28. When two numbers are separated by the minus sign (-), the second is to be subtracted from the first.

(45) What number must be added to 87 to make 565?
(46) What number taken from 3867 will leave 795 ?
(47) How many more than 398 is 56320 ?

(48) How many less than 5000 is 277 ?

(49) The sum of two numbers is 48000136, and one of the numbers is 3871568; find the other.

(50) From 31415687591462387589 take 3715426795186 732894.

(1) Harry is 15 years old, and his brother 9 years. How old was Harry when his brother was born?

(2) A farmer who has seventy-eight sheep, has one hundred and fifty-four sheep and oxen together. How many oxen has he?

(3) A girl had to pay 9 pence for tea, 6 pence for bread, 7 pence for butter, out of 30 pence, how many more pence did she pay than she took home ?

(4) How long was it from the death of Charles II., in 1685, to the death of William IV., 1837?

(5) Find the value of 8736-215+416-3872.

(6) In a school of 154 scholars, 128 can write; how many

cannot write?

(7) A man rode 70 miles from London in one week, and went back 35 miles the next week; 21 miles further away the next, and 52 miles back the next. How far from London was he at the end of the four weeks?

(8) A post standing in the earth is 186 inches in length, 91 inches are above ground. How much longer is the portion above ground than that in the earth?

(9) How old is a person in 1868 who was born in 1839 ? (10) What number added to five hundred and six thousand and seventy nine, will amount to eighty-six less than a million ?

(11) In one parcel of nuts there are 86, and in another 54; but 27 of the first lot are bad, and 36 of the second. How many good ones are there in all ?

(12) How much is paid for three houses, if for the first £1826 is paid, for the second £89 less than for the first, and for the third £256 less than for the second?

(13) A man who had lost £386, previously possessed £5000; how much had he after his loss?

(14) Find the difference between eight hundred and eight, and eight thousand and eighty.

(15) A gentleman whose property is worth £78,509, has property worth £28,876 in London, What is the worth of his property out of London?

(16) In the first of two chests of tea there are 740 lbs., and in the second chest 671 lbs. If 251 lbs. be sold from the first chest, and 359 lbs. from the second, and the remainder be put into one chest, how much will there be?

(17) A house, garden, and stables cost together £1391; the house and garden cost together £1067, and the garden and stable £516. How much more did the house cost than the garden? How much did the stables cost?

(18) From CCXCV take CLXXIX, and find how much greater the remainder is than XLVI.

(19) How old is a person in 1868, who was 30 in 1839 ? (20) What is meant by the difference of two numbers? The larger of two numbers is eighteen thousand and five, and their difference is two thousand four hundred and seventy seven. How much must be added to the smaller to make seventeen thousand?

(21) Find the difference between 23701 and 10732. What difference will be made in the remainder if 200 be added to both these numbers? What use is made of this fact in working subtraction?

Additional Exercises.

The following exercises will furnish 150,000 subtraction sums and verifications of their answers.

(1) Take the quantities in each of the addition sums. Arrange them in order, so that the least is first, and greatest last. Place 0 under the first, the first under the second. the second under the third, and so on. Draw lines and subtract. Add together the results, and the sum should be the largest number.

(2) Take any series of numbers from the table on page 10, and proceed with them as directed in the last exercise.

Simple Multiplication.

29. Multiplication is a process by which we find the amount when a number is added to itself a certain number of times.

30. The number to be repeatedly added is called the Multiplicand. The number showing how many times it is to be added is termed the Multiplier. The result of the multiplication is called the Product.

31. It is necessary at this point to distinguish between abstract and concrete numbers.

Abstract numbers are numbers mentioned without reference to any particular kind of unit; e.g. five, six, seven, etc.

Concrete numbers are numbers mentioned in connection with the names of the units; e.g. five boys, six apples, seven pence.

32. From the above definition of multiplication, we see that one of the numbers must be abstract; because it shows how many times the other is repeated. To multiply 8 stones by 5, is to take a group of 8 stones 5 times over; thus:

8 stones.

8 stones.

8 stones.

8 stones.

8 stones.

40 stones.

The answer, 40 stones, is a concrete number.

33. It would be absurd to ask any one to multiply £8 by £5, for the term multiply requires that one of the numbers shall show how many times the other is to be repeated.

34. Case I.-When the multiplier consists of only one figure.

RULE.-Multiply each figure in the multiplicand by it, and set down and carry as in addition.

EXAMPLE:

439861 multiplicand.
7 multiplier.

3079027 product.