Ray's New Intellectual Arithmetic · Lesson LXV · Unit 8: Percentage and interest
65. Finding a per cent of a number
Goal: Your child finds a per cent of a number and uses it for gain and selling prices.
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
Sixteen problems: per cent of a number, the gain on a cost, a flock's increase, and the price to charge for a given profit.
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 per cent of $20 is one-tenth of $20, which is $2.
To make 25 per cent profit on cloth that cost 12 cents, add a quarter of 12 cents, 3 cents: sell at 15 cents.
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 lady with $20 spends 10% on muslin, then 10% of the rest on calico: how much did she spend?
To make 12½% profit, what must muslin sell for that cost 8 cents a yard?
To make 25% profit, what must delaine sell for that cost 12, 16, 20 and 35 cents?
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) 2. 2) 3. 3) $8. 6) 17 bushels. 7) 7 horses. 8) $2. 9) $1. 10) 38 sheep. 11) 55 sheep. 12) $3.80. 13) 33 cents. 14) 9 cents; 18 cents. 16) 15, 20, 25, 43¾ 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 ↗.