Ray's New Intellectual Arithmetic · Lesson XLI · Unit 4: Working with fractions
41. Dividing by a fraction
Goal: Your child finds how much money buys at a fractional price, which is dividing by a fraction.
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-eight problems on cloth, corn, coffee and tea at fractional prices, then “Divide x by y” drills. The solutions show that dividing by a fraction is multiplying by it turned upside down.
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
SayAt $⅔ a yard, $⅓ buys half a yard, so $1 buys three halves, or 1½ yards, and $4 buys 4 times 1½, or 6 yards.
The short way: 4 divided by ⅔ is 4 times 3/2, 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:
At $⅔ a yard, how many yards will $4 buy?
How many times is ¾ contained in 6?
Divide 5 by ⅝.
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.
Tip
Check the prices in the book itself: the fractions in this part of the scan are hard to read on screen.