REVIEW

47. Questions on subject-matter.

1. Why is the Arabic system called a decimal system?

2. In what table of denominate numbers is the decimal system used? Would it be better if the decimal system

were used in all tables?

3. What is the name of the answer in each of the four different arithmetical processes?

4. Name and give examples of two different classes of numbers.

5. Work a problem in addition, beginning with the lefthand column.

6. Name and make all of the signs used thus far in arithmetic.

7. How would you test the result in a problem in subtraction?

8. How would you test the result in a problem in division?

9. What is a simple number? A compound number? 10. What is an abstract number? A concrete number? 11. In multiplication, which term is always abstract? 12. Why will 5 divide any number that 10 will divide? 13. Why is it that 10 will not divide all numbers that 5 will divide?

14. What is a factor? A prime factor?

15. In what class of problems is a knowledge of factoring important?

16. How many multiples may 2 and 3 have?

17. Can you give a reason for using the least common multiple?

48. Solve:

WRITTEN EXERCISES

1. Express in words the following numbers:

3,001,003, 11,111,101, 4,324,101, 2,002,002.

2. Express in figures the following numbers: One million, forty thousand, ten.

Twenty-seven million, twenty-seven thousand, twenty-seven. 3. Express in Roman notation the number 5555.

4. Add once only the following numbers and test the result: 30,647, 26,004, 10,118, 96, 386, 92,896, 4379.

5. Multiply once only the following numbers and test the result: 8,604,975 by 64,893.

6. Multiply in two different ways the following numbers: 4680 by 50; 640 by 25.

7. Divide the following numbers by the ordinary method. of division, and also by dividing by the factors of the divisor: 8736 by 24.

8. Multiply in two ways the following numbers: 249 by 331.

9. Make a bill of the following transactions, in which you show the debit and credit items and how the account stands :

March 1, Mr. Gray bought of Mr. Smith 10 lb. of sugar at $.06 a pound and lb. of tea at $.90 a pound. He sold Mr. Smith 10 bu. of potatoes at $.60 a bushel and 2 doz. eggs at $.30 a dozen.

He

March 10, Mr. Gray bought of Mr. Smith 5 lb. of coffee at $.40 a pound, 9 cans of sweet corn at $.11 a can. sold him 20-chickens at $.45 each.

March 20, Mr. Gray bought of Mr. Smith 25 lb. of sugar at $.05 a pound, 2 lb. of raisins at $.12 a pound, 11⁄2 lb. of pepper at $.30 a pound. He sold Mr. Smith 4 doz. eggs at $.25 a dozen.

10. Copy the following names of various things, and place after each the price as nearly as you can:

Apples, oranges, eggs, tea, sugar, steak, ice, horse, sheep, pair of your shoes, handkerchief, this book.

11. What numbers will divide the following number: 1728? Give a reason for each one named.

12. Find by inspection three multiples of the following numbers: 2, 3, 4, 6, 12.

13. Find by inspection two common divisors of the following numbers: 40, 64, 16, 56, 32.

14. A circular track is 3 miles in circumference. Three men start from the same point to travel around it until they all come together again at the place of starting. A travels 2 miles an hour, B 3 miles an hour, and C 6 miles an hour. How many hours did they travel? How many miles does each travel?

15. A farmer bought three farms which contained 360 acres, 450 acres, and 240 acres. He gave these to his two sons and two daughters, giving to each son twice as much as to each daughter. How many acres did each receive?

16. A man had $6000. He gave to James of this, to Peter of the remainder, to Susan of this remainder, and the rest to Clara. How many dollars did each receive?

SUMMARY OF CHAPTER I

THE FUNDAMENTAL PROCESSES:

Addition, subtraction, multiplication, division, with tests and appli

cations.

FACTORS AND MULTIPLES:

Greatest common divisor and least common multiple.

CHAPTER II

COMMON AND DECIMAL FRACTIONS

FRACTIONS DEFINED

49. Any quantity considered as a single thing, or used as a measure of other quantities, is called a unit.

1, 5, 20, a pound, an acre, a foot, are units.

50. A fraction is one, or more than one, of the equal parts of a unit, as 1, § of a pound, of an acre.

Write a fraction.

Name its numerator and its denominator.

The numerator and the denominator of a fraction are called the terms of the fraction.

A fraction whose value is less than 1 is called a proper fraction, as

A fraction whose value is 1 or greater than 1 is called an improper fraction, as §.

A number made up of an integer and a fraction written together as one number is called a mixed number, as 11.

51. There are four facts about all fractions that it is well to remember.

(1) Every fraction represents one or more of the equal parts of some unit.

(2) The unit of which the fraction is a part may be any quantity used as a single thing, and not merely the number 1.

For example, may be a fraction of 1 mile or of 30 yards or of an abstract number, as 1 or 24. If the unit is not mentioned, it is commonly understood to be 1.

(3) A fraction may itself be treated as a unit. So we may add, subtract, multiply, and divide fractions as we do whole numbers.

When we say of 1, 1 is treated as a unit.

(4) Every fraction shows a ratio. Its value, considered as a unit, is the quotient of its numerator divided by its denominator.

The value of as a unit is the quotient 2.

REDUCTION

52. REDUCING TO HIGHER OR LOWER TERMS.

Multiply both terms of by 2.

Divide both terms of by 2.

Is the value of the fraction changed in either case? Why? Multiplying or dividing both terms of a fraction by the same number does not change its value.

Changing the form or the terms of a fraction without changing its value is called reduction.

Reduce to their lowest terms:

4

1600 1000" 32009

16, 18, 1025%, 1988, 33, 114.

Give a rule for this process.

444'

54. REDUCING TO A COMMON DENOMINATOR.

How do you reduce to 12ths?

By what factor must you multiply the terms of to reduce the fraction to 12ths?