23. Division is the process of finding how many times one number is contained in another; and the result is called the Quotient. The sign of division is written thus,÷, and, placed between two numbers or quantities, shows that the one on the left is to be divided by the one on the right. 2483 shows that 24 divided by 8 is equal to 3. 12. 1. How many times 9 are 6 times 6? 2. How many times 4 are 5 times 8? 3. How many times 8 are 6 times 12? 4. How many times 10 are 5 times 20 ? 5. How many times 15 are 3 times 25? 6. How many times 20 are 10 times 12? 7. How many times 16 are 8 times 8? 8. How many times 28 are 7 times 16? 9. How many times 25 are 5 times 30? 10. How many times 20 are 12 times 10? 11. 16 times 4 are how many times 8? 9 times 12 are how many times 6? 8 times 14 are how many times 16? 4 times 42 are how many times 12? 15. 7 times 18 are how many times 9? 16. 14 times 10 are how many times 28? 17. 12 times 8+ 4 are how many times 10? 18. 6 times 15 20 are how many times 12?* 19. How many times 9 + 3 are 7 times 13 less 10? 20. How many times 18 4 are 8 times 12 + 2? 21. In 8 x 12, how many times 64 ÷ 8? 22. In 6 × 20+12, how many times 555? 23. In 48 +24 divided by 6, how many times 4? 24. How many times 12 7 are 9 times 8? 13. 14. 25. How many times 9+6 in 6 times 12+ 3? 26. How many times 27 11 + 20 ? 9 7 x 3 are 8 X *Each sign affects only the number placed after it. When there is a remainder in the result, let it simply be mentioned as such. 24. 1. How many vests, at 5 dollars each, will pay for 7 weeks' board, at 6 dollars a week, and 18 dollars borrowed money? 2. If a man receive 16 pounds of sugar in exchange for 20 pounds of cheese at 8 cents a pound, what is the price of the sugar per pound? 3. James paid 36 cents for some oranges at 3 cents apiece, and, after eating 5 of them, he gave the remainder, at 4 cents apiece, for a knife; how much did the knife cost him? 4. Omar bought 30 peaches at the rate of 2 for 3 cents, and, after eating 3 of them and giving 3 to his brother, he sold the remainder at the rate of 3 for 7 cents; did he gain or lose by the bargain, and how much? 5. A farmer sold 9 sheep at 12 shillings a head, and 11 bushels of oats at 2 shillings a bushel; how many yards of cloth, at 10 shillings a yard, will pay the debt? 6. If I buy 40 turkeys at the rate of 5 for 3 dollars, and sell them at the rate of 8 for 7 dollars, how much will I gain by the operation? 7. If a drover buy 24 lambs for 30 dollars, at how much must he sell them a head to gain 18 dollars on the cost? 8. If 5 men buy a mowing machine for 120 dollars, and rent it 3 weeks for 15 dollars a week, and then sell it for 100 dollars, what is each man's share of the gain? 9. If 5 barrels of flour are worth 30 dollars, how many yards of cloth worth 3 dollars a yard will 2 barrels of the flour buy? 10. Four men agree to build 120 rods of wall for 48 dollars, and to share equally; but when the wall is half built, 2 men quit, and the others finish it; how many dollars must each receive? 11. How many sheep can I buy for 75 dollars at the rate of 3 for 7 dollars, and have 12 dollars left? 12. A man, having 80 dollars, bought 9 cords of wood at 4 dollars a cord, 3 barrels of flour at 8 dollars a barrel, and the remainder he expended for cloth at 4 dollars a yard; how many yards of cloth did he buy? .13. If 4 bushels of wheat are worth 12 bushels of corn, how many bushels of corn are equal in value to 10 bushels of wheat? 14. If 12 bushels of wheat make 3 barrels of flour, how many bushels of wheat will make 7 barrels ? 15. A cistern holding 140 gallons has a pipe by which 30 gallons will run into the cistern in one hour, and another that will discharge 20 gallons in an hour; when both are running, in what time will the cistern be filled? 16. If a quantity of provision serve 7 men 12 days, how long would it serve 4 men? 17. A merchant bought 15 bushels of clover seed for 75 dollars; he wishes to keep 3 bushels for his own use, and to sell the remainder so as to make 9 dollars on the first cost of the whole; how much must he ask a bushel? 18. A man bought a span of horses for 80 dollars each; he spent 40 dollars in fitting them for market, and then sold them for 300 dollars; what was his gain on each horse? 19. A tailor bought 15 yards of one kind of cloth for 60 dollars, and 25 yards of another kind for 75 dollars; what was the difference in the price per yard? 20. A thief, having 36 miles the start of an officer, travels at the rate of 6 miles an hour; the officer pursues at the rate of 9 miles an hour; in how many hours will he overtake the thief? 21. Add 5 to 22, divide the sum by 9, multiply the quotient by 12, subtract 6 from the product, and add 10 to the remainder; what will be the result? 22. Divide 40 by 8, multiply the quotient by 9, to the product add 11, from the sum take 6, and what will remain ? 23. Multiply 20 by 4, subtract 40, add 10, divide by 5, multiply by 7, and what is the result? 24. From 36 subtract 6, divide the remainder by 5, multiply the quotient by 12, add 15 to the product, subtract 77 from the sum, divide the remainder by 10, and what will be the quotient? 25. Add 5 and 7 to 8, multiply the sum by 3, from the product subtract 5, divide the remainder by 11, multiply the quotient by 6, add 20 to the product, and what will be the sum? 26. Subtract 10 from 6 multiplied by 8, to the remainder add 4, divide the sum by 6, multiply the quotient by 11, subtract 7 from the product, divide the remainder by 10, add 30 to the quotient, and what will be the sum ? 27. Multiply 15 by 5, add 5, divide by 8, multiply by 6, subtract 10, divide by 5, add 2, multiply by 11, and what will be the product? 28. 10+8÷6 × 9 −7 × 5 + 20 ÷ 10 + 8 how many ? = 29. 8912 + 3 × 5 + 10 ÷ 11 × 8+ 20 — 12+ 4 × 7-3 how many? = 30. 25-52 × 9+10 ÷ 20 × 12 + 15—5 ÷7+8+2= how many? 31. 369 x 12+ 87 x 5+10-25 ÷ 5+ 4 x 9-1110 x 63= how many? NOTE. The above examples will afford a thorough and profitable mental drill to the pupil, and also familiarize the signs and terms used in the preceding pages, and which must be well understood in the commencement of the study of Written Arithmetic. The teacher can extend the number of examples at pleasure. NOTE. Dollars and cents are separated by a period (•); thus, $2.10, is read 2 dollars 10 cents. A Simple Number contains but one name or denomination; thus, 5, 84, 12 bushels, 65 dollars, are simple numbers. A Compound Number contains two or more names or denominations; thus, 5 dollars 25 cents, 16 bushels 3 pecks, 3 days 10 hours, are compound numbers. Reduction is the process of changing numbers from one denomination to another, without altering their value; thus, changing pounds to ounces, ounces to pounds, dollars to cents, &c., is reduction. 1. How many mills in 2 cents? in 3 cents? 2. How many cents in 1 dime? in 3 dimes? 3. How many dimes in 3 dollars? in 4 dollars? 4. How many dollars in 2 eagles? in 5 eagles? 5. How many cents in 4 dimes and 7 cents? 6. How many dimes in 3 dollars and 6 dimes? 7. If James earned 12 dollars, and his father 3 eagles, how many dollars did they both earn? 8. A man has 4 eagles, 4 five dollar bills, and 4 dimes; how many dollars and cents has he? 9. How many dimes are equal to 40 cents? to 70 cents? 10. What is the difference in the cost of 8 yards. of cloth at 2 dimes a yard, and 6 yards at 30 cents a yard? |