Ray's New Practical Arithmetic · Arts. 166–167 · Unit 14: Percentage
78. Finding the base
Goal: Your child finds a number when a per cent of it is known (Case III), and when the number plus or minus a per cent of it is known (Case IV).
You'll need
- Paper and pencil, or a slate or small whiteboard
What's in the book
Page 201 gives Case III (Art. 166) with two worked examples. Page 202 has its problems and Case IV (Art. 167) with two worked examples and the rule, and page 203 continues the problems. Answers are printed.
The lesson, step by step
Warm-up
Ask: 5 is 10% of what number? (50.) How did you know?
Case III
Given the rate and the percentage to find the base.
15 is 25% of what number?
25% is 1/4. If 15 is 1/4 of a number, the number is 4 × 15 = 60.
4.93 is 17% of what number?
4.93 ÷ .17 = 29.
SayDivide the part by the rate.
Case IV
A number, plus 35% of itself, equals 675: what is the number?
The number plus 35% of itself is 1.35 of it, so 675 ÷ 1.35 = 500.
Divide the sum by 1 plus the rate, or divide the difference by 1 minus the rate; the quotient will be the base.
Guided practice
Do these together:
60 is 20% of what number?
What number, increased by 25% of itself, amounts to 2125?
Independent practice and check
Your child works the Case III problems on page 202 and the Case IV problems on pages 202–203. 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: 8 is 50% of what? 3 is 10% of what? 110 is 10% more than what?
Tip
The common mistake in Case IV is to take 35% of 675 and subtract it. Check with the answer: 500 + 35% of 500 = 675, but 675 − 35% of 675 is not 500.