10. Samuel Rogers in account current with Joseph H. Carter.

Dr. 1848.

Cr.

1848.

Apr. 1, To mdse. at 8 mo., $500.00 July 15, By cash,

$400.00

66

24,

66 66

May 27,
June 15,

cash,
at 2 mo.,

350.00
75.00 Oct. 15, 66

66

23,

66

What is the equated time for paying the balance of the above account? Ans. Feb. 10, 1849.

11. If the account, example 9, were to be settled Jan. 1, 1849, what sum would pay the balance, reckoning interest at per cent. per annum ?

6

NOTE. Either find the amount of each item up to Jan. 1, 1849, (110, Ex. 3, 4, and 5,) or the value of the balance, $175, Jan. 1, 1849; that is, the amount of $175 on interest for 9 days, at 6 per cent. Do it by both methods.

12. What sum would pay the balance of the account in example 10, Jan. 1, 1849, interest at 8 per cent.? (110 and 113.)

The following notes refer to the account current and interest account on the next page, and should have followed that account; but for want of room on that page they are placed here.

NOTE 1. As W. F.'s note is not due till 1 month and 14 days after Sept. 1, the interest for that time is not added in the Cr. column, but in the Dr. In making up interest accounts, the time and interest of such items are usually written in red ink. Hence, the entry on the Dr. side, "To interest on Cr. side in red." 2. The interest of the Dr. items being more than that of the Cr., the balance of interest is to be added to the Dr. side of the account. 3. Some merchants state the time in days, and compute the interest by taking one sixth of the number of days as the interest in mills of $1 for the time. This method makes the interest more than the above. For example: the interest of $1000 from May 17, 1847, to Feb. 29, 1848=9 mo. 12 d., or 288 days, is $47, if the time be stated in months and days; and $48, if the time be stated in days. But as the interest on both the Dr. and Cr. items is reckoned in the same manner, the balance of interest will generally be nearly the same by both methods.

Copy upon paper the accounts on pages 166 and 167, stating the time in days, and find the balance of each account.

600 00 June 20,

1848.
Sept. 1,

To balance due this day,

14. John Smith in account current with H. Brown.

Interest Account to July 1, 1848.

Errors and omissions excepted.

Salem, July 1, 1848.

H. B.

* See note 1, page 165.

What abbreviation do merchants

QUESTIONS. What is barter? use for bought? for company? for merchandise? for bill of parcels? for received payment? for gross? for each? for at? How are shillings and pence expressed? the time at which a note falls due on which days of grace are allowed? How is per cent. often expressed? What is an account current? For what is the term Dr. used? the term Cr.? to? by? What does the word current indicate? How often are accounts current usually made up? What is the practice in regard to interest in such accounts? In how many different ways may accounts current be arranged and settled? What is the first? the second? the third? What items are usually written in red ink? What if the interest of the Dr. items is more than that of the Cr.? What if that of the Cr. items is the larger? What is said of stating the time in days in computing the interest?

SECTION XII.-RATIO-PROPORTION.

126.

RATIO.

Ratio is the relation which one quantity bears to another of the same kind, and expresses the part that one quantity is of another. Thus, expresses the relation of 3 to 5; it also expresses what part 3 is of 5. The two given numbers arecalled the terms of the ratio. The first term is called the antecedent, and the second the consequent.

The ratio of one quantity to another is obtained by dividing the antecedent by the consequent. It is expressed either in the form of a common fraction, (86,) or the terms are written after each other with the sign (÷) expressing division between them. Thus, the ratio of 5 to 7, is written, or 5: 7, which is read, either, the ratio of 5 to 7, or, as 5 is to 7.

Obs. In expressing a ratio, the sign (÷) is usually written thus, (), without the horizontal line between the dots.

The question what is the ratio of 5 to 7 is the same as the question, what part of 7 is 5? (86.)

If the terms of the ratio are not expressed in the same denomination, they must be reduced to the same denomination.

When the terms of a ratio are not prime to each other, the ratio may be reduced to lower terms, just as common fractions may be reduced to lower terms.

1. Write the ratio of 7 to 3; 8 to 5; 5 to 9; 9 to 16; 87 to 150; 16 to 9.

2. Write and reduce to its lowest terms each of the follow

ing ratios: 18 to 4; 4 to 18; 15 to 9; 25 to 15;

105 to 45; 800 to 150.
3. What fraction expresses the ratio of 7 to 8?
24? Of 2 to 31? Of 4 to 6? Of to ?

NOTE. Reduce the pare the numerators.

of 15 to 18.

27 to 45;

Of 15 to

fractions to a common denominator, and comThus, the ratio 15 to 18 is the same as that

4. Express in a common fraction the ratio of ratio of of to §; of to 7; of 1 to 31; of 4

NOTE. ; 11⁄2=15. The ratio of 18 to

as the ratio of 16 to 15.

127. PROPORTION.

to; the to 78.

is the same

A proportion consists of two equal ratios. When four numbers are so related to each other, that the first has the same ratio to the second that the third has to the fourth, they constitute a proportion. Thus the numbers 4, 5, 12, 15, form a proportion, because the ratio of 4 to 5 is equal to the ratio of 12 to 15. The proportion may be expressed thus: 4:5 12: 15; or, 4:5;:12: 15; or 1; which is read, 4 is to 5 as 12 is to 15; or, 4 divided by 5 is equal to 12 divided by

15.

=

The first and fourth terms of a proportion are called the extremes; and the second and third, the means. When the proportion is expressed in a fractional form, the numerator of the first fraction and the denominator of the second are the extremes, and the denominator of the first and the numerator of the second the means. In every proportion the product of the extremes is equal to the product of the means. In the above proportion 4:5-12: 15, or 1; the product of the extremes, 4 × 15, is equal to the product of the means, 5 X 12.

As the product of the extremes is always equal to the product of the means, we see that if the product of the means be divided by one of the extremes, (97,) the quotient will be the other extreme; and if the product of the extremes be divided by one of the means, the quotient will be the other

mean.

In questions in simple proportion, there are always three numbers or terms given, to find a fourth term or answer. Two

1