ADDITION OF DECIMALS. 146. Addition of decimals is the operation of finding the sum of two or more decimals. 1. What is the sum of and? + 1% This expressed by means of the decimal point, is written thus, .4, and read four-tenths. 2. Add .1, .3, and .5. .1 + .3 + .5 = .9. 3. What is the sum of .21 and .35? .21 + .35 = .56. 4. If an arithmetic cost 5 tenths of a dollar, and a grammar 8 tenths, what do they both cost? 5. What is the sum of 37.04, 704, 3 and .0376 ? ILLUSTRATION. 37.0400 704.3000 .0376 741.3776 EXPLANATION.-We write the numbers so that units of the same order stand in the same column; this brings the decimal points also in the same column. We commence at the right and add as in integers; bring down the decimal point and place it beneath, at the left of tenths' place. RULE. Write the decimals so that units of the same order shall stand in the same column and add as in simple numbers; and place the decimal point in the amount under the decimal points in the numbers added. 9. Add .7, .07, .175, and 2.0325. 10. Add 17.215, 3.056. .009, and 2.079. PRACTICAL PROBLEMS. 1. A man bought a horse for $203.75, a buggy for $305.50, a harness for $43.25, and a whip for $3.75; what was the cost of the whole? Ans. $556.25. 2. A farm consists of 33.125 acres of woodland, 24.876 acres of pasture land, 14.886 acres of meadow, and 13.888 acres of plough land; how many acres in the farm ? Ans. 86.775 acres. 3. A farmer sold a pair of horses for $287.755, a yoke of oxen for $173.865, and 7 cows for $213.825; what did he receive for them all? 4. A man bought a lot for $874.75, built a house on it that cost $5,843.795, a barn that cost $563.254, and then expended $2,811.345 for furniture; what was the cost of the whole? What is addition of fractions? Give the rule for addition of decimal fractions. SUBTRACTION OF DECIMALS. 147. Subtraction of Decimals is the operation of finding the difference between two decimal numbers. 1. A boy having 7 tenths of a dollar, paid 2 tenths for a trip to the park; how much had he left? from leaves, which expressed by means of the decimal point is .5. 50 = 10%; .78.50 = .28. 5. From 56.403 subtract 18.6. ILLUSTRATION. 56.403 37.803 = = 13. EXPLANATION. We write the subtrahend under the minuend, so that units of the same order shall stand in the same column; this will bring the decimal points in the same column. We then subtract as in simple numbers. Hence the following RULE. Write the subtrahend under the minuend so that units of the same order shall stand in the same column; then subtract as in simple numbers and place the decimal point in the remainder under the decimal points of the subtrahend and minuend. 1. A man had $18.75, but spent $4.755; how much had he left? Ans. $13.995. 2. A farmer bought groceries to the amount of $117.743, of which he paid $93.817 in oats, and the remainder in cash; how much did he pay in cash? Ans. $23.926. 3. A dealer bought goods for $8,743.85, and sold them. for $11,342.81; how much did he gain? 4. Two fields contain 87.3142 acres, and the smaller one contains 32.8954 acres; what does the larger one contain? 5. From a hogshead of sugar weighing 993.142 lbs., 418.387 lbs. were sold; how much remained? What is subtraction of decimals? What kind of fractions can be subtracted? Give the rule for subtraction of decimals. What is the minuend? What the subtrahend? What is the result in subtraction? MULTIPLICATION OF DECIMALS. 148. Multiplication of decimals is the operation of finding the product of two decimals, 1. Multiply by 3. 10 × = 3 expressed by means of the decimal point, .3. If tenths are multiplied by units, the product is tenths. If tenths are multiplied by tenths, the product is hundredths. If tenths are multiplied by hundredths, the product is thousandths. If tenths are multiplied by thousandths, the product is ten thousandths. The denominator of the product will therefore contain as many ciphers as there are ciphers in the denominators of the factors. If the decimal be expressed by means of the decimal point, the number of decimal figures is still determined by the number of ciphers in the denominator; hence, the number of decimal figures in the product must equal the number of decimal figures in the factors. 5. Multiply .5 by 7. Since tenths multiplied by units give tenths, .5 × 7 units 35 tenths = 3.5. |