ADDITION OF DECIMALS 1. What kind of fractions can be added or subtracted ? In adding or subtracting decimals, like units must always be written under one another; thus, .8+.85 +.096 may be written thus : .8 .8+ .8=1.6 Added .85 Test: .05 +.09 = .14 .096 .006 = .006 1.746 1.746 2. In how many of the decimals were there tenths to be added? hundredths ? thousandths ? 3. Why must tenths be written under tenths, hundredths under hundredths, etc.? A mixed decimal is a whole number and a decimal united ; thus, 4+.05=4.05. Written Work 1. Add 45.5 +6.005 + 40. 45.5 6.005 Keep the decimal points and units of the same order in a 40. column, and add as in whole numbers, placing the decimal 91.505 point in the sum under the points above. Find the sums of the following: 2. .1+.2+.35 +.365 = ? 20. Find the sum of 15.38, 9.17, 3.07, and 20.35. 21. A boy picked on Monday, .75 of a bushel of berries ; on Tuesday, .875 of a bushel ; on Wednesday, 1.125 of a bushel. How many bushels did he pick in the three days ? 22. Helen paid $.25 for a handkerchief, $ 2.75 for a pair of shoes, $.45 for lace, and $1.49 for a waist. How much did they all cost ? 23. A train runs the first hour 19.625 miles; the second hour, 20.5 miles; the third hour, 20.75 miles; the fourth hour, 21.225 miles. How far does it run in the four hours ? 24. Find the number of pounds in the following purchases : 1.25 lb. of cheese, 3.5 lb. of sugar, .5 lb. of cloves. 25. The distance from Harrington to Houston is 4.31 miles, thence to Ellendale 11.25 miles, thence to Georgetown 8.37 miles. How far is it from Harrington to Georgetown? SUBTRACTION OF DECIMALS Find differences : 1. .5-.3 = ? 2. .9 -:8=? 3. 15.8 - 11.7 = ? 4. 4.7 -3.2= ? 5. .008 - .002 = ? Written Work 1. From 16.35 subtract 11.76. 16.35 Keep the decimal points in a column and sub11.76 tract as in whole numbers, placing the decimal 4.59 point in the difference under the points above. 14. Warren had $7.50 and spent $3.75. How much had he remaining ? 15. The distance between two towns is 9 miles. After I have walked 3.625 miles, how far have I yet to walk ? 16. A man having 120 acres of land, sold to one man 28.75 acres, and to another, 35.5 acres. How many acres had he left ? 17. If I pay $1.25 for car fare, $.65 for dinner, and $.90 for an umbrella, how much change have I left from a fivedollar bill? 18. The second floor of a house is 18.78 feet above the floor of the cellar, and the first floor is 7.92 feet above it. How far is it from the first floor to the second ? 19. Four lots measure in width 123.08 ft. Three of them are respectively 25 ft., 32.72 ft., and 36.9 ft. wide. What is the width of the fourth? 20. A boy having $4.25 spent for skates $1.25, for a cap $.50, and for a hockey stick $.45. How much had he left? 21. A lady having 25.75 pounds of butter sold to one customer 3.25 pounds, to another 8.5 pounds, to another 7.25 pounds, and the balance to a fourth customer. How many pounds did the fourth customer buy? 22. From a ham weighing 18.125 lb. a butcher sold 3.25 lb., 4.50 lb., 2.75 lb., and 2.5 lb. How many pounds had he left ? 23. A fisherman brought home four trout weighing respectively 1.25 pounds, .875 pounds, 1.375 pounds, and 1.125 pounds. How much did they all weigh? 24. A farmer cut 40 tons of hay in 1905. He sold 6.85 tons one man, and 5.55 tons to another. He fed the rest to his stock. How many tons did he feed to his stock? 25. A lady bought 4.75 yards of woolen cloth, 11.625 yards of cotton cloth, and 6.875 yards of silk. How many yards did she buy? 26. A man having $20 spent $4.75 for board, $2.80 for a room, $.88 for laundry, $1.75 for a pair of gloves, and $3.50 for a pair of shoes. How much had he left? 27. A merchant purchased the following: coffee $15.25, sugar $18.35, cakes $11.65, fruit $27.75, canned corn $8.45, canned peaches $12.30, and vegetables $21.90. What was the amount of his bill? MULTIPLICATION OF DECIMALS = 1.5. Multiplying a decimal by an integer. 1. 5x.3 means that .3 is taken as an addend 5 times. Thus, .3+.3+.3+.3+.3= 15 tenths or 1.5. By multiplication 5 x.3 2. 5x.03 means that .03 is taken as an addend 5 times. Thus, .03 +.03 +.03+.03 +.03= 15 hundredths or .15. By multiplication 5 x.03 = .15. 3. 5 x 1.007 means that 1.007 is taken as an addend 5 times. Thus, 1.007 + 1.007 + 1.007 + 1.007 + 1.007 = 5.035. By multiplication 5 x 1.007 = 5.035. 4. In each problem above, how many decimal places are there in the multiplicand ? how many in the product ? Observe that in multiplying a decimal by an integer, the product contains the same number of decimal places as the multiplicand. Written Work 1. Multiply 5.75 by 6. 6 x 5 hundredths = 30 hundredths, or 3 tenths and 5.75 no hundredths. Write naught in hundredths' place 6 and carry the 3 tenths. 6 x 7 tenths = 42 tenths; 42 tenths + 3 tenths 45 tenths, or 4 units and 5 34.50 tenths. Write 5 in tenths' place and carry the 4 units. Place the decimal point. 6 x 5 units = 30 units; 30 units + 4 units = 34 units. Find products : 2. 8 X.015 6. 7 *.97 - 10. 86 x .861 14. 55 x .066 3. 9.005 7. 12 x .025 11. 74 x .037 15. 39 x .467 4. 8 x .17 8. 6 x.604 12. 67 x.92 16. 48 x .095 5. 11 x.207 9. 9 x .054 13. 44 x .705 17. 36 x .081 HAM. INT. ARITH. - 6 |