wool; what is the value of his wool crop when wool is worth 36 cents a pound? 9. Two couriers travel toward each other, the first at the rate of 35 miles and the second at the rate of 42 miles a day; at the end of 9 days they are separated by 411 miles; how far apart were they at first? 10. A person bought 30 yds. of muslin at 20 cts. a yard, 4 yds. of silk at $1.75 a yard, and 14 books at 77 cents each; what was the amount of his bill? 11. What is the difference between 118 times 327 and 211 times 82 ? 12. (2134 + 506) × (1800 – 500) × = ? = 13. (32 × 6) + (48 x 9) (17 x 4-3) + 160 = ? 14. (82478 $1032) x (2041 + 453) x 9-7 ? 15. What is the sum of 512 times 384, and 81 times 611? 16. (3042 yds. - 2106 yds.+ 218 yds.) × (354 — 214) × (27+3)=? 17. 2304 + 38 — (640 — 84) × 16 — 6. REVIEW QUESTIONS. Recite the multiplication table. What is multiplication? What is the multiplicand? What is the multiplier? What is the product? Make the sign of multiplication; tell how it is used and how it is read. Which of the two factors is always considered abstract? In the operation of multiplication how are the multiplier and multiplicand written when the sign is not used? Give the rule when the multiplier consists of but one figure. Give the rule when the multiplier consists of more than one figure. What is meant by the factors of the product? What is a composite number? How do you multiply by the factors of a composite number? What is the process when ciphers occur on the right of one or both factors. What is the use of the parentheses in Examples 12, 13, 14 and 16. DIVISION. 68. How many boys in this picture? Into how many groups are they divided? How many boys in each group? 1. If 10 boys are divided into two equal groups, how many boys are there in each group? 2. If 15 apples are separated into 3 equal piles, how many apples in each pile? 3. If 12 pears are divided among four boys, how many pears will each boy receive? 4. If 20 cents will buy 5 oranges, how many cents will buy 1 orange? 5. If a man earns $18 in 6 days, how many dollars does he earn in 1 day? 6. In 2 days there are 48 hours, how many hours in 1 day? 7. If 3 yards of silk cost $12, what will 1 yard cost? 8. There are 24 boys in 2 classes, with an equal number in each, how many boys in each class? 9. Paid 30 cents for 5 oranges, how many cents did 1 orange cost? 10. How many barrels of apples can be bought for $40, if each barrel costs $5. In the first example we are required to find one of two equal parts of ten. In the third we find the number of equal parts in 12, each of which contains 3 units. Hence, in division, we aim at one of two objects; either to find the number of units in each of the equal parts of a given number, or the number of equal parts into which a given number is to be divided. The number divided is called the Dividend. The number which shows into how many parts the dividend is divided is called the Divisor. That which shows how many times the divisor is contained in the dividend is called the Quotient. DEFINITIONS. 69. Division is the operation of finding how many times one number is contained in another, or of finding one of the equal parts of a number. 70. The Dividend is the number to be divided. 71. The Divisor is the number by which the dividend is to be divided. 72. The Quotient is the result of the division, and shows how many times the divisor is contained in the dividend. Examine carefully the 10 examples given, pages 75 and 76, and tell which is the dividend in each example, which the divisor, and what is the quotient. 73. There are three methods of indicating division. 1. By a horizontal line with a point or period above and below it; thus, . This sign, when standing between two numbers, shows that the first is to be divided by the second; thus, 8÷2 is read 8 divided by 2. 2. By a horizontal line with the dividend written above, and the divisor below; thus,, read 8 divided by 2. 3. By a curved line with the divisor at the left, and the dividend at the right; thus, 2)8, read 8 divided by 2. Write the expression 16 divided by 2, by each of the three methods. |