Three in 19-6 times and 1 over-carry the 1 to 6 makes 16; three in 16-5 times and 1 over-carry the 1 to 2 makes 12-three in 12-4 times-three in 9-3 times three in 6—2 times three in 3-once ; down with 1.

Four times 9 are 36; set down 6 and carry 3-4 times 8 are 32, and 3 I carried are 35; set down 5 and carry 3-4 times 7 are 28, and 3 I carried are 31; set down 31.

Answer in words, Three thousand one hundred and fifty-six.

Proof by Division.

4)3156

789 Proof of lesson 3. Fours in 31, 7 times and 3 over-carry 3 and prefix it to 5 makes 35-4 in 35, 8 times and 3 overcarry 3 and prefix it to 6 makes 36-4 in 36, 9 times.

LESSON 4.

In 987 five dollar bills, how many dollars?
5 dollars in each bill.

4935 Dollars-sum total, or product.

Five times 7 are 35; set down 5 and carry 3- -5 times 8 are 40, and 3 that I carried are 43; 3 and carry 4-5 times 9 are 45, and 4 that I carried are 49-set down 49.

Answer in words, Four thousand nine hundred and thirty-five.

Proof by Division of lesson 4th.
5)4935

987 Quotient or Proof, Five in 49-9 times and 4 over 5 in 43-6 times and 3 over-5 in 35-7 times.

KEY TO CARD No. 11.

LESSON 5.

In 246 fathom of 6 feet each, how many feet?

6

1476

Place the figures as on the card.

Begin under the 6 and say 6 time 6 are 36-6 and carry 3-6 times 4 are 24 and 3 1 carried are 27-7 and carry 2-6 times 2 are 12 and 2 I carried are 14. Answer in words, One thousand four hundred and seventy-six.

Proof of lesson fifth by Division.

6)1476
246

Six in 14-twice and 2 over; set down 2 and carry the 2 over to 7-6 in 27-4 times and 3 over6 in 36-6 times.

LESSON 6.

In 400 weeks how many days?

Ans. 2800 days.

Place 7, the number of days in a week, under the 4, and say, 7 times 4 are 28; set down 28, then bring down the two ciphers to the right hand of 28.

Answer in words, Two thousand eight hundred. Proof of lesson six by Division.

7)2800

400

Say 7 in 28-4 times-set down 4-7 in 0-0-in 0-0-or

Begin and say, 7 in 28-4 times-set down 4 and place the two ciphers on the right hand side of the 4. LESSON 7.

In 9460 dollars of 8 shillings each, how many shillings?

9460
8

Ans. 75680 shillings.

Place the 8 under the 6, take no notice of the cipher till you have multiplied the figures: say 8 times 6 are 48; set down 8 and carry 4-8 times 4 are 32, and 4 that I carried are 36-6 and carry 3-8 times 9 are 72, and 3 I carried are 75: now bring down the cipher on the right hand side of the 8.

Answer in words, Seventy-five thousand six hundred and eighty.

Proof of lesson seventh by Division.

8)75680

9460

Eight in 75-9 times and 3 over-carry the 3 to 6 makes 36-8 in 36-4 times and 4 over-4 on the left side of 8 will make 48-8 in 48-6 times-8 in ◊ no times-set 0 on the right of 6.

LESSON 8.

In 20000 kegs, each containing 9 galls. how many gallons?

20000

9

Ans. 180000 gallons.

Place 9 for a multiplier under the 2, and pay no regard to the ciphers at present: but say 9 times 2 are 18-set down 18 and place as many ciphers on the right of 18 as there are in the multiplicand.

Answer in words, One hundred and eighty thousand.

E

Proof of lesson Eighth,
9)180000
20000

Say 9 in 18-2 times-set down 2 and bring down the ciphers on the right side of 2.

When the multiplier consists of any number of 9s, you may annex as many ciphers to the multiplicand; then from that number subtract the multiplicand; the remainder will be equal to a true product as if you had multiplied.

1

4 10 9 3 4 7 4 4-2 remain.

1 1 2 2 3 3 4 4 4--6 remain,

* Recollect, cutting off a figure divides by 10; and annexing a cipher multiplies by 10. Prove Division by Multiplication ;-bring in the remainder, if any, as in lessons 13 and 14.