Ray's New Intellectual Arithmetic · Lesson XXVII · Unit 3: What fractions are
27. Lowest terms
Goal: Your child reduces a fraction to its lowest terms by dividing both numbers.
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 fourteen problems. A note says a fraction is in its lowest terms when no number greater than 1 divides both terms. The model divides both terms by 2, then by 2 again.
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
Draw 6/8 on a bar, then show the same amount as 3/4.
SayDivide both terms by 2: 6/8 is 3/4. No number but 1 divides 3 and 4, so 3/4 is in lowest terms.
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:
Reduce 6/8 to its lowest terms.
Reduce 10/18.
Reduce 12/16, dividing by 2 and then by 2 again.
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
Only one answer could be read clearly in the scan: 10/18 is 5/9. See the Key for the rest.
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 ↗.