Ray's New Intellectual Arithmetic · Lesson XLII · Unit 4: Working with fractions
42. Dividing fractions by whole numbers
Goal: Your child divides a fraction or mixed number by a whole number.
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
About seventeen problems. Model: 10 acres among 6 children is 1⅔ acres each.
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
Say10 acres shared among 6 children: each gets 10/6, which is 1⅔ acres.
To divide a fraction by a whole number, divide the numerator if you can, or multiply the denominator: ⅔ divided by 2 is ⅓; ¾ divided by 2 is ⅜.
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:
A man divided 10 acres equally among his 6 children: how much did each get?
Divide ¾ by 2.
If a man travels 9 miles in 1¼ hours, how far in 1 hour?
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
1) 1⅔ acres. 7) 4 cents.
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 ↗.