23. Multiply 4926 by 6. 24. Multiply 3624 by 4. 25. If it takes 5428 shingles for the roof of a house, how many shingles will it take for 5 such houses? Multiply 4829 by 7. FIRST PROCESS. 425 7 X 425 30 X 425 37 × 425 2975 12750 15725 EXPLANATION.-The numbers are written as before. Since in multiplying we multiply by the parts of a number, to multiply by 37 we multiply by 30 and by 7, and add the results. 7 times 425 are 2975, the first partial product; 30 or 3 tens times 425 are 1275 tens or 12750, the second partial product. The sum of these partial products will be the entire product. Hence the entire product is 15725. SECOND PROCESS. 425 7 X 425 = 2975 3 X 425 1275 15725 EXPLANATION.-In this process the cipher at the right of the partial product is omitted and the significant figures placed in their proper places. Thus, in multiplying by 3 tens, the product is 1275 tens or 12 thousands 7 hundreds and 5 tens, which are written in their proper places in the partial product. In multiplying by tens the lowest denomination of the product is tens, in multiplying by hundreds it is hundreds, by thousands it is thousands. Hence, The first figure of each product should be placed under the figure by which we multiply. 1. How many barrels of flour at 8 dollars a barrel, can be bought for 72 dollars? 2. If there are 3 feet in a yard, how many yards are there in 27 feet? . 3. At 4 dollars a cord, how many cords of wood can be bought for 40 dollars? 4. If a man can walk 4 miles per hour, how long will it take him to walk 36 miles? 5. If 5 paces are a rod of distance, what is the length in rods of a piece of land which is 30 paces long? 6. If paper is put in packages containing 6 sheets each, how many packages can be made out of 48 sheets? 7. If 5 bushels of wheat make a barrel of flour, how many barrels of flour can be made from 40 bushels of wheat? 8. At 6 dollars a ton, how many tons of hay can be bought for 54 dollars? 9. If a man can build 7 rods of fence in one day, in how many days can he build 35 rods? 10. If a teacher earns 9 dollars a week, in how many weeks can she earn 90 dollars? DEFINITIONS. The process of finding how many times one number is contained in another is called Division. The number to be divided is called the Dividend. The number by which the dividend is to be divided is called the Divisor. The result in division is called the Quotient. The part of the dividend remaining when the division is not exact is called the Remainder. The Sign of Division is, read divided by. Thus, 246 is read, 24 divided by 6. 1. How many times is 3 contained in 369? FIRST PROCESS. Divisor. Dividend. Quotient. 3)369(100 300 20 3 69 60 123 9 9 EXPLANATION. For convenience the divisor is written at the left of the dividend, and the quotient at the right. Beginning at the left we divide. 3 is contained in 369 1 hundred times and a remainder. The 100 is placed in the quotient, and the divisor is multiplied by it. The product 300 is written under the dividend. Subtracting there is a remainder of 69. 3 is contained in 69, 20 times and a remainder. The 20 is placed in the quotient and the divisor multiplied by it. The product 60 is written under the partial dividend. Subtracting the remainder is 9. 3 is contained in 9, 3 times and no remainder. The 3 is placed in the quotient, and the divisor multiplied by it. The product 9 is written under the partial dividend. Subtracting, there is no remainder. The true quotient is therefore the sum of the partial quotients, which is 123, and 3 is contained in 369, 123 times. 1. How many times is 6 contained in 1398? PROCESS. 6) 1398 (233 12 19 18 18 EXPLANATION.-For convenience the divisor is written at the left of the dividend and the quotient at the right. Beginning at the left of the dividend we divide. 6 is not contained in 1 thousand any thousand times, therefore the quotient can not be higher than hundreds. Hence we must find how many times 6 is contained in all the hundreds of the dividend. 1 thousand is equal to 10 hundreds. 10 hundreds plus 3 hundreds equal 13 hundreds. 6 is contained in |