always made me feel good that the food would be given to needy families after the service.

A hundred years ago did Grandma also gather produce for Harvest Home, and help create the display?