NOTE. in 9 tens and 6 units 1 ten time, and 1 ten and 6 units remainder; 8 in 1 ten and 6 units, or 16, 2 times; answer, 12. 63 by 7; 88 by 4. 8. 126 contains 6 how many times? NOTE. 126 equals 12 tens and 6 units. 9. How many times will 126 contain 7? Divide 133 by 7; 184 by 8; 224 by 8. 10. Divide 252 by 3; by 4; by 6; by 7; by 9. 11. How many quarts of milk, at 6 cents a quart, can you buy for 9 dimes and 6 cents? How many for 2 dollars, 2 dimes, 2 cents? 12. If 1 dozen bottles of beer cost 96 cents, how much costs 1 bottle? How much cost 26 bottles? How many bottles can be bought for $3.12 ? 13. Find the quotient of 336 divided by 8. 18. Divide 169 by 7; 168 by 7; 168 by 8. 19. How many times is 7 contained in 169? In 172? In 175? 20. How many barrels of flour, at $9 a barrel, can be bought for $162? 21. Divide 868 by 8; 808 by 8; 848 by 8; 888 by 8. NOTE. 80 tens divided by 8, gives 10 tens, or 1 hundred. 22. Divide 896 by 7. NOTE. We find the hundreds in the quotient first; 7 is contained in 8 hundreds 1 hundred times, and 1 hundred over. 23. Divide 968 by 8; 1048 by 8; 1136 by 8. 24. How many times is 8 contained in 968? 1048? In 1136? 25. How many times is 5 contained in 644? 1425 ? 26. Divide 1448 by 8; 1656 by 8. In In 27. What is the quotient of 867 divided by 9? 28. How many times is 8 contained in 1843? In 1544? 29. How many hours will it take a steamer to sail 999 miles, at 9 miles an hour? 30. If $1000 be divided among 9 men, how much will each man receive? 31. How many times is 9 contained in 10? In 100? 32. How much is left when you divide 176 by 9? NOTE. 1 hundred divided by 9 leaves 1 remainder; 7 tens divided by 9 leaves 7 remainder; 6 units divided by 9 leaves 6 remainder. Therefore, 176 divided by 9 leaves 1 and 7 and 6 remainder; but 1 and 7 and 6 are 14, which, divided by 9, leaves 5 remainder. Every number divided by 9, leaves just as much remainder as all its figures, taken as units and added together, would. For every unit, ten, hundred, or thousand, leaves 1 remainder when divided by 9. 33. How much is left after dividing 172 by 9? 876 by 9? 929 by 9? 34. How many pounds of sugar can be bought for $14.24, at 8 cents a pound? 35. At 7 cents apiece, how many slates can be bought for $16.38? 36. How many pecks in 3853 quarts? In 6353 quarts? 37. If 9 yards are required for 1 cloak, how many cloaks may be made from 6354 yards? LESSON LIX. 1. Divide 121 by 11. NOTE. We first seek how many figures on the left of 121 will contain 11 more than once, and less than 10 times: 11 will go into 1 not at all; into 12 it will go once, and a remainder. Then, as there is one figure left after 12, in the dividend, the quotient will have two figures. 11 goes into 12 tens, 1 ton time, and 1 ten over; 1 ten and 1 unit are 11, into which 11 goes 1 time ; 1 ten and 1 unit, or 11, is the answer. 2. Divide 132 by 11; tained 16 times in 256 ? 143 by 11. 180 by 12. 168 by 12; 216 by 18; 225 by 15. that which will be con 6. What number is that which will be contained 18 times in 270 ? 7. How many school libraries of 230 volumes may be selected from 1840 volumes? 8. How many companies of 80 soldiers each may be formed from 1920 soldiers? 9. How many cases of 48 pieces cach can be put up from 2400 pieces? 10. At 16 cents a yard, how many yards of calico can be bought for $13.12? 11. Divide the product of 74 and C3 by 18. 12. How many times will 16 go into 512? 13. What number will go into 512 16 times? 14. If the dividend is 666, and the divisor 18, what is the quotient? 15. If the dividend is 666, and the quotient 18, what is the divisor? 16. If the divisor is 21, and the quotient 23, what is the dividend? 17. If the quotient is 21, and the divisor 23, what is the dividend? 18. If the multiplicand is 27, and the multiplier 23, what is the product? 19. Divide 621 by 23; 621 by 27. 20. If the product is 621, and the multiplier 23, what is the multiplicand? 21. If the product is 621, and the multiplicand 27, what is the multiplier? 792 by 24; 912 by 24. 868 by 28; 980 by 28. 22. Divide 672 by 24; 23. Divide 784 by 28; 24. Divide 1001 by 11; 1920 by 24; 2304 by 24.. 25. IIow many times will 37 go into 1369? 45 into 2160? 31 into 992 ? 26. If the dividend is 1216, and the divisor 44, what is the quotient? 27. How many times will 39 go into 1209 ? Into 1755? Into 2496 ? 28. Find the number of times 41 is contained in 2829; in 2501; in 3321. 29. Required the number of times 47 is contained in 2444; in 3666. 30. Find how many times 59 will go into 4012; into 4661. NOTE. 50 will go 80 times into 4720; 4661 is how much less than 4720? 31. If a train of cars move at the rate of 34 miles an hour, how many hours will it be in moving 1187 miles ? 1189 miles? 32. How many days will 3484 gallons of water supply a family, if 67 gallons of it are used daily? 3188 gallons? 5025 gallons? 33. Divide 4212 by 78; 5109 by 78; 6097 by 78. NOTE. In any case, when it can be readily done, reduce the fraction formed by writing the divisor under the remainder, to its lowest terms. 34. If 94 bushels of corn can be produced on 1 acre, at the same rate, how many acres will be required to produce 5264 bushels? 5292 bushels? LESSON LX. 1. Find the factors of 32.* NOTE. Factors of a number are such numbers as will, by being multiplied together, produce that number. Unity, or 1, is not regarded as a material factor, since multiplying or dividing any number by 1 does not alter its value. It will be disregarded, therefore, when speaking of the factors of numbers. 2 is a factor of any even number. 2 and 16 are factors of 32. 2. Find the factors of 16; of 8; of 4; of 2. NOTE. When a number has no factor but itself and unity, it is called a prime number. 2 is therefore a prime number. Factors that are prime numbers are called prime factors. The factors of 32, if we take account of them all, are either 5 twos, or 3 twos and 1 four, or 2 twos and 1 eight, or 1 two and 1 sixteen, or 1 two and 2 fours. 3. Find the prime factors of 12; of 6; of 3. NOTE. 3, having no factors but itself and 1, is a prime number. 4. What prime numbers are there under 10? 5. Required the prime factors of 14. 6. Which are the two factors of 56 which are nearest equal?. NOTE. 56 = 28 X 2, or 14 X 4, or 8 X 7. 7. Divide 63 into 3 factors. 8. What are the prime factors of 49? Of 77? Of 91? * The process of resolving a quantity into its factors is called factoring. |