Ray's New Intellectual Arithmetic · Lesson XXIX · Unit 3: What fractions are
29. Common denominators
Goal: Your child gives two or more fractions the same denominator, using the least one where possible.
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 or more problems. The note: a common denominator can be found by multiplying the denominators; the least common denominator is the least number all of them go into. Model: ⅓ and ¾ become 4/12 and 9/12.
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
SayThirds and fourths both go into twelfths. One-third is 4 twelfths; three-fourths are 9 twelfths.
Find the smallest number both denominators go into: count up by the bigger one until the smaller one fits.
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 ⅓ and ¾ to a common denominator.
Reduce ⅔ and ⅞ to a common denominator.
Reduce ½, ⅓ and ¼ to their least common denominator.
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) 4/12 and 9/12. 2) 16/24 and 21/24.
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 ↗.