For convenience in reading, numbers are separated by commas into groups of 3 figures, beginning at ones. The 3-figure groups are called periods, thus:

In reading these numbers the figures of each period are read as though they stood alone and then the name of the period is added, thus:

2. The number 2,461,375 shows the beginning of a new

period, called millions. This number is read:

2 million 461 thousand 375.

The method, just described, of representing numbers by

figures is called the Arabic notation.

READING AND WRITING NUMBERS

287

There is another method of writing numbers, in which letters are used. It is called the Roman notation.

1. Write the Arabic figure for each of the following:

I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XX.

100, Ꭰ

If a letter is followed by one or more letters of equal or less value, the sum of all is the value of the number represented. Thus: VI = 6; XI = 11; XX = 20; CLX 160; DC 600.

=

=

If a letter is followed by another of greater value, the difference of the two is the value of the number represented. Thus: IV = 4; IX=9; XIX = 19; XL = 40; CD = 400. 2. Give the value in the Arabic notation of the following numbers:

Write the following numbers in the Roman notation: 9, 4, 6, 14, 29, 13, 78, 44, 83, 59, 94, 96, 104, 199, 335, 549, 2000, 1908.

Write answers to the following in Roman numerals:

3. Columbus discovered America in MCDXCII. 20 years later Florida was explored. In what year was Florida explored?

4. The first battle of the Revolution was fought in MDCCLXXV. The last battle was fought 6 years later. What was the year of the last battle?

5. Washington was elected President in MDCCLXXXIX. Roosevelt was elected 115 years afterward. In what year was Roosevelt elected?

In long columns the number to be carried may be indicated by writing it underneath the column as in problem (1). To prove the work, add from the top, downward.

2. Add the following problems in the usual way:

Another method of proof is to think the columns divided

into parts, add the parts, then add these partial sums.

EXERCISES IN ADDITION AND SUBTRACTION

289

The Minuend is the number subtracted from.

The Subtrahend is the number subtracted.

1. 6384 1945

4439

The Difference, or Remainder is the result.

6384 The sum of the difference and subtrahend should be the minuend. If so, the work is

(24)

(19) (20) (21) (22) (23) 381487 592173 600840 821380 727248 917288 191598 394205 236450 291653 570649

129399

3. A man began business with $5275.75; in five years he had $22,794.50. How much had he gained?

4. One road is 20 mi. 160 rd. long; another is 14 mi. 80 rd. long; how much longer is the first than the second?

5. A cotton dealer bought 328,900 lb. of cotton one year, and 715,600 lb. the next. How many pounds more did he buy the second year than the first?

6. One vessel is valued at $1,250,000; another at $975,800. What is the difference in value?

1. Multiply 892

Which number is the multiplicand?

by 235

The multiplier? The product?

To how many times 892 is the sum of 5 times 892 +30 times 892 + 200 times 892 equal?

FULL FORM

Multiply 892
by 235

4460

CONVENIENT FORM

892

235

4460

3. Multiply (1) 729 by 460; (2) 476 by 308.

4. Compare 4 x 5 with 5 × 4.

Compare 892 × 235 with 235 X 892. In multiplication why do we commonly use the smaller number for the multiplier? Give a way of proving that a product is correct.

5. A steamer burns 378 lb. of coal in going 1 knot. How many pounds will it burn in going 15,288 knots?

6. A man's daily income is $3.65. How much is his yearly income?