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 13 hundreds 2 hundred times and a remainder. The 2 is written in hundreds' place in the quotient and the divisor multiplied by it. Subtracting this product from the partial dividend, 13 hundreds, there is a remainder of 1 hundred. 1 hundred remainder is equal to 10 tens. 10 tens plus 9 tens equal 19 tens. 6 is contained in 19 tens 3 tens times and a remainder. The 3 is written in tens' place in the quotient, and the divisor multiplied by it. Subtracting this product from the partial dividend, 19 tens, there is a remainder of 1 ten in the quotient. The 1 ten remainder equals 10 units. 10 units plus 8 units equal 18 units. 6 is contained in 18 units 3 times and no remainder. The 3 is written in units' place in the quotient, and the divisor multiplied by it. 9) 49842 ( 7) 54285 ( 9) 32616 ( 8) 42856 ( The solution of examples having a small divisor, may be shortened by performing the multiplications and subtractions without writing the results. This process is called Short Division. The solution of Example 1, by short division, is: PROCESS. 6)1398 233 EXPLANATION.-6 is contained in 13 hundreds 2 hundred times and 1 hundred remainder. The 2 is written in the quotient under units of the same order in the dividend. 1 hundred remainder and 9 tens make 19 tens. 6 is contained in 19 tens 3 tens times and 1 ten remainder. The 3 is written in the quotient under tens in the dividend. 1 ten remainder and 8 units make 18 units. 6 is contained in 18 units 3 times. The 3 is written in the quotient under units. Hence the quotient is 233. LESSON LXXVII. 1. Divide 4825 by 26. PROCESS. Divisor. Dividend. Quotient. 26) 4825 (185 26 222 208 145 130 Remainder 15 EXPLANATION.-26 is not contained in 4 thousands any thousands times, hence, the thousands are united with the hundreds, making 48 hundreds. 26 is contained in 48 hundreds 1 hundred times and a remainder. The 1 is written in hundreds' place in the quotient and the divisor multiplied by it, giving a product of 26 hundreds. Subtracting this product from the partial dividend 48, there is a remainder of 22 hundreds. 22 hundreds united with 2 tens make 222 tens. 26 is contained in 222 tens 8 tens times and a remainder. The 8 is written in tens' place in the quotient and the divisor multiplied by it, giving a product of 208 tens. Subtracting this product from the partial dividend there is a remainder of 14 tens. 14 tens united with 5 units make 145 units. 26 is contained in 145 units 5 times and a remainder. The 5 is written in units' place in the quotient and the divisor multiplied by it, giving a product of 130 units. Subtracting, there is a remainder of 15. Therefore the quotient is 185, and the remainder, 15. |