SIMPLE NUMBERS. 1. Seventeen is an integral number. 2. Five eighths is a fractional number. 3. Seventeen and five eighths is a mixed number. 4. 25 is an number. 5£ is a number 5. ^ is a number. 3.5 is a number. 6. .8 is a number. 18 is an number. 7. A number is exactly divisible by 2 if the right-hand figure is 0, 2, 4, 6, or 8. Tell which of the following are exactly divisible by 2: 241, 136, 274, 393, 247, 826. 8. A number is exactly divisible by 5 if its right-hand figure is 0 or 5. Tell which of the following are exactly divisible by 5: 184, 275, 320, 145. 9. The following are exactly divisible by 2: 16, 38, 54, 68, , , , . 10. The following are exactly divisible by 5: 85, 140, 175, 180, , —, —, . 11. The following are exactly divisible by 10: 30, 40, 80, 120, , , , . 12. There are twice as many 5's as there are 10's in a number. 90 is tens. 90 is fives. (a) Divide $2150 by 50.* (b) Divide $215.00 by 50. (c) Divide $2295 by 51. (d) Divide $290.70 by 51.f (e) Divide $2058 by 49. (f) Divide $156.80 by 49. (g) Divide $3276 by 52. (h) Divide $322.40 by 52. (i) Divide $2496 by 48. (j) Divide $254.40 by 48. * This means, find 1 fiftieth of $2150. 1 fiftieth of $2150 is dollars. Story If 50 acres of land cost $2150,1 acre cost . t In solving such problems as (b), (d), etc., require the pupil to write the decimal point in the quotient, immediately after writing the units' figure of the quotient. If the pupil thinks what the problem means, he will easily " point off" correctly. COMMON FRACTIONS. 1. ^ and -J. (Change to .) X = ^ = (a) | and f (b) \ and \. (c) f and J. 2. Add f and f (Change to -ths.)* (d) Find the sum of 248f and 467f 3. From | subtract |. (Change to ths.)f (e) Find the difference of 837f and 284f. 4. Divide 6 by |. This means, find how many times J are contained in 6. I can change 6 to thirds. 6 = -j. 2 thirds are contained in thirds . times. Story.% (f) Find the quotient of 48 divided by f. Story.% 5. Divide 8£ feet by 2. This means, find 1 half of 8£ feet. 1 half of 8£ feet = Story. (g) Find the quotient of 86£ miles divided by 2. Story.|| (h) 3£ miles)154 miles. This means, find how many times 3 J miles are contained in 154 miles. (Change 3J and 154 to halves.) Story—A canal-boat moved at the rate of 3 J miles an hour; to move 154 miles would require hours. (i) 3)165i- miles. This means, find 1 third of 1651 miles. "~ _ Story — A train moved 165J miles in 3 hours; it moved at the rate of miles an hour. * See page 12, problem 6. t See page 12, problem 7. t See note (4), page 6. § 48 feet of ribbon was cut into pieces J of a foot long; there were pieces. I A train moved 86J miles in 2 hours; this was at the rate of miles an hour. DECIMAL FRACTIONS. 1. One thousandth of a dollar is mill. 2. Four thousandths of a dollar are 4 . 3. Four hundredths of a dollar are 4 — . 4 Four tenths of a dollar are 4 . 5. .1 of $60 = .1 of $4 = .1 of $64 =• 6. .1 of $.1= .1 of $.5= .1 of $.7 = 7. .1 of $6 = .1 of $8.5 = .1 of $5.3 = 8. .1 of $.01 = .1 of $.03 = .1 of $.07 = 9. .1 of $6.42 = .1 of $7.56 = .1 of $8.42 = 10. .1 of $875 = .1 of $74.2 = .1 of $5.35 =* (a) Multiply $374 by .3. This means, find 3 tenths of 374. Operation. 1KS74+ Explanation. 3' One tenth of $374 = — Three tenths of $374 = $112.2 NUMBER STORY. 1 tenth of an acre of land is worth ——. (b> (c) (d) (e) (f) Multiply. Multiply. Multiply. Divide. Divide 346 23-5 2.73 $.05)$.85± 5)$.85S — -A __J * By means of problems 5 to 10 and other similar exercises, lead the pupil to see that he can obtain 1 tenth of an integral number by " pointing off" one figure on the right, and of a mixed decimal by removing the point one place to the left t The pupil should understand that he multiplies $37.4 (not $374) by 3 and should be taught to write the decimal point in the product immediately after writinr the tenth* figure of the product. See page 10, paragraph 3. t This means, find how many times 5 hundredths are contained in 86 hundredths I This means, find 1 fifth of 85 hundredths. DENOMINATE NUMBERS. A bushel of oats weighs 82 lb. A bushel of wheat weighs 60 lb. A bu. of corn (shelled) weighs 56 lb. A bu. of corn (not shelled) weighs 70 lb.* 1. Two bushels of oats weigh lb.; 5 bu. weigh . (a) How much more than 1 ton do 75 bu. of oats weigh? 2. Two bu. of wheat weigh ;3 bu. weigh . (b) Seventy-five bushels of wheat weigh how much more than two tons? (c) How much less than three tons? 3. Two bushels of shelled corn weigh ;3 bu. weigh (d) Forty-five bushels of shelled corn weigh how much more than 1^ tons? (e) How much less than 1^ tons? 4. Two bushels of corn (not shelled) weigh ;3 bushels weigh ■——; 4 bushels weigh . (f) How much more than three fourths of a ton do 25 bushels of corn (unshelled) weigh? (g) How much less than one ton? 5. One hundred pounds of oats are bushels and pounds, or and 32nds bushels. (h) Five hundred pounds of oats are how many bushels? (i) How many bushels in one and one half tons of wheat? (j) How many bushels in two tons of unshelled corn? (k) (1) (m) (n) 32 lb.)768 lb. 32 lb.)769 lb. 32 lb.)770 lb. 32 lb.)772 lb. * Explain to the pupil that the expression "a bushel of corn (not shelled)," means, the amount of unshelled corn required to make 1 bushel of shelled corn. 1. A 3-foot square (or its equivalent) is called a square yard. It contains square feet. 2. A 3-foot cube (or its equivalent) is called a cubic yard. It contains cubic feet. 3. The area of a 4-foot square is square feet, or and square yards. 4. The solid content of a 4-foot cube is cubic feet, (a) How many cubic yards in a 4-foot cube? 5. The area of a 5-foot square is square feet. or and square yards. 6. The solid content of a 5-foot cube is cubic feet. (b) How many cubic yards in a 5-foot cube? 7. The area of a 6-foot square is square feet, or square yards. 8. The solid content of a 6-foot cube is cubic feet. (c) How many cubic yards in a 6-foot cube? 9. Find the area of— Find the solid content of— (1) A 7-foot square. (d) A 7-foot cube. (2) An 8-foot square. (e) An 8-foot cube. (3) A 9-foot square. (f) A 9-foot cube. |