Ray's New Intellectual Arithmetic · Lesson XLIII · Unit 4: Working with fractions
43. Dividing by fractions in stories
Goal: Your child uses dividing by a fraction in stories, and finds a number from a fraction of it.
You'll need
- The book page (press “📖 Book page”, or use a printed copy)
- Paper for jotting, though the work is meant to be done in the head
What's in the book
Twenty-two problems: how many yards money buys, how many times one number contains another, and “x is ⅔ of what number?”
The lesson, step by step
Warm up
Ask three or four problems from the last lesson again, out of order. Your child answers and says why.
Show the reasoning
SayOne bushel of rye is worth three-fourths of a bushel of wheat. So 4½ bushels of wheat buy as many bushels of rye as ¾ is contained in 4½, which is 6.
Work the problems aloud
Read each problem on the page aloud. Your child answers, then explains in a full sentence, the way the book's model solutions do. The problems go like this:
Wheat is shared among poor persons, a fraction of a bushel each: how many persons?
At a fraction of a dollar a gallon, how many gallons of vinegar for $2½?
One bushel of rye is worth ¾ of a bushel of wheat: how many bushels of rye for 4½ bushels of wheat?
Ask “Why?”
After each answer ask “Why?” or “How do you know?” Ray's wants the reasoning said aloud, not just the number. If your child stalls, go back to the model and say the first half of the explanation together.
Wrap up
Pick the two problems that were hardest today. Tomorrow, start with those as the warm-up.
Afterwards
Do the rest of the lesson's problems over the next day or two, a few at a time. Move on when your child can explain them without help.
Answers to the book's problems
22) 6 bushels; 11⅓ bushels.
Worked out for this site from the scan. If a number in your copy differs, trust the book. Every answer is in Ray's own Key ↗.