QUESTIONS.

389. 1. Define discount; present worth; true discount. Tell how to find present worth and true discount.

2. Define bank discount; proceeds; day of maturity; term of discount.

Tell how to find bank discount and proceeds.

Tell how to find face of note when proceeds, time, and rate are given.

3. What is a stock company? What are stocks? Bonds? Shares?

4. Define par value; market value.

5. What is a stock certificate?

6. Define dividend; assessment.

7. Upon what are premium, brokerage, dividends, and assessments reckoned?

8. What is the average of payments? Equated time? Average term of credit?

RATIO AND PROPORTION.

390. Oral.

1. 5 bears what relation to 10? Ans. 5 is of 10.

2. 10 bears what relation to 5? Ans. 10 is 2 times 5.

3. What part of 16 is 4?

4. How does $7 compare with $14?

5. John has 20 and Mary 5¢. What is the relation of John's money to Mary's? Of Mary's money to John's?

6. What is the relation of 15 to 3? Of $8 to $16? Of 28 men to 7 men? Of 2 bushels to 2 pecks?

391. Ratio is the relation between two like numbers. It is found by dividing one by the other; thus:

The ratio of 4 to 8 is 4÷8=

The sign of ratio is (:). It is the division sign with the line omitted.

The ratio of 6 to 3 is expressed thus, 6:3. It may also be expressed fractionally, thus, §.

392. The Terms of a ratio are the two numbers compared.

The first term of a ratio is the Antecedent, and the second the Consequent.

In the ratio 6: 12, 6 is the antecedent, and 12 the consequent.

393. A ratio formed by dividing the consequent by the antecedent is an Inverse ratio.

126 is the inverse ratio of 6: 12.

394. The two terms of a ratio taken together form a Couplet.

395. Two or more couplets taken together form a Compound ratio.

3:6

8:5 = 96: 150 4:5

A compound ratio may be changed to a simple ratio by taking the product of the antecedents for a new antecedent, and the product of the consequents for a new consequent. Antecedent Consequent Ratio.

Multiplying or dividing both terms of a ratio by the same number does not change the ratio.

NOTE. Fractions with a common denominator have the same

ratio as their numerators.

terms by 10.

Prove this in Ex. 10, by multiplying both

30

17.1? #8: 7 = ? 11:11=?

3

18. :? :? := ? }:{=?

19. Find the inverse ratio of 75 to 25. Of 15 to 225.

20. 16: (?). 14: (?) 2.

=

21. (?):54. (?):8.

22. Find the value of the compound ratio,

8:10)
5:6

396. Oral.

PROPORTION.

23. Give three fractions having the same value as 3.

24. Give two numbers that have the same ratio as 5 to 10

25. Give a fraction equal to .

26. Give a ratio equal to 3:4.

27. How does the ratio of 5 men to 10 men compare with the ratio of $5 to $10?

28. How does the ratio of 8 lb. to 4 lb. compare with the ratio of 40% to 20%?

29. Name two numbers that have the same relation as 5 to 10. As 4 to 24. As 8 to 16. As to 1.

30. What number has the same relation to 5 as 12 to 3? 31. Find a number whose ratio to 4 equals 3: 6.

32. Give three ratios equal to $100: $50.

33. Give any two ratios that equal each other, and express their equality.

397. An equality of ratios is a Proportion. Thus, 4:2 = 12:6. The ratio of 4 to 2 equals the ratio of 12

to 6.

A proportion is usually expressed with the sign (::) "between the ratios; thus, 4:2::12:6. This is read 4 is to 2 as 12 is to 6.

A proportion has four terms, of which two are antecedents and two are consequents. Each term is a proportional.

398. The first and fourth terms are called Extremes, and the second and third terms are called Means.

NOTE. In the proportion 2:6::6:18, the two means are the same number, 6. The 6 is called a mean proportional.

PRINCIPLE. -The product of the extremes equals the product of the means.

Rule.

·To find an extreme, divide the product of the means by the given extreme.

To find a mean, divide the product of the extremes by the given mean.

399. An equality of two simple ratios is a Simple Proportion.

It is employed in solving questions having three given terms, two of which have the same relation to each other as the third to the required term.

44. If 12 bushels of oats cost $4, what will 60 bushels cost? SOLUTION.-There must be the same relation between the cost of 12 bu. and the cost of 60 bu. as exists between 12 bu. and 60 bu.

12: 60: $4: ($)

60 × 4 12

=

$20.

We place $4 for the third term. The answer will be the fourth. We must now form a ratio of 12 and 60 that shall equal the ratio of $4 to the answer. Since the third term is less than the required answer, the first must be less than the second, and we have 12: 60 for the first ratio. The product of the means divided by the given extreme will give the other extreme, or $20. Ans.

By analysis, Since 12 bu. cost $4,

1 bu. will cost $, and

60 bu. will cost $20. Ans.