20. If a teacher receives a salary of $800 a year, and pays $210 a year for board, $75 for clothing, $50 for books, and $100 for other expenses, how much will he save in 3 years?

DIVISION.

69. DIVISION is the process of finding how many times one number is contained in another.

The DIVIDEND is the number to be divided.

The DIVISOR is the number by which to divide.

The QUOTIENT is the number of times the dividend contains the divisor.

If the dividend does not contain the divisor an exact number. of times, the part of the dividend which is left is called the REMAINDER.

NOTE. The remainder is always of the same kind as the dividend, because it is a part of the dividend. /

Ex. 1. How many oranges, at 4 cents each, can be bought for 12 cents?

Ans. As many oranges as there are times 4 cents in 12 cents; 4 cents are contained in 12 cents, 3 times; .. 3 oranges, at 4 cents each, can be bought for 12 cents.

2. How many apples, at 2 cents each, can be bought for 10 cents?

Ans. As many as there are times 2 cents in 10 cents, or as there are times 2 in 10, viz. 5.

70. The sign of division, ÷, indicates that the number before it is to be divided by the number after it; thus, 8÷2 4, i. e. 8 divided by 2 equals 4, or 2 in 8, 4 times. 3. How many are 6 ÷ 2?

Ans. 2 in 6, 3 times.

69. What is Division? What the Dividend? Divisor? Quotient? Remain

der? Of what kind is the remainder? 70. The sign of Division, what does it

4

In the same manner, let the pupil explain and recite the fol

lowing

DIVISION TABLE.

6+1=612÷2=618÷3=6

5÷15 | 10÷2=515÷3=5

71714÷2=7|21÷3=7

8+1=8162824÷3=8 9÷1918÷2=927÷3=9

5÷5=1 6÷6=1 7÷7=1

105212÷6=214÷7=2

155318÷6=3

1682

21÷7=3 2483

2054246428÷7=4

255530÷6=535÷7=5

30÷5-6366642÷7=6

3557426749÷7=7

405848÷6=856÷7=8

4559546963÷7=9

408 5

3284

4886

5687

6488

7289

189 2

9÷9=1 1010111÷11=112÷12=1

2010-222÷11=2

24122

279330÷10-333÷11=336÷12=3

3694401044411-448÷12=4

459550÷10 = 555÷11=560÷12=5

549660÷10666÷11=672÷12=6

639770÷10=7 77117184÷12=7

72988010888÷11=896÷12=8

819 = 99010999÷11=9 108÷12=9

Ex. 4. 32 are how many times 4? 8? 2? 16?

5. 48 are now many times 4? 6? 12? 8? 3? 16? 6. 36 are how many times 12? 6? 9? 3? 4? 2. 7. 40 are how many times 8? 4? 2? 10? 5? 20?

71. Division is also indicated by the colon; thus, 8:2=4. Also by writing the divisor before the dividend, with a curved line between; thus, 2)846, or thus, 2)846(, the quotient to be placed under or at the right of the dividend, and separated from it by a line.

Also by writing the divisor under the dividend, with a line between; thus, & = 3; i. e. 6 divided by 2 equals 3; or, more familiarly, 2 in 6, 3 times.

Ex. 8. How many are ?

Ans. 2 in 8, 4 times.

The fourth mode of indicating division gives the the following compact and convenient

= 3

=3 =3=3=3=3

= 4

44=423 424 4

=5=5=52452=538=5 f=6=6=624=6=6=6

=7=7=7247 377

=8=82=832=8=8=8

= 9

=9=9=9=9=9

19. How many are 72 ÷ 12, or ?

72. When the dividend is large the division may be performed in two ways, as follows:

20. Divide 1384 by 4.

FIRST OPERATION.

4)1384(346

12

18

16

24

24

0

Having written the divisor and dividend as in the margin, we first inquire how many times 4 is contained in 13, (the fewest figures at the left of the dividend that will contain the divisor,) and find the quotient to be 3, which we set at the right of the dividend. We then multiply the divisor by the quotient, 3, and set the product, 12, under the 13 of the dividend, and subtract it therefrom. To the remainder, 1, we annex 8, the next figure of the dividend, and then inquire how many times the divisor is contained in 18, the second partial dividend; the result, 4, we set as the second figure of the quotient, and then multiply, subtract, annex, etc., as before, until all the figures of the dividend have been taken..

Since the 13 of the dividend is hundreds, the 3 of the quotient is also hundreds; since the 18 is tens, the 4 is also tens; and, universally, any quotient figure is of the same order as the right-hand figure of the dividend taken to obtain that quotient figure.

The foregoing operation is called Long Division, but the work may be much shortened by carrying the process in the mind, in

SECOND OPERATION.

Divisor, 4)1384 Dividend.

stead of writing it; thus, having written the divisor and dividend as be

Quotient, 346

fore, say, 4 in 13, 3 times and 1 remainder; set the

quotient, 3, under the 3 of the dividend, and then, imagining the remainder, 1, placed before the 8, say, 4 in 18, 4 times and 2 remainder; set down the 4 as the second figure of the quotient, and imagine the 2 set before the next figure, and so proceed.

This operation is called Short Division, which is usually adopted when the divisor is so small that the process may be readily carried in the mind. Hence,

73. To perform Short Division :

RULE. Divide the left-hand figure or figures of the dividend, (the fewest figures in the dividend that will contain the divisor,) and set the quotient under the right-hand figure taken in the dividend; if anything remains, prefix it MENTALLY to the next figure in the dividend, and divide the number thus formed as before, and so proceed till all the figures of the dividend have been employed. Ex. 21. Divide 24864 by 8.