Ray's New Practical Arithmetic · Arts. 168–169 · Unit 14: Percentage
79. Percentage formulas and mixed problems
Goal: Your child uses the short formulas for the four cases and solves mixed percentage word problems.
You'll need
- Paper and pencil, or a slate or small whiteboard
What's in the book
Page 203 gives the formulas for the four cases (Art. 168) and starts the Miscellaneous Examples (Art. 169), which run through page 205.
The lesson, step by step
Warm-up
Ask your child to tell you, in their own words, the four cases from the last two guides.
The formulas
The book writes b for base, r for rate and p for percentage:
b × r = p; p ÷ b = r; p ÷ r = b; and for Case IV, the sum ÷ (1 + r) or the difference ÷ (1 − r) gives b.
For many children this is their first taste of algebra. Write the four on a card to keep beside the book.
Work an example together
I had $800 in bank and drew out 36% of it: how much had I left?
The base is $800. 36% of it is $288; $800 − $288 = $512. Or: 64% of $800 = $512.
Guided practice
Do these two together, naming base, rate and percentage first:
A man sold a horse for $175, which was 12½% less than the horse cost: what did the horse cost?
A pupil at an examination answered 17 of the 20 questions correctly: what per cent did he make?
Independent practice and check
Your child works problems 2–4 and 6–20 (or a selection). Some are about gold dollars and "greenbacks", Civil War paper money that in the 1870s was worth less than gold. The book prints the answer at the end of each problem line. Have your child cover the answers with a strip of paper, work the problem, then slide the strip down to check.
Mental-math wrap-up
Aloud: 30% of 60; 20 is what per cent of 80; 12 is 25% of what?