8. This short line, - is called minus, which means less. I write 4-2-2, which means that 4 is lessened by 2, and leaves 2. Now then, what is 5-2, or 6-3, or 8-4, &c., &c. ?

GENERAL EXERCISES.

added

4586

3394

1192

RULE. Place the less number under the greater, so that units may stand under units, tens under tens, hundreds under hundreds, &c., as in the example :Begin at the units, 4. Take 4 from 6 and 2 remain. Put down the 2 under the 4. Take 9 from 8, which for proof. 3394 cannot be done; in this case add 10 to the upper figure 8, which will make it 18. and 9 remain. Put down the 9.

Take 9 from 18,
Whenever 10 has

4586

been added, as it was to the 8, one must be added to the next figure, 3, which makes 4. Take 4 from 5 and 1 remains. Then take the next figure 3 from 4 and 1 remains. The sum 1192 is called the Remainder, the Difference, or the Excess.

PROOF. Add the remainder and the less of the given numbers together; if the sum be equal to the greater, the work is correct.

28. What number added to 8643 will make it 9499 ?

Ans. 856.

29. Take five thousand and six from 5 millions.

Ans. 4994994.

30. I was born in 1801, what age shall I be in 1852 ?

Ans. 51.

31. In a box were 750 eggs. One man bought 499, another man 66, and I bought the rest, how many did I buy? Ans. 185. 32. How much is 8654 less than 10,000? Ans. 1346.

33. My father left to me and my brother £15648; my share was £8921; how much did my brother get? Ans. £6727.

34. America was discovered by Columbus in 1492, how long is it from that time to 1852 ? Ans. 360 years.

35. What is the difference betwixt half a dozen and a dozen dozen ? Ans. 138. 36. What is the difference betwixt a dozen and half a dozen dozen ? Ans. 60. 37. I owe A £175, B £30; I have £15 on hand; how much shall I require to pay them? Ans. £190. 38. A tradesman commenced business with £10,000; he gained £1250 the first year; but in the second year he lost two thousand four score pounds and ten; how much had he left?

39. Take 30 millions from 2 billions.

Ans. £9160.

Ans. 1.999,970.000,000

SIMPLE MULTIPLICATION.

MULTIPLICATION is a short way of adding several numbers into one sum, as 2+2+2=3 times 2, making 6.

The number to be multiplied is called the Multiplicand, the number you multiply by is called the Multiplier; and the number resulting from the operation is called the product of the two factors, that is, the Multiplicand and the Multiplier.

12 13

144 13

156 13

12

156 14 12

13

169 14 13

14

16 .. 208 14

12..

17 204 13

17 .. 221 14

..

12.. 18.. 216 13.. 18.. 234 14

12.. 19 228 13 ..

.. 19 .. 247 14

..

182 14.. 14 ..196 15 14 .. 210 16.. 14 .. 224

15 195 14.. 15 210 15..

12 20 240 13.. 20 .. 260 14 20 280 15

17times1 are 17 18times1 are 1819timesl are 19 20times1 are 201

20

.. 320

5.. 75 16

80

6.. 9016

8.. 112 15

126 15

..

180 16

SIMPLE EXERCISES.

1. How many twos have I here written? | | are 2 times 2?

2. How many threes are here? | | | times 3, 3 times 3, or 4 times 3, &c.?

3. How many fours are here? ||||

how many

; how many are 2

how many are 3 times 4, 4 times 4, 5 times 4, &c.?

4. I have 4 pence in one pocket, 4 pence in another, and in my desk, how many are 3 times 4 pence?

5. What must I pay for 6 oranges at 1d. each?

6. I bought 5 eggs at a 1d. each, how much did I pay?

pence

7. Let 3 boys each hold up all his fingers, how many tens do the 3 boys hold up? How many are 2 times 10, 3 times 10, &c. ?

8. A horse has 4 legs, how many have 2, or 3, or 4 horses, &c. ?

9. In this room are 4 windows, and in each window 10 panes of glass, how many panes in the whole ?

10. A boy has 2 legs and 2 arms, how many legs and arms have 3 boys, 4 boys, &c. ?

11. I met 3 carts, and each cart contained 10 sacks of apples, how many sacks did the 3 carts carry ?

12. There are 7 days in a week, how many in 2 weeks, 3 weeks, &c. ?

GENERAL EXERCISES.

24

3

72

RULE. Place the Multiplier under the number to be multiplied, as in the example. Multiply by the unit figure of the Multiplier. Thus, 3 times 4 are 12; put down 2 and carry 1. Then 3 times 2 are 6, and 1 to carry added make 7; put down 7. The 24 is called the Multiplicand, the 3 is called the Multiplier, and the 72 is called the Product. The Multiplicand and the Multiplier are called Factors; therefore in the example 24 and 3 are the Factors. PROOF. 1. Change the factors, and repeat their operation, or when acquainted with Division, divide the product of the sum by the multiplier, and, if the operation be correct, their quotient will exactly correspond with the multiplicand.

2. The usual way of proving Multiplication is, by casting out the nines from the multiplicand and multiplier; the remainders put on each side of a cross; multiply the figures on each side together, cast out the nines from the product, and put the overplus at the top; then cast out the nines from the product of the multiplication, and its remainder place at the bottom; if it agree with the top, the work is supposed to be right.

CASE. II.

When the multiplier is more than 12, and less than 20, multiply by the unit figure in the multiplier, adding to the product the remainder to be carried, also the last figure multiplied.

0

2341

432

4682

7023

9364

When the Multiplier consists of several figures. Put down the Multiplier under the Multiplicand, units under units, &c., as in the example :-Then multiply by the unit figure of the Multiplier, 2; 2 Proof. times 1 are 2; put down 2 and proceed; 2 times 4 are 8; put down 8; 2 times 3 are 6; put down 6; 1+0 2 times 2 are 4. Now begin with the next figure of 0 the Multiplier, 3; 3 times 1 are 3; put down 3; 3 times 4 are 12; put down 2, and carry 1 to the next figure; 3 times 3 are 9 and 1 to carry are 10; put down 0, and carry 1; 3 times 2 are 6, and 1 to carry are 7. Proceed with the next figure of the Multiplier, 4; 4 times 1 are 4; put down 4; 4 times 4 are 16; put down 6, and carry 1; 4 times 3 are 12, and 1 to carry are 13; put down 3, and carry 1; 4 times 2 are 8, and 1 to carry are 9. Then add the 3 lines of figures, which will give the product required.

1011312

Ans. 2060667. Ans. 1016412000. Ans. 7453035496.

Ans. 4267833180.

Ans. 248713373271. Ans. 1709035023584.

When the ciphers are intermixed with the figures in the Multiplier omit the ciphers, and let the first figure of each product be placed under its respective multiplier.