SIMPLE NUMBERS* 1. Four, 6, 8, 10, 12, etc., are multiples of 2. 2. Six, 9, 12, 15, 18, etc., are multiples of 3. 3. Twelve is a multiple of 2. 12 is also a multiple of 3, and of 4, and of 6. 4. Twelve is a common multiple of 2, 3, , and . 5. Fifteen is a common multiple of and . 6. Common multiples of 4 and 6 are, 12, 24, , etc. The least common multiple of 4 and 6 is 12. 7. Common multiples of 6 and 8 are, 24, 48, , eta The least common multiple of 6 and 8 is . 8. Common multiples of 8 and 12 are, , , etc. The least common multiple of 8 and 12 is . 9. Common multiples of 6 and 9 are, , , etc. The least common multiple of 6 and 9 is . 10. The prime factors of 18 are , , and . 11. The prime factors of 70 are , , and . (a) What are the prime factors of 140. (b) Of 160? (c) Of 135? (d) Of 175? (e) Of 250? (f) Of 225? Multiply. Divide. Divide. (g) 635 by 53. (h) 944 lb. by 56 lb.f (i) 1536 lb. by 12.f (j) 728 by 54. (k) 846 lb. by 56 lb. (1) 1445 lb. by 12. (m) 834 by 52. (n) 739 lb. by 56 lb. (o) 1374 lb. by 12. (p) 947 by 51. (q) 873 lb. by 56 lb. (r) 1653 lb. by 12. (s) 836 by 55. (t) 965 lb. by 56 lb. (u) 1738 lb. by 12. * Do much oral work in preparation for this page. By using these terms, make the pupil as familiar with multiple, common multiple, and least common multiple, as he is with house, schoolhouse, and stone schoolhouse. t Tell the meaning. Tell a number story. COMMON FRACTIONS. L. c. m. is the abbreviation for least common multiple. 1. Add | and |f (a) |+f. L. c. m. of 8 and 12 is . (b) f + |. (o) |+f (d) * + f (e) l-i- (g)A-l- DECIMAL FEACTIONS. 1. One tenth of $432 is . .2 of $432 = 2. One hundredth of $432 is . .02 of $432 = (a) Multiply $432 by .25. This means, find 2 tenths of $432, plus 5 hundredths of $432. Operation. Explanation. $432 One hundredth of $432 is . .25 5 hundredths of $432 are . One tenth of $432 is . 2 tenths of $432 are . $21.60+ $86.4 = $108.00 NUMBER STORY. 5 hundredths of an acre are worth 1 tenth of an acre is worth . 2 tenths of an acre are worth . 25 hundredths of an acre are worth (b) Multiply $325 by .23. (d) Multiply $278 by .43. (f) Multiply $536 by .07. (h) Multiply $249 by 2.6. 0) (k) (1) Add. Subtract. Multiply. 8.75 56£ 675 7.324 12.9 .36 * The pupil should understand that he multiplies $4.32 (not $432) by 5, and should be taught to write the decimal point in the partial product immediately after writing the tenths' figure, 6, of the partial product. t The pupil should understand that he multiplies $43.2 (not $432) by 2, and should be taught to write the decimal point in the partial product immediately after writing the tenths'figure, 4, of the partial product. DENOMINATE NUMBERS. 1. Sixteen and one half feet are 1 rod. 2. Three hundred twenty rods arc 1 mile. 3. One rod is and yards.* 4. Two rods are feet. 4 rods are feet. 5. Six rods are feet. 10 rods are feet. 6. One mile is rods. \ mile is rods. 7. ^ mile is rods. \ mile is . rods. 8. The telegraph poles along the line of a railroad are usually ten rods apart; they are feet apart. From the first telegraph pole to the third it is rods; from the first to the fifth it is rods. (a) How far is it from the first telegraph pole to the thirty-third? 9. The roads in the country are usually 4 rods wide. A 4-rod road is feet wide. 10. A 100-foot street is rods and foot wide. 11. From the schoolhouse to , it is of a mile, or rods. (b) Change 5 mi. to rods. (c) Change 40 rd. to feet. (d) Change 28 rd. to yards. (e) Change 7 mi. to rods. REVIEW. 12. When hay is $12 a ton, 3000 lb. cost . 13. When oats are 30^ a bushel, 96 lb. cost . . 14. When wheat is 800 a bushel, 180 lb. cost . (f) When corn (not shelled) is 45^- a bushel, how much will 3640 lb. cost? (g) When coal is $5.40 a ton, how much will 2600 lb. cost? * Discover by actual measurement the number of yards in a rod. 1. A pile of wood 8 feet long, 4 feet wide, and 4 feet high (or its equivalent) is called a cord. (a) How many cubic feet in a rectangular solid 8 feet by 4 feet by 4 feet? 2. A pile of wood 16 feet long, 4 feet wide, and 4 feet high contains cords. (b) How many cubic feet in 2 cords? 3. A pile of wood 8 feet long, 4 feet wide, and 6 feet higb contains cords. (c) How many cubic feet in 1 ^ cords? (d) In ^ of a cord? (e) How many* cubic feet in 5| cords? (f) In 6\ cords? (g) Find the area of a surface 12 ft. by 24 ft.* (h) Find the volume of a solid 12 ft. by 8 ft. by 4 ft.f *Take care that the pupil understands that he does not (cannot) multiply 24 ft by 12 ft., hut 24 square feet by 12, or 12 square feet by 24. tin this problem the pupil multiplies 12 cubic feet by 8, and the product thus obtained by 4. |