it 5. Bought 56 barrels of flour at $9 per barrel, and in pay for 48 cords of wood at $6 per cord, and the rest in money; how much money did I pay? gave 6. Paid $7 each for 63 sheep, and sold the flock for $425; did I gain or lose? How much? 7. A farmer sold 56 bushels of wheat at $2 per bushel, for which he received 40 yards of cloth at $2 per yard, and the balance in money; how much money did he receive? 8. A merchant bought 846 barrels of flour for $7191; he sold 526 barrels at $9 per barrel, and the remainder at $8 per barrel; did he gain or lose? How much? Ans. Gained $103. 9. A man's income is $1575 a year, and his expenses are $3 a day; what does he save in a year of 365 days? Ans. $480. 10. Bought 18 tons of iron at $39 a ton, and 27 tons at $41; what shall I gain by selling the whole at $43 a ton? 11. A drover bought a herd of 33 oxen, paying as many dollars for each ox as there were oxen in the herd. He paid $500 in money, and gave his note for the balance; for how much did he give his note ? 7) — (3 X 5)? (3 × (3 × 5) - 12? Ans. 7. Ans. 66. Ans. 26. 12. How many are 8+ (2 x 15. The factors of one number are 20, 14, and another 16, 8, and 7; what is the difference of the bers? 23, and of two numAns. 5544. 16. The President of the United States receives a salary of $50000 a year; what will he save in a year of 365 days, if his expenses are $100 a day? Ans. $13500. 17. A man having a journey of 313 miles to perform in 6 days, travels 54 miles a day for 5 days; how far must he go on the sixth day? 18. A man sold three farms; for the first he received $3475, for the second, $925 less than for the first, and for the third, he received twice as much as for the other two; how much did he receive for the three farms? Ans. $18075. 19. What shall I pay for 25 horses, at $75 each, and 12 oxen, at $54 each? Ans. $2523. 20. If a teacher receives a salary of $800 a year, and pays $210 a year for board, $75 for clothing, $50 for books, and $100 for other expenses, how much will he save in 3 years? DIVISION. 69. DIVISION is the process of finding how many times one number is contained in parts of a number. another, or of finding one of the equal The DIVIDEND is the number to be divided. The DIVISOR is the number by which to divide. The QUOTIENT is the number of times the dividend contains the divisor. If the dividend does not contain the divisor an exact number of times, the part of the dividend which is left is called the REMAINDER. NOTE. The remainder is always of the same kind as the dividend, because it is a part of the dividend. Ex. 1. How many oranges, at 4 cents each, can be bought for 12 cents? Ans. As many oranges as there are times 4 cents in 12 cents; 4 cents are contained in 12 cents, 3 times; .. 3 oranges, at 4 cents each, can be bought for 12 cents. 2. How many apples at 2 cents each, can be bought for 10 cents? Ans. As many as there are times 2 cents in 10 cents, or as there are times 2 in 10, viz. 5. 70. The sign of division,, indicates that the number before it is to be divided by the number after it; thus, 824, i. e. 8 divided by 2 equals 4, or 2 in 8, 4 times. 3. How many are 6 ÷ 2? Ans. 2 in 6, 3 times. 69. What is Division? What the Dividend? Divisor? Quotient? Remainder? Of what kind is the remainder? 70. The sign of Division, what does it indicate? In the same manuer, let the pupil explain and recite the fol 2? 16? 8? 3? 16? Ex. 4. 32 are how many times 4? 8? 71. Division is also indicated by the colon; thus, 8:2 = 4. Also by writing the divisor before the dividend, with a curved line between; thus, 2) 846, or thus, 2) 846 (, the quotient to be placed under or at the right of the dividend, and separated from it by a line. Also by writing the divisor under the dividend, with a line between; thus, §=3; i. e. 6 divided by 2 equals 3; or, more familiarly, 2 in 6, 3 times. Ex. 8. How many are §? Ans 2 in 8, 4 times. The fourth mode of indicating division gives the following compact and convenient 71. Second sign of Division, what is it? Third mode of indicating Division, what is it? Where is the quotient to be written? Fourth method, what? How are the dividend and divisor written in the second Division Table? 19. How many are 72 ÷ 12, or 73? 72. When the dividend is large the division may be performed in two ways, as follows: 20. Divide 1384 by 4. FIRST OPERATION. 4) 1384 (24.6 12 16 24 24 Having written the divisor and dividend as in the margin, we first inquire how many times 4 is contained in 13, (the fewest figures at the left of the dividend that will contain the divisor), and find the quotient to be 3, which we set at the right of the dividend. We then multiply the divisor by the quotient, 3, and set the product, 12, under the 13 of the dividend, and subtract it therefrom. To the remainder, 1, we annex 8, the next figure of the dividend, and then inquire how many times the divisor is contained in 18, the second partial dividend; the result, 4, we set as the second figure of the quotient, and then multiply, subtract, annex, etc., as before, until all the figures of the dividend have been taken. Since the 13 of the dividend is hundreds, the 3 of the quotient is also hundreds; since the 18 is tens, the 4 is also tens; and, universally, any quotient figure is of the same order as the right-hand figure of the dividend taken to obtain that quotient figure. 72. How many ways to perform Division? Of what order is any quotient figure? |