Intermediate Arithmetic

INTERMEDIATE ARITHMETIC

PART I- FIFTH YEAR

REVIEW OF NOTATION AND NUMERATION

1. In 364 for what does the 4 stand? the 6? the 3? 364 3 hundreds, 6 tens, 4 ones.

2. Tell for what each figure stands in 2475. Read the number.

Each figure has a value that depends upon its place in the number. The first place beginning at the right of a number is called ones' place; the second, tens' place; the third, hundreds place; the fourth, thousands' place, etc.

3. Show that the left-hand 2 in the number 222 has a value, because of its place, that is 10 times the value of the middle 2, and 100 times the value of the right-hand 2.

When a number contains more than three figures, it is separated into groups or periods of three figures each, beginning at the right. The names of the places in each period are the same. The name of the first period is units; of the second period, thousands; of the third, millions; and of the fourth, billions.

4. In the number 864,203,614,869, what name is given to the period 864 ? to the period 203? to 614? to 869?

Notation is a method of writing numbers by means of symbols.

Numeration is a method of reading numbers represented by symbols.

Beginning at the right, mark off into periods, and then read:

Observe that: naughts are enumerated but never read; that and is never read between integers; and that the first period is simply read but not named, thus 375 is read three hundred seventy-five.

Write:

17. 6 thousand 3 hundred 75.

18. 10 thousand 4 hundred 6.

19. 150 thousand 5 hundred 25.

20. 5 million 825 thousand 5 hundred 4.

21. 205 million 25 thousand 3.

22. 200 million 22 thousand 60.

23. 5 billion 600 million 27 thousand 9.

24. 105 million 5 thousand 5.

25. 8 hundred million 8 thousand 85.

26. Ten thousand ten hundred ten.

27. Five hundred million two hundred fifty.

28. Six million six thousand six.

29. Sixty billion one hundred one million one thousand five hundred seventy-nine.

30. Forty million four.

31. 8 hundred million 8 thousand one hundred.

32. Ninety million six hundred thousand nine hundred two. 33. Eight hundred million two hundred twenty-eight thousand two hundred one.

34. One billion nine hundred million one thousand nine hundred fifty-four.

The other numbers are represented by combinations thus: I. When a letter is followed by the same letter or by one of less value, the values of the letters are to be added: Thus XX represents 20; XI represents 11.

II. When a letter is followed by one of greater value, the value of the smaller is to be subtracted from that of the greater. Thus IV represents 4; IX represents 9.

III. When a letter is placed between two letters of greater value, the value of the smaller is to be subtracted from the sum of the other two. Thus XIV represents 14; XIX represents 19. A bar placed over a letter multiplies its value by 1000. Thus V represents 5000.

The following table further illustrates the system.

3. Express in Roman notation: 8, 25, 39, 43, 52, 67, 79, 86, 94, 107, 119, 125, 408, 525, 693, 709, 844, 915, 1040, 1906, 2645, 5074, 10000.

Dollars and Cents

In writing dollars and cents place a period, called a decimal point, after dollars and before cents. Thus, $8.55 is read 8 dollars and 55 cents. In writing cents alone the dollar sign must precede the decimal point. Thus, 25 cents is written $.25 or $0.25; 5 cents is written $.05 or $0.05. 1. Read: $.05; $.25; $0.07; $6.05; $7.09; $4.72. 2. Read, then change to cents. Thus, $3.85 = 385 ¢. $2.05; $.70; $0.05; $7.09; $8.00; $.75; $3.50.

3. Change to dollars and cents: 55; 85; 870; 1002. 4. Write: eighty-five cents; nine dollars two cents; twenty-two dollars; nine hundred dollars six cents.

REVIEW OF ADDITION

Addition is the process of finding a number that equals two or more other numbers.

The addends are the numbers to be added.

The sum or amount is the result of addition.

Drill thoroughly on these and similar combinations: