3. From 963.75 subtract 585.125.

963.750 585.125 378.625

SOLUTION.-Write the numbers so that figures of the same order shall stand in the same column. Subtract as in subtraction of integers, which gives 378.625, the result required.

These numbers are prepared for subtracting by annexing a cipher to the minuend, which makes its decimal express thousandths, or like parts with the decimal of the subtrahend, without altering the value.

4. From 196.35 subtract 173.91.

5. From 73.007 subtract 68.75.

385. Rule for Addition and Subtraction of Decimals.- Write the numbers so that figures of the same order shall stand in the same column.

Add or subtract in the same manner as in integers, and place the decimal point at the left of the order of tenths in the result.

PROBLEMS.

386.-1. What is the sum of .81, 3.65, 4.5 and 7.315? 2. What is the sum of .9, 14.501, 6.75 and 19? 3. What is the sum of .125 + .62 +.437?

4. What is the difference between 41.634 and 7.595? 5. What is the difference between 18.5 and 9.995? 6. What is the difference between .735 of a ton and .598 of a ton?

7. What is the difference between 98 and .98?

8. Wilson is 63.125 years old, and Johnson is 58.75 years old. What is the sum of their ages ?

9. Horatio has 125.675 thousand feet of box-boards, and his father 239.703 thousand feet. How many more has the one than the other?

10. A farmer received $69.875 for corn, $93.1875 for wheat, and $42.9375 for oats. How much did he receive for the whole?

387. TEST QUESTIONS.-1. What is a decimal? A mixed decimal?

2. Recite the decimal orders from tenths to millionths. What principles of decimals are given?

3. How do you read decimals? How do you write decimals?

4. What is the principle for addition and subtraction of decimals? How do you add or subtract decimals?

SECTION XXXVIII.

MULTIPLICATION OF DECIMALS.

388.-1. How many tenths are 3 times 1 tenth? 3 times 3 tenths? 5 times 4 tenths?

2. How many ones are 5 times 4 tenths? 5 times 9 tenths?

SOLUTION.-5 times 9 tenths are 45 tenths; and since 10 tenths are 1, 45 tenths are 4 ones and 5 tenths, or 4.5.

3. How many hundredths are 3 times 1 hundredth ? 3 times 3 hundredths? 5 times 4 hundredths? 4. How many tenths are 5 times 4 hundredths? 5. When tenths are multiplied by ones, what is the denominator of the product? When hundredths are multiplied by ones, what is the denominator?

6. What is the product of 1 tenth by 1 tenth, or of by? Of 3 tenths by 2 tenths, or by ?

7. What is the product of 1 hundredth by 1 tenth, or roby? Of 3 hundredths by 2 tenths, or 8 by ?

8. When tenths are multiplied by tenths, what is the denominator of the product? When hundredths are multiplied by tenths?

9. How many decimal orders will there be in the product, decimally expressed, if you multiply by 3? by? by 3? by ?

389. Principle.-The number of decimal orders in the product is equal to the number of decimal orders in both factors.

WRITTEN EXERCISES.

390.-1. What is the product of .49 by 6?

.49

6

2.94

SOLUTION.-6 times are 49x6 = 134 = 21%, or

decimally expressed, 2.94.

100

2. What is the product of .49 by .6?

.49

.6

.294

SOLUTION. times are X1= f, or, decimally expressed, .294.

294

3. What is the product of .573 by 5? 4. What is the product of .75 by .06?

49 X 6 100 X 10

391. Rule for Multiplication of Decimals.-Multiply as in integers, and point off as many orders for decimals in the product as there are orders of decimals in both factors.

If there are not as many figures in the product as decimal orders required, supply the deficiency by prefixing ciphers.

13. The distance to a certain place to another place it is 10 times as far. tance to the latter place?

is .75 of a mile;

What is the dis

Since the multiplier is 10, the product may be found at once by removing the decimal point in the multiplicand one order to the right.

14. The standard bushel contains 2150.42 cubic inches. What is the cubic capacity of a bin containing 100 bushels?

15. What is the product of .00365 by 1000?

16. What will 10.25 yards of cloth cost, at $3.40 per yard?

SECTION XXXIX.

DIVISION OF DECIMALS.

393.-1. How many times 3 tenths in 9 tenths? 2. How many times 3 hundredths in 9 tenths?

SOLUTION.-9 tenths are 90 hundredths; 3 hundredths are contained in 90 hundredths 30 times.

3. How many times 2 hundredths in 8 tenths? In 6 tenths?

4. What is the quotient of 9 tenths by 3 tenths, or f by? Of by?

5. What is the quotient of 8 tenths by 2 hundredths, orby? Of by 180?

6. What is the quotient of 5 tenths by 25 hundredths, or .5 by .25? Of 1.2 by .12?

7. What is the quotient of 4.2 by 6, or what is one sixth of 4.2?

SOLUTION.-4.2 is 42 tenths; and one sixth of 42 tenths is 7

tenths.

8. What is the quotient of .42 by 6? Of .42 by .06 ? Of 6 by .6?

9. When .42 is divided by 6, how many more orders of decimals has the dividend than the divisor?

10. When .42 is divided by 6, how many orders of decimals has the quotient?

394. Principle.—The number of decimal orders in the quotient is as many as there are in the dividend less the number in the divisor.

WRITTEN EXERCISES.

395.-1. How many times 6 in 2.94?

6)2.94

SOLUTION.-2.94 is 294 hundredths, and one sixth .49 of 294 hundredths is 49 hundredths, or .49.

2. How many times .6 in .294?

6).294 .49

SOLUTION.-.6 is the same as of 6; 6 is contained in .294 one sixth of .294, or .049, times; and of 6 must be contained 10 times .049 times, or .49 times.

3. How many times 9 in 28.35?

4. How many times .07 in .0938 ?