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INTRODUCTION TO ARITHMETIC,

PART V.

CONTAINING,

COMMON MULTIPLICATION.

MULTIPLICATION.

KEY TO CARD No. 20. Inform the learners that the number to be multiplied is called the Multiplicand.

The number we multiply by, Multiplier, and the result or sum total, the Product.

Let them also know, that the Multiplicand and Multiplier are called Factors: that is, the upper and lower factor; and it makes no difference in the Product which number stands uppermost; only place the smallest Factor under for the case of multiplying.

LESSON 1. Multiplicand, 4 6 4 3 2 upper Factor, Multiplier, 5 2 4 lower Factor,

Here give notice how 1 8 5 7 2 8 Interme- || the figures must be ar

9 2 8 64 2 3 2 1 60

diate Pro- | ranged in the several

ducts. intermediate Products. 2 4,3 3 0,3 6 8 Product.

Always place the first figure of a product exactly under its Multiplier. Begin with the 4 the first figure on the right of the Multiplier.

Four times 2 are 8; set 8 exactly under the 4_4 times 3 are 12; set 2 on the left side of 8 and carry 1-4 times

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KEY TO CARD No. 20.

4 are 16 and 1 I carried is 17 ; set down 7 and carry 1 4 times 6 are 24 and 1 I carried makes 25; set down 5 and carry 2—4 times 4 are 16 and 2 are 18; set down 18.

Second. Twice 2 are 4-set 4 under the 2–Twice 3 are 6; set 6 under the 7-Twice 4 are 8; set 8 under the 5-Twice 6 are 12; set 2 under the 8 above and carry 1–Twice 4 are 8 and one I carried makes 9; set 9 under the 1.

Third. Five times 2 are 10; set 0 under the 6-5 times 3 are 15 and i I had to carry make 16-set 6 under the 8 and carry 1–5 times 4 are 20 and one I carried makes 21; set 1 under the 2 and carry 2–5 times 6 are 30 and 2 I carried are 32; set 2 under the 9 and carry 3—5 times 4 are 20 and 3 I carried are 23; set 23 on the left side of the whole.

Add these 3 products as in addition of whole numbers.

Eight is 844 and 2 are 6–6 and 7 are 13; 3 and carry 1-1 to 6 makes 7 and 8 are 15 and 5 are 20_0 and carry 2–2 to 1 is 3 and 2 are 5 and 8 are 13–3 and carry 1-1 to 2 makes 3 and 9 are 12 and 1 is 13–3 and carry 1-1 to 3 makes 4-2 make 2.

Product in words, Twenty-four million three hundred and thirty thousand three hundred and sixty-eight.

Now let each one become expert in reading figures Let the Numeration Table hang in view.

LESSON 2. Multiplicand, 6 1 2 4 8

Firsi. Multiplier, 7 3 2 Twice 8 are 1646 and carry

1-twice 4 are 8 and 1 is 9 1 2 24 96 1 8 3 7 4.4

twice 2 are 4-twice 1 is 24 2 8 7 3 6 twice 6 are 12.

Second. Product 44,8 3 3,5 3 6

Three times 8 are 24--4 and KEY TO CARD No. 20. carry

2-3 times 4 are 12 and 2 are 14-4 and carry 1-3 times 2 are 6 and 1 is 7-3 times 1 are 3-3 times 6 are 18.

Third. Seven times 8 are 56–6 and carry 5–7 times 4 are 28 and 5 are 33—3 and carry 3–7 times 2 are 14 and 3 are 17—7 and carry 1–7 times 1 is 7 and 1 is 8-7 times 6 are 42.

Add these intermediate Products. Total product in words, Forty-four million eight hundred and thirty-three thousand five hundred and thirty-six.

LESSON 3. Multiplicand, 1 6 7 3 9

First. Multiplier, 2 87 Seven times 9 are 6343 and

carry 6-7 times 3 are 21 and 6 117173 13 3 9 1 2

are 27—7 and carry 2–7 times 3 34 7 8 7 are 49 and 2 are 51-l and

carry 5—7 times 6 are 42 and Product, 4,8 0 4,0 9 3

5 are 47–7 and carry 4-7 times 1 is 7 and 4 are 11.

Second. Eight times 9 are 72-2 and carry 7-8 times 3 are 24 and 7 are 31-1 and carry 3-8 times 7 are 56 and 3 are 59—9 and carry 5—8 times 6 are 48 and 5 are 533 and carry 5—8 times 1 is 8 and 5 are 13.

Third. Twice 9 are 18—8 and carry 1-Twice 3 are 6 and 1 is 7—7 and carry nothing-Twice 7 are 14–4 and carry 1Twice 6 are 12 and 1 is 13–3 and carry 1-Twice 1 is 2 and i is 3.

Add the intermediate Products. Total Product in words, Four million eight hundred and four thousand and ninety-three.

KEY TO CARD No. 20.

LESSON 4. 4 5 6 7

First. 6 5 24 Four times 7 are 28–8 and carry 2-4

times 6 are 24 and 2 are 26-6 and carry 18 2 6 8

2-4 times 5 are 20 and 2 are 22-2 and 91 34 2 2835 carry 2—4 times 4 are 16 and 2 are 18. 27402

Second.

Twice 7 are 14–4 and carry 1-twice 6 29,7 9 5,1 0 8

are 12 and 1 is 13——3 and carry 1-twice 5 are 10 and 1 is 11-1 and carry 1-twice 4 are 8 and 1 is 9.

Third Five times 7 are 35—5 and carry 3—5 times 6 are 30 and 3 are 33—3 and carry 3—5 times 5 are 25 and 3 are 28– 8 and carry 2–5 times 4 are 20 and 2 are 22...

Fourth. Six times 7 are 42—2 and carry 4-6 times 6 are 36 and 4 are 40~0 and carry 4-6 times 5 are 30 and 4 are 34— 4 and carry 3—6 times 4 are 24 and 3 are 27.

Add the intermediate Products. Total Product in words, Twenty-nine million seven hundred and ninety-five thousand one hundred and eight.

LESSON 5. See Card No. 21. Multiplicand, 4 8 7 6 || First figure of the Multiplier, Multiplier, 6 5 4 3

Three times 6 are 1848 1 4 6 2 8

and carry 1-3 times 7 are 1 9 5 0 4

21 and 1 is 22-2 and carry 2 4 3 8 0

2-3 times 8 are 24 and 2 are 2 9 2 5 6

26–6 and carry 2—3 times

4 are 12 and 2 are 14, Product, 3 1,9 0 3,6 6 8

KEY TO CARD No. 21.

Second. Four times 6 are 24–4 and carry 2—4 times 7 are 28 and 2 are 30—0 and carry 3—4 times 8 are 32 and 3 are 35–5 and carry 3-4 times 4 are 16 and 3 are 19.

Third. Five times 6 are 30—0 and carry 3—5 times 7 are 35 and 3 are 38–8 and carry 3—5 times 8 are 40 and 3 are 43—3 and carry 4-5 times 4 are 20 and 4 are 24.

Fourth. Six times 6 are 36—6 and carry 3–6 times 7 are 42 and 3 are 45—5 and carry 4-6 times 8 are 48 and 4 are 522 and carry 5–6 times 4 are 24 and 5 are 29.

Add the intermediate Products. Total product in words, Thirty-one million nine hundred and three thousand six hundred and sixty-eight.

LESSON 6. Multiplicand, 5 6 8

First. Multiplier, 8 7 6 5

Five times 8 are 40-0 and

carry 4-5 times 7 are 35 and 2 8 3 90 3 0 6 8

4 are 39—9 and carry 3---5 3 9 7 4 6

times 6 are 30 and 3 are 33--4 5 4 2 4

3 and carry 3—5 times 5 are

25 and 3 are 28. 4 9,7 67, 67 0

Second. Six times 8 are 48---8 and carry 4-6 times 7 are 42 and 4 are 46---6 and carry 4---6 times 6 are 36 and 4 are 40--O and carry 4-6 times 5 are 30 and 4 are 34.

Third. Seven times 8 are 56---6 and carry 5---7 times 7 are 49 and 5 are 54---4 and carry 5---7 times 6 are 42 and 5 are 47---7 and carry 4---7 times 5 are 35 and 4 are 39.

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