12. Find the value of $1 30 cents; 80 cents - $.6. 13. Find the sum of $2.5, $3, $.4, and 8.15. 14. Find the value of $.75 8.25 +8.5; $1+8.75-$1. How many decimal figures in the sum of tenths and hundredths? Of hundredths and thousandths? Of tenths and thousandths? How many decimal figures in the difference between tenths and hundredths? Between tenths and thousandths? Between hundredths and ten-thousandths? PRINCIPLE.-Only decimals of like orders, expressing parts of like units, can be added or subtracted. 150. Since integers and decimals increase and decrease uniformly by the scale of 10, decimals are added, subtracted, multiplied, and divided in the same manner as integers, and the methods of proof are the same. The arrangement of the given numbers must be such that the decimal points shall fall in the same vertical line. The number of decimal places in the result will be equal to that one of the given numbers which contains the greatest number of places. In like manner, find the value, expressed decimally, 3. Of 16.5.0348 + 7 + .07+ 1.008+. 6. Of $125.75 $41.095. 11. Of 7.005 - .7005. 16. Bought a farm for $2560.50; paid at one time $1046, and at another time $807.87. What remains unpaid? 17. Bought groceries to the amount of $7.18; how much change must I receive for two five-dollar bills? 18. Bought a ton of coal for $73, a barrel of sugar for $281, a chest of tea for $23.08, and a barrel of flour for $10.87. What was the cost of all? 19. A man bought an overcoat for $364, a sack for $18, and pants for $8.12, and gave in payment one fifty and two ten-dollar bills. What change should he receive? 20. A coal dealer bought 570.5 tons of coal, and sold at different times 80.54 tons, 120 tons, and 114 tons. How much had he left? 21. Deposited in the bank $2000, and drew out at one time $2501, at another $322.624; how much remains in the bank? 22. From a piece of cloth containing 56.25 yards, 24ğ yards were cut. How many yards remained? 23. Find the sum of 45 units, 25 tenths, 360 hundredths, 75 thousandths, 52 ten-thousandths, and 406 millionths. 24. A speculator having 7346 acres of land, sold at different times 364 acres, 1235.125 acres, 27003 acres, and 850.65 acres. How much had he left? 25. 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? 26. A man having $14725, gave $3560 for a store, and $7015.87 for goods. How much money had he left? 27. Bought a ton of coal for $6.08, a barrel of sugar for $26.625, a box of tea for $16, and a barrel of flour for $7.40. How much less than $753 was the cost of all? 28. A man bought a farm for $6736.75, which was $325 less than he sold it for. What did he sell it for? 29. How many rods of fence will enclose a field, the sides of which are respectively 34.72 rods, 4811 rods, 152.17 rods, 95 rods, and 56§ rods? Find the decimal value 30. Of ($.87 + $14§) — ($5.10 + 8.75). 31. Of (155.006.32) + (80.0032 + 55.1). 32. Of $70 ($25.4 $10.121) + $7. 33. Of .37+ + 4.2 — (2 — .684). 34. Of $250 ($170 - $141) +$18. MULTIPLICATION. INDUCTIVE EXERCISES. 152. 1. What is 5 times? 6 times .3? 4 times .5? 2. What is 7 times? 5 times .08? 6 times .09? 0 8. What is 8 times $.6? 7 times 8 of a dollar? 9. What is 8x.5? 8x.05? 8x.005? 8×.0005? How many decimal places in the product of units multiplied by tenths? Tenths by tenths? Tenths by hundredths? Hundredths by hundredths? PRINCIPLE. The number of decimal places in any product is equal to the decimal places in both factors. WRITTEN 153. 1. Multiply .64 by .8. EXERCISES. EXPLANATION.-Multiply as in fractions (120, Ex. 5). Multiply as in integers, and since hundredths multiplied by tenths produce thousandths, the product must contain three decimal places. (PRIN.) .64 .8 .512 If there are not so many figures in the product as there are decimals in both factors, supply the deficiency by prefixing ciphers, To multiply by 10, 100, 1000, etc., remove the decimal point in the multiplicand as many places toward the right as there are ciphers in the multiplier (138). What is the value 32. Of 46 mules, at $75.375 each? 33. Of 100 barrels of flour, at $9.621 each ? 38. Of 170 barrels of apples, at $2 cents? a barrel? 39. Of 100 cords of wood, at $4.38 a cord? 40. Of 204 acres of land, at $724 an acre? 41. A farmer sold 125 bushels of oats at $.37 a bushel, and received in payment 75 pounds of sugar at $.09 a pound, 12 pounds of tea at $.60 a pound, and the remainder in cash; how much cash did he receive? 32,93 ANALYSIS.-3.6 equals 36 tenths, and of 36 tenths is 6 tenths. Hence, 3.6÷6 = .6. 7. Divide .36 by 6; .36 by .06; .036 by .006. 8. Divide by 18; .3 by .06; 1.5 by .05. Reduce the fractions to a common denominator. 9. Multiply 10. Multiply by ; .7 by .5. Divide .35 by .7. by 1;.7 by .05. Divide .035 by .7. Of what two factors is the dividend the product? Then how many decimal places must the dividend contain? |