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Can 7 hundredths be taken from 5 hundredths ? What must be done in this case ?

Take 5 dimes, 6 cents, from 8 dimes, 9 cents.
In which order is the number of the subtrahend the lar.

gest ?

Can 9 cents be taken from 6 cents ? What must you do in order to subtract ?

Subtract 7 hundredths, 8 thousandths of a dollar, from 8 hundredths, 7 thousandths.

Can 8 thousandths be subtracted from 7 thousandths ? What must be done in this case ?

RULE FOR DECIMAL SUBTRACTION.

Proceed by the rule for.common Subtraction, and in the answer place a separatrix between the orders of units and tenths.

EXAMPLE. Subtract 2,56 from 24,329. Placing the subtrahend under the minuend, so that units of the same order stand in the same column. They stand thus :

24,329
2,56

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21,769 Let the pupil learn to subtract in this manner :

Nothing from 9 thousandths, and 9 remains to be set down. 6 hundredths cannot be taken from 2 hundredths; we therefore add 10 to the minuend, which makes 12. 6 taken from 12 leaves 6. As 10 was added to the minu. end, an equal quantity must be added to the subtrahend. 1 of the order of tenths is the same as 10 hundredths, we therefore add 1 to the 5 tenths, making it 6 tenths. 6 tenths cannot be taken from 3 tenths, we therefore add 10 to the minuend, which makes 13. 6 taken from 13,

What is the rule for decimal subtraction ? Employ the method above in adding other decimals.

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leaves 7. As 10 was added to the minuend, an equal amount must be added to the subtrahend. 1 of the order of units is the same as 10 tenths, we therefore add 1 to the 2 units, making it 3 units.

Proceed thus through all the orders, remembering to place a separatrix between the orders of units and tenths.

Let the following sums be arranged and subtracted in the same way: Subtract 25,25 from 62,904 790,4

996,409 2,4693

354,268 5,34689

40,62 6,6543

23,3291 432,54916

542,65329 53,00300

646,01201 832,2

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66

9988,659 51,895

64,59432 8,4156

400,21 321,01013

4333,0063 659,09543

679,2941

EXERCISES FOR OLDER Pupils.

1. Subtract two tens, four units, three tenths, five hundredths, and four thousandths; from four tens, two tenths, five hundredths, and four thousandths.

2. Subtract two tens, three units, six tenths, nine hundredths, and three thousandths; from four tens, four units, three thousandths, and five tenths of thousandths.

3. Subtract two units ; four thousand three hundred and seventy-four tenths of thousandths ; from

Twenty-three units; seven thousand five hundred tenths of thous sandths.

4. Subtract ninety-eight units, two thousand nine hundred and eighty. seven tenths of thousandths; from

Seven hundred and seventy-seven units, four thousand three hun dred and twenty-six tenths of thousandths.

5. Subtract seven units, six thousand five hundred and forty-three tenths of thousandths; from Three hundred and sixty-nine units, forty-two hundredths.

6. Subtract seventy-seven units, twenty-four tenths of thousandths ; from

Two hundred and twenty-five units, seven thousand six hundred and fifty-four tenths of thousandths.

7. Subtract twelve units, one millionth ; from Thirty units, ten thousandths.

8. Subtract one hundred units, eleven tenths of thousandths; from Three hundred units, one tenth.

9. Subtract five hundred and fifty millionths ; from Ninety-five hundredths.

10. Subtract ninety-eight units, fifty-four thousand tenths of thou. sandths ;'from

Eight hundred and eighty-seven units, thirty.four thousand tenths of thousandths.

11. Subtract twenty units, seven thousand three hundred and twenty. one tenths of thousandths ; from

Thirty-nine units, eighty-four thousand, three hundred and twen. ty-one hundredths of thousandths.

12. Subtract forty units, twenty-five thousands, nine hundred and eighty-three hundredths of thousandths ; from

Eight hundred and forty-one units, six hundred and forty-three tenths of thousandths.

13. Subtract eight units, forty-one tenths of thousandths; from Seventy-seven units, forty-three thousand and eleven millionths.

14. Subtract eight units, one thousand and fourteen millionths; from Eight hundred units, twenty-one tenths of thousandths.

15. Subtract four hundred units, sixty hundredths; from One thousand units, three tenths.

16. Subtract fifteen hundred millionths ; from

Eighteen hundredths of thousandths.

17. Subtract eighty units, eighty thousandths; from Eight hundred units, and eighty millionths.

18. Subtract two units, seventy-six thousand and eight millionths ; from

Nine hundred and eighty-seven units, forty-four hundredths of thousandths.

COMPOUND SUBTRACTION. A man has 5 yds. 3 quarters of cloth, and cuts off 2 yds. 1 qr. how much is left ?

1 A man has 6 lbs. 3 oz. of beef, and sells 4 lbs. 2 oz. how much is left ?

If 4 bushels, 3 pecks, are taken from 8 bushels, 5 pecks, how many remain ?

A man has 12 bushels, 6 pecks of grain, and sells 7 bushels 5 pecks, how many will remain ?

If 4 yards, 3 quarters, 2 nails, be taken from 6 yds. 4 qrs. 3 nails, how many will remain ?

If 4£ 38. „ 4d. be subtracted from £6 8s. 5d. how many will remain ?

If the same quantity be added to the minuend and sub. trahend, is the remainder altered ?

Can you add a certain quantity to the minuend in one order, and the same quantity to the subtrahend in another order? Give an example.

If you wish to subtract 1 yd. 3 quarters, from 5 yds. 2 qrs. can you subtract the 3 qrs. from the 2 qrs. ?

What can you do to get the right answer?

If 4 shillings, 4 pence, be taken from 6 shillings 3 pence, how many will remain ?

In which order is the subtrahend larger than the minu. end? Can 4 pence be taken from 3 pence? What must you do in order to subtract ?

From 10 lbs. 8 oz. subtract 9 lbs. 9 oz.

In which order is the subtrahend larger than the minu. end ? What must be done in this case ?

From 7 feet 4 inches, subtract 5 feet 6 inches.

In which order is the subtrahend larger than the minu. end? What must be done in this case ?

RULE FOR COMPOUND SUBTRACTION. Write the subtrahend under the minuend, placing units of the same order under each other. Subtract each order of the subtrahend, from the same order of the minuend, and set the remainder under. If in any order the subtrahend is larger than the minuend, add as many units to the minuend as make one of the next higher order; then add one unit to the next higher order of the subtrahend.

EXAMPLE.
Subtract 29€ 198. 8d. from 36£ 15s. 7d.
Placing them according to rule they stand thus :

£.

d. 36 15 on 29 19 8

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11

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6 15 Subtract thus: 8 shillings cannot be taken from 7; therefore add as many units of this order to 7, as are required to make one unit of the next higher order; that is, 12 (as 12 pence make one shilling). 12 added to 7 are 19. Subtract 8 from 19, and 11 remain to be set down.

As 12 pence have been added to the minuend, an equal quantity must be added to the subtrahend; therefore car. ry 1 shilling to the 19, which makes 20. This cannot be subtracted from 15; therefore add to the 15 as many of this order, as are required to make one unit of the next higher order; that is 20. This being added to 15 makes 35. Subtract 20 from 35, and 15 remain to be set down; as 20 shillings have been added to the minuend, I pound must be carried to the subtrahend of the next higher or.

What is the rule for compound subtraction ? Perform the operation by the method given above.

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