CASE IV. When the Multiplier is a Composite Number. A composite number is a number that can be produced by multiplying two or more numbers together : thus, 24 is a composite number, and its component parts or factors may be 4 and 6, which multiplied together are equal to 24 ; or they may be 2x3x4=24, or 3 X 8=24, &c. RULE. 1. Find two or more numbers which multiplied together will, exactly make the multiplier. 2. Then multiply by one of those factors and that product by another, &c., and the last product will be the Answer. EXAMPLES. 1. What will 35 acres of land come to at 56 dollars an acre ? 56=price of 1 acre. 7=one of the component parts or factors of 35. 392=price of 7 acres. 5=the other factor. Ans. 1960=price of 5 times 7 or 35 acres. 2. Multiply 576421 by 36, Ans. 20751156. 3. Multiply 764131 by 48, Ans. 36678288. 4. Multiply 844792 by 64, Ans. 54066688. 5. Multiply 91738 by 81, Ans. 7430778. 6. Multiply 43564 by 108, Ans. 4704912. 7. Multiply 814352 by 144, Ans. 117266688. 8. Multiply 218541 by 112, Ans. 24476592. NOTE. 8, 7, and 2 are factors of 112. EXAMPLES FOR PRACTICE. 1. If 35 men receive each 137 dollars, how many dollars will they all receive ? Ans. 4795. 2. In a certain orchard there are 125 rows of trees, each row containing 96 trees ; how many trees does the orchard contain ? Ans. 12000. 3. How much will 145 tons of hay come to at 15 dollars à ton ? Ans. $2175. 4. It takes 320 rods to make 1 mile ; how many rods are there in 596 miles ? Ans. 190720. 5. If a ship sail 192 miles a day, how many miles will she sail in 56 days ? Ans. 10752 miles. 6. A merchant bought 46 bales of cloth, each bale containing 35 pieces, and each piece 28 yards ; how many yards did he buy in all ? Ans, 45080. 7. Multiply 35860205 by 365, Ans. 13088974825. 8. Multiply 2703682 by 8409, Ans. 22735261938. 9. Multiply 15569800 by 8300, Ans. 129229340000. Questions. 1. What does Simple Multiplication first figure in the product ? teach? What does it perform the work 6. What do you do with the several of ? products! 2. What is the number to be multipli 7. How do you prove multiplication ? ed called? What is the number you 8. When there are ciphers on the right multiply by, called ? hand of the factors, how do you mul3. What is the number found by the tiply? operation; called ? What are the mul 9. How do you multiply by 10, 100, tiplier and multiplicand called ? 1000, &c. ? 4. When the multiplier is not greater 10. What is a composite number? than 12, how do you multiply?. 11. When the multiplier is a compo5. When the multiplier consists of se site number, how do you multiply? veral figures, how do you write it down? 12. What is the sign of multiplication ? In multiplying, where do you place the Let me see you write it down. DIVISION. 1. If you divide 15 apples equally among 3 boys, how many will each have ? How many times 3 in 15 ? 2. If 15 apples be divided equally among 5 boys, how many will each have? 5 in 15, how many times? 3. James has 16 cents to buy pencils with ; how many can be buy at 4 cents apiece ? How many times is 4 cents contained in 16 cents ? 4. How many oranges, at 6 cents apiece, can you buy for 36 cents ? 6 in 36 how many times ? 5. A man bought 9 lemons for 81 cents ; how much did he give apiece ? 9 in 81 how many times ? 6. How many barrels of cider, at 3 dollars a barrel, can be bought for 27 dollars ? 7. In an orchard there are 48 trees, standing in 8 rows ; how many trees are there in a row? How many times is 8 contained in 48 ? 8. How many barrels of flour can you buy for 84 dollars, at 7 dollars a barrel ? 9. If 9 yards of cloth cost 27 dollars, what is 1 yard worth? 10. A man worked 8 days for 40 shillings; how much was that a day? 11. A man divided 72 cents equally among 18 poor boys ; how many cents did he give to each ?-He divided themi as follows, viz: 72 We find that 1. He gave 1 cent to each, making 18 18 can be sub tracted from 72, He then had 54 left. 4 times; there2. He gave fore 18 is con tained in 72, 4 He then had 36 left. times. 3. He gave another cent to each =18 By this we that the He then had 18 left. operation may 4. He gave another cent to each =18 be performed by subtraction ; O left. but when the sum is large, and would require a great many subtractions, the operation is more easily performed by the Rule called Division. =18 see SIMPLE DIVISION Teaches to find how many times one simple or whole number is contained in another, and also what remains. Hence it performs the work of several subtractions in a concise manner. There are four principal parts in division, viz: 3. The Quotient, or answer to the question, which shows how many times the divisor is contained in the dividend. 4. The Remainder, which is always less than the divisor, and of the same name of the dividend. SHORT DIVISION RULE. 1. Find how many times the divisor is contained in the first lest hand figure, or figures of the dividend ; place the figure expressing the number of times under the dividend, and carry the remainder, as so many tens to the next figure, and divide the sum it makes as before ; and if the divisor is not contained in this sum, place a cipher under it, and carry the whole as so many tens to the next figure : thus proceed till you have divided all the figures of the dividend. Proof.—Multiply the divisor and quotient together, and add the remainder (if there be any) to the product; and if the work be right the sum will equal the dividend. EXAMPLES. 1. How many yards of cloth, at 3 dollars a yard, can be bought for 654 dollars ? Operation. We must find how many times Dividend. 3 dollars is contained in 654 dolDivisor 3)6 5 4 lars; that is, we must divide 654 by 3. We find that the divisor 3 Quotient 2 1 8 yds. Ans. is contained in 6, the first figure of the dividend, 2 times. Then 3 is contained in 5, the next figure of the dividend, 1 time and 2 remain. This remainder we carry to the next figure as so many tens; thus, 2 tens =20, which added to 4, the next figure, makes 24, and 3 is contained in 24, 8 times. In this example, observe, that the 6 which we first divide, means 6 hundred, and the 2 which we place under it means 2 hundred, showing that 3 is contained in 600, 200 times, and the 5 means 5 tens, and the l which we place under it means 1 ten, &c. If 3 contained in 654, 218 times, then Quotient 2 1 8 it is evident that 218 times 3, or which is Divisor x 3 the same thing, 3 times 218, will just make 654; and by multiplying them together Dividend 6 5 4 we find the product to be 654, = the dividend ; therefore right. Proof. 2. A father left his 6 children 2436 dollars to be equally livided among them; how many dollars had each? Operation. Here 6, the divisor, is not conDividend. tained in 2, the first figure of the Divisor 6) 2 4 3 6 dividend; therefore we join the 2 (thousands) to the 4 (hundreds) Quotient = 40 6 Ans. making 24 (hundreds ;) and 6 is contained in 24 (hundreds) 4 (hundred) times. Then 6 is not contained in 3, the tens of the dividend, therefore we put a cipher under, (that is, in the quotient,) and join the 3 (tens) to the 6 (units;) making 36; and 6 is contained in 36, 6 times. Ans. Each had $406 Divisor 2)114351 4)85412 5)94307 6)142207 7)157215 9)281359 Rem. 9. How many times is 6 contained in 7326 ? Ans. 1221. 10. How many times is 5 contained in 4565 ? : Ans. $13. 11. How many times is 7 contained in 84637 ? Ans. 12091. 12. Divide the number 9784 into 8 equal parts. Quot. 1223. 13. Divide 366024 by 12. Quotient 30502. 14. If 7 dollars will buy 1 barrel of flour, how many barrels of flour may be bought for $3822 ? Ans. 546. 15. A market man received 2943 cents for melons that he sold at 9 cents apiece ; how many did he sell ? Ans. 327. 16. How many times is 7 contained in 6680, and how many over ? Ans. 954 times, and 2 over. 17. A merchant has $5122 to purchase flour with ; how many barrels can he buy at 8 dollars a barrel, and how many dollars will he have left? Ans. 640 barrels and 2 dollars left: 18. A prize of 3825 dollars was divided equally among 4 men; how much was each man's part ? Note. We divide the 3825 dollars among the 4 men, and find that each must have 956 dollars, and there is $1 left, which we must divide. Now if we divide 1 dollar into 4 equal parts, each part will be of a dollar. Ans. Each man must have 9567 dollars |