REVIEW. 1. Two is an exact divisor of 28, 274, 3. Ten is an exact divisor of 80, 4. Twenty is an integral number. and .5 are numbers. 51 and 3.2 are 5. The fractions, 20 denominator. and nator. numbers. have a common do not have a common denomi 6. The sum of .135 and .6 is .135.06: = 7. Divide .045 by .009. (This means (a) Find the quotient of .875 divided by .005. 8. Divide .045 by 9. (This means (b) Find the quotient of 54.063 divided by 9. 9. When hay is $8 a ton, 2500 lb. cost 10. Five bushels of wheat weigh 5* pounds. (c) Sixty-five bushels of wheat weigh how much more than 65 bushels of oats? 11. The area of a 10-inch square is square inches. (d) How many square feet in a 15-foot square? (e) How many square yards in a 15-foot square ? 12. The solid content of a 10-inch cube is (f) How many cubic feet in a 15-foot cube? (g) How many cubic yards in a 15-foot cube? 13. Three fourths of 60 are (h) Find & of 132. cu. in. 60 is 3 of 14. Two thirds of 27 are 1 half of (j) Two thirds of 132 are 1 half of what number? * These figures refer to notes on page 8. MISCELLANEOUS PROBLEMS. 1. Byron bought 6 melons for 544; he sold them at 15¢ each; on each melon he gained cents. (a) A merchant bought 6 barrels of apples for $13.50, and sold them at $2.75 a barrel. How much did he gain on each barrel? 2. James carried 4 dozen eggs to market; he sold them for 124 a dozen; the dealer paid James for the eggs with sugar at 5¢ a lb.; James should receive pounds of sugar. and (b) A farmer took four cords of wood to market; he sold it for $6.75 a cord and took its value in coal at $6 a ton. How many tons of coal should he receive? 3. At 54 a quart, 1 gallon of milk is worth cents. (c) At 54 a quart, how much are 45 gallons of milk worth? 4. Two and 1 half feet are days. inches. 4 weeks are (d) Forty-six and 1 half feet are how many inches? (e) Fifty-two weeks are how many days ?* (f) Seventy-five gallons are how many quarts? 5. William had 304; he spent & of his money for ink and pencils and the remainder for paper; the paper cost cents. (g) William's father had $585; he spent of his money for a carriage and harness and the remainder for horses. How much did the horses cost? *The pupil should see that in the solution of this problem he may take fifty-two 7's or seven 52's. If he adopts the latter method his thought may be-One day in each week would make 52 days, and seven days in each week would make 7 times 52 days; or he may think that fifty-two 7's are equal to seven 52's, and that, as a matter of convenience, he finds seven 52's. SIMPLE NUMBERS. 1. A number that has no exact integral divisors except itself and 1, is called a prime number. 1, 2, 3, 5, 7, 11, 2. Integral numbers that are not prime are said to be 4. If an integral number is expressed by two or more figures, and the right-hand figure is 5, the number is (a) Write all the prime numbers from 1 to 53 inclusive, and find their sum. *This means, find how many times $52 are contained in $7436. $52 are contained in $7436, 143 times. Story-A man paid $7436 for land at $52 an acre; there were 143 acres. †This means, find 1 fifty-second of $7436. 1 fifty-second of $7436 is $143. StoryA man paid $7436 for 52 acres of land; one acre cost $143. ths.) 4. Add,, and . (Change to (j) Find the sum of 75%, 86%, and 474. 5. From subtract. (Change to ths.) (k) Find the difference of 946 and 3881. 6. Divide 7 by 3. This means Story.† (1) Find the quotient of 36 divided by 3. Story.‡ (m) 24 gallons)126 gallons. This means, find how many times 2 gallons are contained in 126 gal. (Change 21 and 126 to fourths.) Story.§ (n) 4)276 gallons. This means, find 1 fourth of 2761 gallons. Story-In 4 days Mr. Smith sold 276 gallons of milk; this was at the rate of gallons per day. *The pupil is expected to find by trial that he can change halves, thirds, and eighths, to twenty-fourths. See note (4) page 6, and problem 4, page 22. Mr. Brown put 36 bushels of peaches into -bushel baskets; there were baskets. ? Put 126 gal. of milk into 21-gal. cans. If 1 ton of coal is worth $2.45, 1 tenth of a ton of coal is worth (b) Multiply $3.65 by 2.4.* (1 of $3.65 is $.365.) 2. I bought 7 yards of print at 6¢ a yd. and gave the salesman half a dollar; I should receive in change (d) I bought 5.3 tons of coal at $4.20 a ton and gave the salesman 3 10-dollar bills. How much change should I receive? * Write the decimal point in each partial product immediately after making the figure that represents the tenths in that product. †This means, find how many times 5 tenths are contained in 475 tenths. This means, find 1 fifth of $47.5. |