KEY TO CARD No. 6.

Begin at the right hand 2 and say, 2 from 3 and 1 remains-3 from 10 and 7 remain-carry 1-1 to 2 makes 33 from 9-6 remain-6 from 11 and 5 remain-carry 1 to 6 is 7-7 from 12 and 5 remain-carry 1 to 2 makes 3-3 from 8 and 5 remain, Answer in figures 555671.

LESSON 7.

Received from Government, $781210

Expended in purchases,

521621

Remains on hand, 259589

One from 0, I cannot ; but 1 from 10 and 9 remain; carry 1 to 2 makes 3-3 from 11 and 8 remain-carry 1 to 6 is 77 from 12 and 5 remain-carry 1 to 1 makes two-2 from 11 and 9 remain-carry 1 to 2 is 3-3 from 8 and 5 remain -5 from 7 and 2 remain.

Answer, in figures 259589.

In words, Two hundred

and fifty-nine thousand five hundred and eighty-nine.

PROOF BY ADDITION.

Add the two lower lines to make a total equal to the upper line; thus,

Second line, 521621

Third line, 259589

Like the first line, 781210 Proof.

LESSON 8.

If 641315 Soldiers enter Russia,

and 426436 are lost, how many return?

Ans. 214879 return.

Six from 5 I cannot; borrow 10, and say, 6 from 15, and 9 remain-carry 1 to 3 makes 4-4 from 11 and 7 remain→

KEY TO CARD No. 6.

carry 1 to 4 makes 5-5 from 13 and 8 remain-carry 1 to 6 makes 7-7 from 11 and 4 remain-carry 1 to 2 makes 3-3 from 4 and 1 remains-4 from 6 and 2 remain.

Answer in figures, 214879. In words, Two hundred and fourteen thousand eight hundred and seventy-nine.

LESSON 9.

What is the difference between 456781, and 326879 ?Place the figures as on the card.

456781 326879

129902

Nine from 1, I cannot; borrow 10 and say, 9 from 11 and 2 remain-carry 1 to 7 makes 8-8 from 8, 0 remains-8 from 7 I cannot; borrow 10 and say, 8 from 17 and 9 remain-carry 1 to 6 makes 7-7 from 6, I cannot; borrow 10 and say 7 from 16 and 9 remain-carry 1 to 2 makes 3-3 from 5 and 2 remain-3 from 4 and 1 remains.

Difference in figures 129902. In words, One hundred and twenty-nine thousand nine hundred and two.

PROOF BY ADDITION.

Place the second line on your slate-Under that place the third line, then add,

Second line, 326879

Third line,

129902

Like unto the first line 456781 Proof.

LESSON 10.

If I have on hand 642137 Shingle nails, and use 472318,

Place

KEY TO CARD No. 6.

your figures as in Lesson 10, on the card.

642137 Nails on hand,

472318 Made use of,

169819 Remain on hand.

Eight from 7, I cannot; borrow 10 and say, 8 from 17 and 9 remain-carry 1 to 1 makes 2-2 from 3 and 1 remains-3 from 1, I cannot; borrow 10 and say, 3 from 11 and 8 remain-carry 1 to 2 makes 3-3 from 2 I cannot; borrow 10 and say, 3 from 12 and 9 remain-carry 1 to 7 makes 8-8 from 4 I cannot; borrow 10 and say, 8 from 14 and 6 remain-carry 1 to 4 is 5-5 from 6 and 1 remains. Answer in figures, 169819. In words, One hundred and sixty-nine thousand eight hundred and nineteen.

PROOF BY ADDITION.

I made use of 472318 Nails,

Remain on hand 169819

Like the first line 642137 on hand before any were used.

LESSON 11.

Bought 460210 Awl blades,

Sold 340012 how many remain?

Answer, 120198

Two from 0, I cannot; borrow 10 and say, 2 from 10 and 8 remain-carry 1 to 1 makes 2-2 from 11 and 9 remain-carry 1 to 0 makes 1-1 from 2 and 1 remains-0 from 0 and 0 remains-4 from 6 and 2 remain-3 from 4 and 1 remains. Answer in figures, 120198. In words, One hundred and twenty thousand one hundred and ninetyeight.

N. B. Dollar characters are made thus $.

Now let the learners omit their phrases in saying, "borrow 10." They may mentally consider it without speaking aloud. See Lesson 12.

From 900000

LESSON 12.

Take 426436 how many remain?

Answer, 473564

Six from 10 and 4 remain-carry 1 to 3 is 4-4 from 10 and 6 remain-carry 1 to 4 is 5-5 from 10 and 5 remaincarry 1 to 6 is 7-7 from 10 and 3 remain-carry 1 to 2 is 3-3 from 10 and 7 remain-carry 1 to 4 is 5—5 from 9 and 4 remain.

Answer in figures, 473564. In words, Four hundred and seventy-three thousand five hundred and sixty-four.

LESSON 13.

$ 54321 Received, April 17th, 1815.

18765 Paid, May 1st, 1815, how many dollars remain due?

Ans.35556 Remain due.

Five from 11 and 6 remain-carry 1 to 6 makes 7-7 from 12 and 5 remain-carry 1 to 7 is 8-8 from 13 and 5 remain-carry 1 to 8 is 9-9 from 14 and 5 remain-carry 1 to 1 is 2-2 from 5 and 3 remain.

Answer in figures, 35556. In words, Thirty-five thousand five hundred and fifty-six.

KEY TO CARD No. 6,

LESSON 14.

Borrowed 628134 Dollars.

Paid

419243 What remains due?

Answer, 208891 Dollars remain due.

Three from 4 and 1 remains-4 from 13 and 9 remaincarry 1 to 2 is 3-3 from 11 and 8 remain-carry 1 to 9 makes 10-10 from 18 and 8 remain-carry 1 to 1 makes 2-2 from 2-0 remains-4 from 6-2 remain.

Answer in figures, 208891. In words, Two hundred and eight thousand eight hundred and ninety-one.

LESSON 15,

Lent 644310 dollars. Received back 421536 dollars. I wish to know how many dollars are yet due? The sum lent, 644310 dol.

Six from 10 and 4 remain--carry 1 to 3 is 4-4 from 11 and 7 remain-carry 1 to 5 is 6-6 from 13 and 7 remain-carry 1 to 1 is 2-2 from 4 and 2 remain-2 from 4 and 2 remain-4 from 6 and 2 remain. Answer, 222774.

The Numeration Table must be attended to in the next place, and copied over and over repeatedly on the slates. The pupils must also be instructed in reading figures with precision and expertness. SEE CARD NO. 7.

NOTE. It is necessary to show the learners the analogy between Multiplication and Addition, as, 2 and 2 are 4, and 2 are 6, and 2 are 8, or

times 2 are 8, &c. And in Division, teach them that Subtraction will answer problems in that Rule.