Written Exercises+ REVIEW PROBLEMS. 1. Multiply 325 - (15 × 15) by 47 × (1861 — 1814). - 2. Multiply 801 169 533 by 624 Ans. 220900. 25 × 21. 3. Multiply (40 × 50) — 1850 by (91 × 19) — 1579. -849 Ans. 22500. 1393. 4. Multiply (75 × 24) 849 by (63 × 38) · Ans. 951951. 5. Multiply 42 + (13 × 43) by 1761 — (38 × 23). 6. 75 + 8 × (25 + 38) × (89 — 72) × 7 Ans. 533087. - 100= ? Ans. 59951. 7. 20 × (16 × 5-14 × 3) + (42 - 18 x 2) - 700 = ? Ans. 66. 8. 15291 1342 +863 14812 =? - 9. 176491426 92190 + 111 = ? 10. What sum must be added to 271 x 300 to make the amount 131313? 11. What is the difference between 75011 and 463 × 201 - 86394 ? 12. (463+537-901) × 990 = ? 13. 96+8 × (35+40) by (56-40 × 8)—5 = ? Ans. 85608. 14. A speculator bought 800 acres of land at $20 an acre; he sold at one time 350 acres at $25 an acre; at another time 250 acres at $30 an acre. At what price must he sell the remainder in order to gain on purchase $8250. Ans. $8000. SECTION VI. DIVISION 96. Division is the process of finding how many times one number is contained in another. The Terms in Division are Dividend, Divisor, and Quotient. 97. The Dividend is the number to be divided. 98. The Divisor is the number by which to divide. 99. The Quotient is the result obtained by Division. 1. When there is nothing left after division, the division is said to be exact; and the divisor is called an exact divisor. 2. That part of the dividend which is left when the division is not exact is called the Remainder. 3. The remainder must always be of the same denomination as the dividend, because it is really a part of it. 4. A true remainder is always less than the divisor. 100. The Sign of Division is a short horizontal line placed between two dots (÷), and when placed between two numbers signifies that the one on the left is to be divided by the one on the right. Thus, 62 means that 6 is to be divided by 2, and is read "6 divided by 2." Division is sometimes indicated by writing the dividend above, and the divisor below a short horizontal line. Thus. is read "6 divided by 2." In writing numbers for solution, the Divisor and Dividend may be separated by a curved line. Thus, 2)6, or 6 (2 is read “6 divided by 2." INTEGERS. 101. DIVISION TABLE. ONE. 1)1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 SEVEN. 7) 7 14 21 28 35 42 49 56 63 1 2 3 4 5 6 7 8 9 102. The Object of Division is twofold: First. To find how many times one number is contained in another. Second. To find one of the equal parts of a number. First. EXAMPLE.-A man has 10 dollars with which he wishes to buy books at 2 dollars each. How many books can he buy? SOLUTION.-Since 2 dollars are contained in 10 dollars 5 times, he can buy 5 books. Or, 2 dollars are contained in 10 dollars 5 times. Therefore, he can buy 5 books. Second. EXAMPLE.—If a man divides 10 dollars equally between 2 persons, how much does each receive? SOLUTION.-Since 2 persons receive 10 dollars, one person receives ONE-HALF of 10 dollars, or 5 dollars. Or, ONE-HALF of 10 dollars is 5 dollars. Therefore, each person receives 5 dollars. The preceding are representative examples of the two kinds of problems to which Division is applied. In the first, the Divisor and Dividend are like numbers and the Quotient is an abstract number. Hence, 103. The Quotient is an abstract number, when the Divisor and Dividend are both abstract, or both concrete numbers. In the second example, the Divisor and Dividend are unlike numbers and the Quotient is the same kind as the dividend. Hence, 104. When the Divisor and Dividend are unlike numbers the Quotient is always the same kind as the Dividend. The mode of reasoning in the solution of these two classes of examples is somewhat different; but in reality the operation is the same, viz.: to find how many times one number is contained in another, which is in harmony with the definition of Division (96). |