obtain 325 hundreds, which subtracted from 372 hundreds, leave 47 hundreds 470 tens. To this we add the 4 tens of the dividend, or which is the same thing, annex the 4 tens to the 47 hundreds, and we have 474 tens for a new dividend, or partial dividend, because it is a part of the original dividend.

65 is contained in 474 tens 7 tens times, and we write the 7 tens in the quotient. 65 multiplied by 7 tens = 455 tens; and 474 tens 455 tens leaves 19 tens 190 ones. Adding the 5 ones of the dividend, we have for a new dividend 195 ones.

65 is contained in 195 ones 3 times. We write 3 in the ones' place in the quotient. 65 × 3195. 195 from 195 leaves no remainder, and the required quotient is 573.

EXAMPLE.-Divide 54397 by 132.

54397 Dividend. Called Product in Multiplication.

108. RULE. Write the divisor at the left or right of the

dividend, with a curved line between them.

Separate mentally from the left of the dividend the figures expressing the smallest number that will contain the divisor. Divide this number by the divisor, and write the result as the first figure of the quotient.

Multiply the divisor by this quotient figure, and subtract the product from that part of the dividend which was used.

To the right of the remainder, if there is any, annex the next figure of the dividend, and divide the number thus formed by the divisor, writing the result as the second figure of the quotient.

Proceed in this manner until all the figures of the dividend have been used.

If any remainder with the next figure of the dividend annexed, does not contain the divisor, write a cipher in the quotient, annex to the remainder another figure of the dividend, and proceed as before.

PROOF.-Multiply the divisor and quotient together, and to the product add the remainder, if any. If the result is equal to the dividend, the work is correct.

Ans. $50000.

11. Divide three million twenty-five thousand six, by four thousand eighteen. Remainder, 3470. 12. In 638 days a government's revenue was $246356682. How much was that per day? Ans. $386139. 13. If a railroad earns $2600000 in 52 weeks, how much is that per week? 14. A railroad 357 miles long cost $2502927. How much was that per mile ? 15. In one gallon of wine there are 231 cubic inches. How many gallons in 8547 cubic inches? Ans. 37 gallons. 16. Sound travels 1119 feet in 1 second. How long would it take it to travel one mile, or 5280 feet?

Ans. $7011.

Ans. 4 seconds, and 804 feet remainder.

Written Exercises+

CASE III.

109. When the Divisor is 1 with ciphers annexed.

EXAMPLE.-Divide 1462 by 100.

SOLUTION.

Divisor. Dividend. Quotient. 100) 1462 (14

100

462

400

62 Remainder.

EXPLANATION.-We divide according to Explanation and Rule in 107 and 108, and obtain the quotient 14, and remainder 62.

We can obtain the same result by a much shorter process, namely, cutting off the two right-hand figures of the dividend, thus 14/62, in which we have 14 for the quotient, and 62 for the remainder as before.

EXAMPLE.-Divide 17563 by 1000.
SOLUTION.-17563÷1000 = 17, with 563 remainder.

EXPLANATION.-We cut off from the right, three figures (the number of ciphers in the divisor) and have 14 as the quotient, and 563, the remainder.

In any number all the figures to the left of ones, express tens; to the left of tens, hundreds; to the left of hundreds, thousands; etc. Therefore, in the number 17563, 17 must express 17 thousands, and 563 must be the remainder.

110. RULE.-Cut off from the right of the dividend as many figures as there are ciphers at the right of the divisor. The remaining figures form the quotient, and the figures cut off, the remainder.

PROBLEMS.

1. Divide 48729 by 100; by 1000; by 10000. 2. Divide 637591 by 1000; by 100000; by 10. 3. Divide 1234567 by 1000000; by 10000.

111. When the divisor is any number with ciphers annexed, the following RULE answers our purpose:

RULE.-Cut off from the right of the dividend as many figures as there are ciphers at the right of the divisor. Then divide the remaining figures in the dividend by the divisor exclusive of its right-hand ciphers.

To the remainder, if any after this division, annex the figures cut off from the dividend for a true remainder.

SECTION VII.

Written Exercises

REVIEW PROBLEMS.

1. The addends of a number are 64, 92, 436, 7859, and 436177. What is the number?

Ans. 444628.

2. The parts of a number are 4876, 73, 23756, 400009,

and 99999. What is the number?

3. The minuend is 48639 and the What is their difference?

Ans. 528713.

subtrahend is 29048.

Ans. 19591.

Ans. 54069.

4. The minuend is 93470 and the subtrahend is 39401.

What is the remainder?

5. The minuend is 47319 and the difference is 12499.

What is the subtrahend?

Ans. 34820.

6. The minuend is 311409 and the remainder is 76234. What is the subtrahend?

Ans. 235175.

7. The subtrahend is 4008 and the difference is 17296. What is the minuend?

Ans. 21304.

8. The subtrahend is 93000 and the remainder is 639421. What is the minuend?

Ans. 732421.

Ans. 1302435.

9. The multiplicand is 4215 and the multiplier 309. What is the product?

10. The multiplicand is 937 and the product is 40291. What is the multiplier?

Ans. 43.

11. The multiplier is 319 and the product is 320276. What is the multiplicand?

Ans. 1004.