Ray's New Intellectual Arithmetic · Lesson XXXV · Unit 4: Working with fractions
35. Multiplying mixed numbers
Goal: Your child multiplies a mixed number by a whole number by doing the whole part and the fraction part separately.
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 forty-eight problems. The model: 12 times 3¾ is 12 times 3, which is 36, and 12 times ¾, which is 9, so 45.
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
Say12 times 3 is 36; 12 times three-fourths is 9; 36 and 9 are 45.
Splitting a mixed number into its whole and its fraction makes it easy to do in the head.
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:
If 1 bushel of wheat costs $1½, what will 2 bushels cost?
What are 12 times 3¾?
What are 8 times 2⅝?
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) 3 oranges. 15) 45.
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 ↗.