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(7) (a) What number is less than 45? % of 45 = 18; 45-18 = 27; .'. 27 Ans.

(b) What number is .016 less than 125? .016 of

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(c) What number is 20% less than 120? 20% of · 24; 120-24 =96; .'. 96 Ans.

120=

(8) (a) 45 is less than what number?

--}; % of

No. 45, of No. 15; of No. = 75 Ans.

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(b) 168 is .3 less than what number? 1.0-.3 .7;
.7 of No. = 168; No. 168÷.7=240 Ans.
(c) 120 is 20% less than what number? 100%-
20% = 80% = ; of No. = 120; of No. = 30;

of No. 150; .'. 150 Ans.

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(9) (a) 27 is what part less than 33? 33-27=6; 6 = 33

2

of 33; 31.

6 33

Ans.

(b) 40 is what decimal part less than 64? 64-40=

24; 24 is

(c) 20 is what %

of 64; 4.375 Ans.

less than 120? 120-20= 100; 100

100

is 198 of 120; 1985-833% Ans.

120=

It will be noticed that (a) and (b) of (6) and (9) are unusual and somewhat vague. It is not wise to lay much stress on them.

The above problems are type problems, and involve no difficulty so far as the numbers themselves are concerned. The chief difficulty is in the meaning of the language. This should be made familiar to the pupil by many simple problems.

Many concrete problems should be given.

The pupil is not ready to begin percentage till he has mastered 6, 7 and 8 above.

High Seventh.

PERCENTAGE.

Success in Percentage depends upon the mastery of three things; the foundation, the language, and the customs of the business world. The foundation consists of decimal and fractional parts. This work is outlined in 7 and 8 of the low seventh. The teachers should see that this is understood, and should spend as much time as is necessary on it. The type problems make (c) in (1) to (9) division 8 of the low seventh involve what must be mastered about the meaning of the language of Percentage. These should be reviewed and impressed as the occasion arises in advancing. Give concrete problems and have the pupil frame the question and tell to what type it belongs.

A tree 150 feet tall in June had increased 4% in height by October. What was its height in October? 4% of 150 ft. = 6 ft.; 150 ft.+6 ft. 156 ft. Ans. Type. What number is 4% greater than 150 ft.?

Give problems involving easy number combinations till. the principle is mastered.

The customs of the business world should be given to the pupil in connection with the special study of each subject.

I.

PROFIT AND LOSS.

Terms used.

Custom.

(1) The cost is 100% for reckoning losses and gains.

(2) The selling price is less than 100% when there is a

loss.

The selling price is more than Ico% when there is a

gain.

Give the

(3) The gain or loss is reckoned on the cost. custom for (3) and have the pupils assist in determining Nos. (1) and (2).

A scheme like that given below will be found helpful.

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Cloth was sold at $4.00 a yard which was a gain of 25%. What was the cost and what the gain?

100% Cost.

125% S. P. $4.00.

25% Gain.

125% = $4.00.

125% = 4.

of Cost

$4.00.

14 of Cost = $.80.

of Cost $3.20 Cost.

$4.00-$3.20 $.80 Gain.

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(b)

(1) Selling price is 100% for reckoning Commission.
(2) Proceeds is less than 100%.

(3) Commission is reckoned on the selling price.

Give (3) and require assistance in getting (1) and (2).

Terms.

In buying.

Custom.

(1) Purchase price is 100% for reckoning Commission. (2) Entire cost is more than 100%.

(3) Commission is reckoned on the purchase price.

Give (3) and require (1) and (2). Use a scheme similar

to that given in Profit and Loss.

3.

Make a similar outline for Taxes and Trade Discount.

INTEREST.

(a) Find the time from one date to another.

(b) Reduce any number of days and months to a fraction of a year. In doing this it is not always best to reduce

the months to days.

Reduce 4 months 24 days to a fraction of a year. 24 days months; 4 months 4 months years. Reduce 6 months 9 days to a fraction of a year.

9 days_ 3 month; 6,3 month month or of a year. 63 1636

0

120

(c) Multiply the principal by the rate to get the interest for a year. Then multiply by the number of years. It is usually best to indicate the operation and employ cancel

lation. In cancelling always cancel the ciphers in the denominator first.

Find the interest on $643.29 for 1 year, 6 months and 9 days @5%%.

6 months 9 days years; 1 years
21

11 61

$'643.29 × 200

7.07619 424.5714

8)431.64759

53.9559

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4 years.

(How did I perform the multiplications?

Compare this work with the 6% method.)

Use one method only. The 6% method may be taught later and used when the rate is 6%.

4. Use a compact intelligible form.

PARTIAL PAYMENTS.

The following is a good form:

Compute the amount due on the following note at the date of settlement:

A note for $5,600 was given May 1, 1895, and was endorsed as follows: Oct. 17, 1895. $350; Feb. 18, 1896, $455; What was due May 1, 1897,

July 10, 1896, 318.50.

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After the pupils have learned the principle of Partial Payments give this form. Add two or more times when the interest exceeds the payment.

5. Bank discount is very little used in California. In San Francisco the interest is deducted in advance on short loans. Elsewhere in the State notes given to a bank bear interest the same as other notes. If a bank buys a note that is not due it deducts the interest on the face of the note for the time remaining from the date of discount to the date of maturity. If the note bears interest, interest is calculated on the amount of the note at the time of maturity. It is not customary, however, to sell notes to banks. They are generally deposited as collateral security and money is borrowed on them. No days of grace are allowed in California.

6.

COMPOUND INTEREST.

Use good compact form.

Find the interest on $475 for 1 year, 8 months and 20 days @ 6%, interest compounded semi-annually.

I year, 8 months, 20 days 3 half-years, 2 months, 20 days. Prin. $475.03 $14.25 1st Int.

Int.

14.25

Amt. $489.25 × .03 - $14.6775 2nd Int.
Int.

14.68

Amt. $503.93 x .03 -$15.1179 3rd Int.

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7

Int. $50.97

PROBLEMS IN INTEREST.

Give simple problems this year.

(a) To find the principal when the interest, rate, and time are given.

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