ADDITION.

152. 1. What is the sum of 3.703, 621.57, .672, and

20.0074?

OPERATION.

3.703 621.57 .672 20.0074 645.9524

ANALYSIS. Write the numbers so that figures of like orders of units shall stand in the same columns; that is, units under units, tenths under tenths, hundredths under hundredths, etc. This brings the decimal points directly under each other. Commencing at the right hand, add each column separately, and carry as in whole numbers, and in the result place a decimal point between units and tenths, or directly under the decimal point in the numbers added.

RULE. I. Write the numbers so that the decimal points shall stand directly under each other.

II. Add as in whole numbers, and place the decimal point, in the result, directly under the points in the numbers added.

4. Add 1152.01, 14.11018, 152348.21, 9.000083.

Ans. 153523.330263.

Ans. 5038.4514.

5. Add 37.03, 0.521, .9, 1000, 4000.0004.

6. What is the sum of twenty-six, and twenty-six hundredths; seven tenths; six, and eighty-three thousandths; four, and four thousandths? Ans. 37.047.

Explain the operation of addition of decimals. Give rule, first step. Second.

7. What is the sum of thirty-six, and fifteen thousandths; three hundred, and six hundred five ten-thousandths; five, and three millionths; sixty, and eighty-seven ten-millionths? Ans. 401.0755117.

8. What is the sum of fifty-four, and thirty-four hundredths; one, and nine ten-thousandths; three, and two hundred seven millionths; twenty-three thousandths; eight, and nine tenths; four, and one hundred thirty-five thousandths? Ans. 71.399107.

9. How many yards in three pieces of cloth, the first piece containing 18.375 yards, the second piece 41.625 yards, and the third piece 35.5 yards?

10. A's farm contains 61.843 acres, B's contains 143.75 acres, C's 218.4375 acres, and D's 21.9 acres; how many acres in the four farms?

11. My farm consists of 7 fields, containing 12 acres, 18 acres, 9 acres, 241 acres, 41 acres, 8% acres, and 1518 acres respectively; how many acres in my farm?

Reduce the common fractions to decimals before adding.

Ans. 93.6375.

12. A grocer has 2 barrels of A sugar, 5 barrels of B sugar, 3 barrels of C sugar, 3.0642 barrels of crushed sugar, and 8.925 barrels of pulverized sugar; how many barrels of sugar has he?

Ans. 23.8642.

13. A tailor made 3 suits of clothes; for the first suit he used 24 yards of broadcloth, 3 yards of cassimere, and yards of satin; for the second suit 2.25 yards of broadcloth, 2.875 yards of cassimere, and 1 yard of satin; and for the third suit 5 yards of broadcloth, and 14 yards of satin. How many yards of each kind of goods did he use? How many-yards of all? Ans. to last, 18.375.

SUBTRACTION.

153. 1. From 91.73 take 2.18.

OPERATION.

91.73

2.18

Ans. 89.55

2. From 2.9185 take 1.42.

OPERATION.

2.9185

1.42

Ans. 1.4985

3. From 124.65 take 95.58746.

OPERATION.
124.65

95.58746

Ans. 29.06254

ANALYSIS. In each of these three examples, we write the subtrahend under the minuend, placing units under units, tenths under tenths, etc. Commencing at the right hand, we subtract as in whole numbers, and in the remainders we place the decimal points directly under those in the numbers above. In the second example, the number of decimal places in the minuend is greater than the number in the subtrahend, and in the third example the number is less. In both cases, we reduce both minuend and subtrahend to the same number of decimal places, by annexing ciphers; or we suppose the ciphers to

be annexed, before performing the subtraction.

RULE. I. Write the numbers so that the decimal points shall stand directly under each other.

II. Subtract as in whole numbers, and place the decimal point in the result directly under the points in the given numbers.

4. Find the difference between 714 and .916. Ans. 713.084. 5. How much greater is 2 than .298? 6. From 21.004 take 75 hundredths. 7. From 10.0302 take 2 ten-thousandths.

8. From 900 take .009.

Ans. 1.702.

Ans, 10.03.

Ans. 899.991.

Ans. .999999.

9. From two thousand take two thousandths.

10. From one take one millionth.

Explain subtraction of fractions. Give the rule, first step. Second.

11. From four hundred twenty-seven thousandths take four hundred twenty-seven millionths. Ans. .426573.

12. A man owned thirty-four hundredths of a township of land, and sold thirty-four thousandths of the township; how much did he still own? Ans. .306.

MULTIPLICATION.

154. 1. What is the product of .35 multiplied by .5?

OPERATION.

.35
.5
.175, Ans.

ANALYSIS. We perform the multiplication the same as in whole numbers, and the only difficulty we meet with is in pointing off the decimal places in the product. To determine how many places to point off, we may reduce the decimals to common fractions; thus, .35 = 85% and .5 = 5. Performand this product,

35

35

10

=

ing the multiplication, we have × expressed decimally, is .175. Here we see that the product contains as many decimal places as are contained in both multiplicand and multiplier.

RULE. Multiply as in whole numbers, and from the right hand of the product point off as many figures for decimals as there are decimal places in both factors.

1. If there be not as many figures in the product as there are decimals in both factors, supply the deficiency by prefixing ciphers.

2. To multiply a decimal by 10, 100, 1000, etc., remove the point as many places to the right as there are ciphers on the right of the multiplier.

EXAMPLES FOR PRACTICE.

2. Multiply 1.245 by .27.

3. Multiply 79.347 by 23.15.

Ans. .33615. Ans. 1836.88305.

4. Multiply 350 by .7853.

5. Multiply one tenth by one tenth.

6. Multiply 25 by twenty-five hundredths.

Explain multiplication of decimals. Give rule.

Ans. .01. Ans. 6.25.

If the product

have less decimal places than both factors, how proceed? How mul tiply by 10, 100, 1000, etc.?

7. Multiply .132 by .241.

Ans. .031812.

8. Multiply 24.35 by 10.

9. Multiply .006 by 1000. 10. Multiply .23 by .009.

11. Multiply sixty-four thousandths by thirteen millionths. Ans. .000000832.

12. Multiply eighty-seven ten-thousandths by three hundred fifty-two hundred-thousandths.

13. Multiply one million by one millionth. Ans. 1. 14. Multiply sixteen thousand by sixteen ten-thousandths. Ans. 25.6.

15. If a cord of wood be worth 2.37 bushels of wheat, how many bushels of wheat must be given for 9.58 cords of wood? Ans. 22.7046 bushels.

DIVISION.

155. 1. What is the quotient of .175 divided by .5?

OPERATION.

.5).175

Ans. .35

ANALYSIS. Performing the division the same as in whole numbers, the only difficulty we meet with is in pointing off the decimal places in the quotient. To determine how many places to point off, we may reduce the decimals to common fractions; thus, .175%, and 5. Performing the division, we have

and this quotient, expressed decimally, is .35. Here we see that the dividend contains as many decimal places as are contained in both divisor and quotient.

RULE. Divide as in whole numbers, and from the right hand of the quotient point off as many places for decimals as the decimal places in the dividend exceed those in the divisor.

Explain division of decimals. Give rule.