KEY TO CARD No. 24.

Fifth.

How many times 346 in 2567? seek how many times 3 in 25-8 times but allow one and say 7 times.

Set 7 in the quotient and multiply 346 by 7-place the product under 2567-subtract-the remainder is 145. The quotient or answer is 23477148.

LESSON 12.

Divide 123,456,789 by 123.

123)123456789(1003713

123

...456

369

,877

861

.168

123

.459

369

.90

First.

How many times 123 in 123?we readily say one-set 1 in the quotient.

Multiply 123 by 1--the product is 123-place this product under the number 123 in the dividendsubtract-there remains 0-bring down the next figure 4 from the dividend.

Second.

How many times 123 in 4?— not one; set 0 in the quotientbring down the next figure 5; it makes 45. Third.

How many times 123 in 45 ?-not one; set 0 in the quotient-bring down the next figure 6; it makes 456.

Fourth.

How many times 123 in 456? 3 times set 3 in the quotient-Multiply the divisor 123 by 3-place the product under 456-subtract-the remainder is 87-bring down the next figure 7; it makes 877.

Fifth.

How many times 123 in 877? To make a guess, say 12 in 87-7 times-place 7 in the quotient.-Multiply the di

KEY TO CARD No. 24.

visor 123 by 7-place the product under 877-subtractthe remainder is 16-bring down the next figure 8; it makes 168.

Sixth.

How many times 123 in 168? one-set 1 in the quotient.. Multiply and subtract—the remainder is 45-bring down 9 the last figure in the dividend; it makes 459.

Seventh.

How many times 123 in 459? seek how many times 12 in 45-3 times-set 3 in the quotient.-Multiply the divisor 123 by 3-place the product under 459-subtract— the remainder is 90.

The quotient or answer is 1,003,713, which number, in words, will read thus, One million three thousand seven hundred and thirteen, and ninety, one hundred and twenty-threes.

NOTE. The three following questions may be wrought by Short Division, if you cut off the cipher in the divisor, and the right hand figure in the dividend.

Although this mode of cutting off ciphers, will sometimes expedite business; yet it is not advisable except when the calculator understands his problem, and is master of the subject then under consideration.

LESSON 13.

In 78,433 shillings, how many pounds? 20)78433

Answer,

Here cut off the 0 in the di3921 £. 13s. visor 20, and the right hand 3 in the dividend, then divide 7843 by 2. How many times 2 in 7? 3 times and 1 over; set 3 under the 7. One over carry to the left side of 8 makes 182 in 18-9 times; set 9 under 8--2 in 4---twice; set 2 under the 4. Then 2 in 3-once and 1 over-set 1 under the 3 and carry the 1 over to the left side of the 3 cut off, which will make 13 shillings for a remainder.

This gives a quotient number, Three thousand nine hun

KEY TO CARD No. 24.

dred and twenty-one pounds thirteen shillings, for an answer, or thus, 392113.

LESSON 14.

If 40 rods make 1 furlong, I wish to know how many furlongs are in 98643 rods?

How many times 4 in 9? twice, and 1 over; set down 2 under 9 and carry 1 to the left side of 8 makes 18-How many times 4 in 18? 4 times and 2 over; set 4 under 8 and carry 2 to 6 makes 26-How many times 4 in 26? 6 times and 2 over; set 6 under 6 and carry 2 to 4 makes 24-How many times 4 in 24? 6 times; set 6 under 4. The quotient is 2466, and the figure cut off the dividend, is of a furlong, or 3 rods remaining.

LESSON 15.

Sixty seconds make 1 minute. How many minutes in 39645 seconds?

How many times 6 in 39?-6 times and 3 over-6 in 36? 6 times---6 in 4? 0, but 4 remains to be placed on the left side of the 5 cut off---this makes 45 seconds for a remainder, or of a minute.

The Quotient is 660 and 45 the Remainder.

NOTE. When the Remainder is less than the Divisor, it is a sign that the work is correct; but if the Remainder happen greater than the Divisor, the work is wrong. Let us prove a few Lessons in Long Division, by Multiplication.

RULE.

Multiply the Divisor and Quotient together, the Product will be like unto the Dividend.

If there be a Remainder, add it to the Product.

KEY TO CARD No. 24.

For examples take the six following Lessons on Card No. 23, and right hand page of Card 24.

In this Lesson 7th, take the Divisor for a Multiplicand,. because the Quotient 190 has a cipher at the right; which cipher may be omitted in Multiplication, and only annexed in the place of units.

The ciphers are to be omitted in Multiplication, and ad

ded in the place of units and tens.

END OF PART SIXTH.

INTRODUCTION TO ARITHMETIC,

PART VII.

CONTAINING,

COMPOUND DIVISION, ARITHMETICAL CHARACTERS,

AND

DECIMALS.

COMPOUND DIVISION.

KEY TO CARD No. 25.

LESSON 1.

Divide £784 16s. 4d. between 4 men.

£. S. d.

4)784 16 4

196 4 1

Pounds.

Four in 7-1 and 3 over-4 in 38-9 and

2 over-4 in 24-6 times.

Shillings.

Four in 16--4 times.

Pence.

Four in 4-1. ·

Quotient in words, One hundred and ninety-six pounds four shillings and one penny. This is each man's part.

LESSON 2.

Divide £1454 19s. between 8 men.

8)1454 19 0 0 How many times 8 in 14? 1 and 6 181 17 4 2 over-How many times 8 in 65? 8 and 1 over-How many times 8 in 14? 1 and 6 over to carry to the shillings.