Ray's New Intellectual Arithmetic · Lesson XXXI · Unit 4: Working with fractions
31. Subtracting fractions
Goal: Your child subtracts fractions and mixed numbers, borrowing a 1 when needed.
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
Fifteen problems: “how much more did one receive” stories, “take a from b”, and mixed numbers such as “Take 3¾ from 7⅝”, with a model showing how to borrow 1 from the whole 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
SayTake 3¾ from 7⅝. Change to eighths: 3 6/8 from 7 5/8. 6 eighths can't come from 5 eighths, so borrow 1 from the 7: 6 13/8. Now 13 less 6 is 7 eighths, and 6 less 3 is 3. The answer is 3⅞.
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:
One boy got ¾ of an orange and another ½: how much more did the first get?
Take ⅓ from ⅚.
Take 3¾ from 7⅝.
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
15) 3⅞.
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 ↗.