Practical and Mental Arithmetic on a New Plan

days? A.. Is 9 days? A. . Is 15 days? 3o. A. 15 =3. Is 20 days? A. 38=3.

22. How much is of? of? of of?

23. How much is of ? of?

24. How many times is 2 contained in? How much is of?

25. How many times 2 in? (To divide a fraction, we multiply the denominator, or divide the numerator.) 2 in ? 3 in

38 of a month?

of of a month? How much is of

27. James has of a dollar, Rufus, and Thomas the remainder of the dollar; what is Thomas' part?

28. William had of a ticket, Henry, and James; what part of a ticket did they all own? (Find how many 8ths each had first.)

29. What kind of fractions are the following, viz. 1, §, 51, 71, 29, £ of +?

30. Reduce to a decimal.

31. What decimal is equal to ??

32. James has 2 of a ticket, William ,5, Thomas,2, and

Harry the remainder; how much does Harry have?

33. What is the amount of 3+,4+,1 ?

34. Multiply,6 by ,5.

35. How much is ,5 of,5?

36. How much is ,3 multiplied by,4?

37. Divide,24 by,6.

38. Divide ,8 by,2.

39. Divide,6 by,15.

40. From ,5 take,25.

41. of 14 is 2; 2, then, is of 4 is 2; 2, then, is of what number?

42.

43. 3 is

of what number? of what number?

+ d.+ 13 d. =

+ 10 d. + 15 s. +1 s. 6d A. 122£. 6 s. 4 d. 1 qr.

A. 15 s. 11 d. 1 qr.

A. 10.

A. 25.

9. From 1£. 15 s. take 19 s.
10. Multiply 16 by 3.
11. Divide 16 by . A. 24.

12. Multiply by 30.

13. Divide by 30. A. 3.

14. Multiply of 2 by 15. A. 5§.

15. Divide of by 15. A..

16. A man bought 4 hogsheads of molasses: the first con tained 763 gallons; the second 634 gallons; the third *93 ga1 lons; and the fourth 594 gallons. How many gallons in tut whole? (Reduce the fractional parts to a common denomina tor before you proceed to add.) A. 279–28.

17.

3700+80+185+6+37,5+1008000A. 3744,200005 18. What is the value of ,990625 of a pound? A. 19 s. 9 d. 3 qrs.

19. From 29 years, 5 mo. 3 days, take 23 hours 40 minutes A. 29 years, 5 mo. 2 days, 0 hours, 20 minutes. Note. When it is required to find the distance of time from one date to another, it may be easily done by subtracting the first date from the last, reckoning the months according to their order in the year; thus, January is 1st mo., February 2d mo., &c.

20. What is the difference of time between March 27, 1827, and February 15, 1828?

(12) (30)
1828, 2d mo. 15th day.
1827, 3d mo. 27th day.

Ans. 10 mo. 18 days.

21. What is the difference of time between April 14, 1827, and March 16, 1828? A. 11 mo. 2 days.

22. A note, dated July 1, 1826, was paid June 20, 1828; how long was the note on interest? 23. A note, dated Nov. 15, 1820, 1828; how long was it at interest?

Ꭿ. 1 year, 11 mo 19 lays was not paid till Dec. 1, A. 8 years, 0 mo. 16 days.

INTEREST.

TLXI. Q. If the interest of 100 dollars for 1 year is 6 dollars, what will be the interest of 200 for the same time? Of 300? Of 400? Of 600?

Q. What will be the interest of 100 for 2 years? For 4 vears? For 10 years?

Q. What is that which is paid for the use of money called? A. Interest.

Q. How, then, may it be defined? A. Interest is an allowance made by the borrower to the lender for the use of money. Q. What is that which is paid for the use of 100 for 1 year called? A. The rate per cent.

Q. Why called the rate per cent.? A. Because per cent., or per centum. means, by the 100.

Q. How, then, is interest computed? A. At so many dollars for each 100 dollars, so many cents for each 100 cents, so many pounds for each 100 pounds, &c. for 1 year.

Q. How is it computed on a greater or less sum than 100, or a longer or shorter time than 1 year? A. In the same proportion.

Q. What is the meaning of per annum? by the year.

A. Each year, or

Q. What, then, is the meaning of 6 per cent. per annum? A. 6 dollars for the use of 100 dollars, 6 cents for 100 cents, &c., for 1 year.

Q. When the rate per cent. is established by law, what is the interest called? A. The legal, or lawful interest.

Q. What is the legal interest in the New England States? A. 6 per cent.

Note. In the state of New York, it is 7 per cent.

Q. When there is no mention made of the rate per cent., what rate per cent. is understood? A. The legal rate.

Q. What is the sum lent called? A. The principal.

Q. When the interest and principal are both added together, what is it called? A. The amount.

Since, at 6 per cent., the interest of 100 cents for 12 mo. is 6 cents, the interest will always be as many cents as there are months; that is, the num ber of months will express in cents the interest of $1 for said months, thus the interest of $1 for 12 months being 6 cents, 8 mo. will be 4 cents, for 4 is of 8 mo. ; and in the same proportion for any length of time.

Now, as the interest of any sum over 1 dollar is proportionally more, as 5 dollars for instance, the interest of which is 5 times as many cents as the interest of $1, and as cents are 100ths of a dollar, it follows, that, multiplying any denomination, as pounds, dollars, cents, &c., by the number of months, will give a product that will be the interest, either in cents or 100ths, which are easily brought into dollars, or whole numbers, by cutting off two figures in the product, (that is dividing by 100.)

Hence, To find the interest of any sum of dollars, pounds, shillings, or eagles, for one year or more, we have the following

RULE.

I. How do you proceed? A. Multiply by months, and cut off two figures at the right, 100.)

Mental Exercises.

the number of (for dividing by

1. What is the interest of $8 for 4 months? A. 16 cents. 2. What is the interest of $4 for 4 months? A. 8 cents. 3. What is the interest of $2 for 6 months? A. 6 cents. 4. What is the interest of $20 for 2 months? A. 20 cents. 5. What is the interest of $80 for 10 months? A. $4,00. 6. What is the interest of $40 for 1 yr., or 12 mo.? A. $2,40. 7. What is the interest of $8 for 1 yr. 4 mo. ? A. 64 cents. 8. What is the interest of $5 for 1 yr. 6 mo. ? 9. What is the interest of $1 for 4 years? A. 24 cents. 10. What is the interest of $8 for 2 mo.? A. 8 cts. is the amount? A. $8,08.

.4. 45 cents.

What

11. What is the interest of $6 for 1 yr.? A. 36 cts.

What

is the amount? A. $6,36.

12. What is the interest of $1 for 4 yrs.? A. 24 cts.

is the amount? A. $1,24.

What

13. What is the interest of 100 £. for 2 months? A. 1£. What is the amount? A. 101 £.

14. What is the interest of 10 £. for 1 yr. 8 mo.? A. 1 £ What is the amount? A. 11 £.

15. What is the interest of $2,50 for 2 mo. ?, A. 2 cts. 5 m What is the amount? A. $2,525.

16. What is the interest of $6,50 for 2 mo.? A. 6 cts. What is the amount? A. $6,564.

Exercises for the Slate.

1. What is the interest of $240,30 for 3 yrs. 4 mo. ?

3 yrs. 4 mo. 40 mo.÷2=20, half the number of months

OPERATION.

240,30 20

$48,0600, Ans.

In this example, as there are two places for cents in the multiplicand, there will be two also in the product then, cutting off two more figures, (for dividing by 100, we have $48,06, Ans.

2. What is the interest of $400 for 2 yrs. 6 mo.? A. $60. 3. What is the amount of $500 for 4 yrs. 1 mo.? A. $622,00. 4. What is the interest of $75 for 2 yrs. 6 mo.? (1125) Of $250? (3750) Of $800? (120) Of $95? (1425)` Of $650 ? (9750) A. $280,50.

For 6

5. What is the interest of $1500 for 4 mo.? (30) mo.? (45) For 10 mo. ? (75) For 1 yr. 2 mo. ? (105) For 1 yr. 8 mo.? (150) For 4 yrs. 2 mo.? (375) For 6 yrs. 6 mo.? (585) A. $1365.

6. What is the amount of $75 for 2 yrs. 6 mo. ? (8625) $250? (28750) Of $800? (920) Of $95? (10925) Of $650? (74750) A. $2150,50.

7. What is the amount of $615,75 for 5 yrs.? (800475) For 11 yrs. 1 mo.? (1025223) For 7 yrs. 2 mo.? (880522) A. $2706,22 +

8. What is the interest of $7650 for 3 yrs. 3 mo. ? (149175) For 3 yrs. 4 mo.? (1530) For 6 yrs. 6 mo.? (298350) For 2 mo.? (99450) A. $6999,75.

2 yrs.

9. What is the amount of $7,50 for 10 yrs. 1 mo. ? (12037) For 2 yrs. 3 mo? (8512) For 1 mo.? (7537) For 11 mo. ? (7912) For 1 yr. 7 mo.? (8212) A. $44,21 +.

¶ LXII. Since days are always either 30ths of a month, or some greater part, as halves, 3ds, 4ths, 5ths, &c. ; thus, 1 day =; 2 days = 3, which, being reduced to its lowest terms, is; 3 days or ; 5 days = 30, or; 20 days, or ; it follows, that, if these parts be diminished in the same proportion as the months, that is, if half the fractional part be taken for a multiplier, the product will express the interest for the days in cents, or 100ths, which, divided by 100, as before, will be the interest required. To halve any thing, we divide by 2.

Note. It will be recollected, that, to divide a fraction by 2, we can

Multiply the denominator,or divide the numerator.
1. What is the interest of $60 for 15 days'
15 days = 15 or 1 mo. ÷ 2 = , multiplier.

2. What is the interest of $24 for 10 days?
mo. = = 1 ÷ 2 = 1, multiplier

10 days

$60