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When the sign minus is placed between two numbers it shows that the one after it is to be subtracted from the ono before it.

Thus, 9-5 is read 9 minus 5, and means that 5 is to be subtracted from 9.

61. PRINCIPLE.—1. Only like numbers can be subtracted.

2. The sum of the subtrahend and remainder must be equal to the minuend.

TABLE.

1–1–0 2–2–0 3–3–0 4–430 5- 5-= 0 2-1--1 3-2=1

3–2=1 4-3= 1 4= 1 6- 5= 1 3—1= 2 4–2= 2 5—3= 2 644 2 7- 5=2 4-1= 3 5-2= 3 6—3— 3 744= 3 8- 5= 3 5—1= 4 6-2= 4 7-3= 4 8-48 4 9. 5= 4 6-1= 5 7-2= 5 8–3. 5. 9-4= 5 10— 5= 5 7—1= 6 8–2= 6 943 6 10—4= 6 11- 5-= 6 8—1=7 9-2= 710—3=- 7 11–4= 7 12- 5= 7 9-1= 810—2- 8 11-3= 8 12-4- 8 13- 5= 8 10—1= 9 11–2= 9 12—3= 9 1344= 9 14- 5= 9 11-1=10/12-2=1013-3=1014-4=10 15— 5=10

6—6= 0 747 08-8 09-9= 0110—10= 0 7–6=1 847 1 9 8. 1 10 9- 1 11-10= 1 8–6= 2 947 2 1048 2 11 9 2 12—10— 2 9—6= 3 10—7 3 11 -8 3 12–9= 3 13–105 3 10—6= 411–7 4112-8 4 13-9 4 14-10-= 4 11-6= 512—7 5 13-8- 5 14—9 5 15-10=: 5 12-6 6 13–7: 6 14-8= 6 15-9 6 16—10= 6 13—6=714--7= 715-8= 7 16—95 7 17-10= 7 14–6= 8 15-7= 816—8= 8117—9= 8 18-10= 8 15—6= 9 16—7= 9.17—8- 918-9= 9 19-10= 9 16—6=-10 17-7-10 18-8=10 19-9=10 2010=10

CASE I.

62. When no figure of the subtrahend has a greater value than the corresponding figure of the minuend.

1. A merchant had 15 barrels of flour, and sold 4 of them. How many had he left?

ANALYSIS.—Since he had 15 barrels of flour and sold 4 of them, he had left the difference between 15 barrels and 4 barrels, which is 11 barrels.

2. Alice bought 18 cakes, and ate 6 of them. How many had she left?

3. James saw 17 birds on a tree, but 7 soon flew away. How many remained ?

4. If a man earns $19 a week, and spends $9, how much will he save each week ?

5. Lewis owed his brother $7, and paid him $3. How much did he still owe him?

6. Eliza had 16 plums, but gave 5 to her father. How many

had she left? 7. James had $12, and lost $2. How many had he left?

8. If John is 19 years old, and Maggie 13, how much younger than John is Maggie?

9. In the same shop 6 boys and 17 men work. How many more men than boys are there in the shop?

10. There were 18 girls and 7 boys in a class. How many more girls than boys were there?

11. Laura had 14 cents, and lost 3 cents. How many had she then?

12. Henry solved 19 examples, and George solved 8. How many more did Henry solve than George?

13. William wrote 16 lines in his copy-book, and Peter wrote 5 lines less. How many did Peter write?

14. One piece of cloth contained 20 yards and another 10 yards. How many yards more were there in the larger piece?

15. A boy had 24 chickens, and 10 of them died. How many bad he left?

16. Julia gave me 11 cents. If she had 16 cents at first, how many had she left?

17. A girl bought 18 eggs, and, on her way home, fell and broke 5 of them. How many had she left? 18. Subtract by 2's from 22 to 0; thus: 22, 20, 18, 16,

etc. 19. Subtract by 3's from 35 to 2. From 45 to 0. 20. Subtract by 4’s from 48 to 0. From 45 to 1. 21. Count back by 5's from 35 to 0. From 59 to 4.

14, 12,

WRITTEN EXERCISES.

63. 1. From 547 subtract 235.

PROCESS.

ANALYSIS.For convenience we write the less Minuend 547 number under the greater, units under units, tens Subtrahend 235

under tens, etc., and subtract each order of units

separately from the same order of the minuend. Remainder 312 Thus, 7 units — 5 units = 2 units, which we

write under the units. 4 tens — 3 tens=1 ten, which we write under the tens.

5 hundreds --- 2 hundreds=3 hundreds, which we write under the hundreds. Hence the remainder is 312.

PROOF.-312, the remainder, plus 235, the subtrahend, equals 547, the minuend. Hence the result is correct.

Copy, subtract, and prove: (2.) (3.) (4.) 713

458 986 302 134 732

[blocks in formation]

(8.)
$48.25
23.13

(9.)
$64.29
30.29

(10.) $45.78 34.65

(11.) $38.94 27.83

(12.) $41.89 20.45

13. A drover, having 1583 sheep, sold 1441 of them. How many had he left?

14. A speculator bought some land for $5849.75, and sold it for $6959.95. How much did he gain?

15. A cotton factory made 9875 yards of cloth in one week, and sold, during the same time, 7652 yards. How much more was made than sold?

16. A money-lender received for interest, during 1875, $1685.49, and during 1876, $2796.59. In which year did he receive the greater sum, and how much?

17. A man bought 7467 bricks, and carted away 3136. How many remained to be moved?

18. A has 736 sheep, and B has 213 less than A. How many sheep has B?

19. A man gave his note for $6792, without interest. In two years he had paid $3401. How much did he still owe on the note?

20. A man bought a house for $1765, and afterward sold it, thereby losing $504. For how much did he sell it?

21. A man bought a span of horses for $364, and a yoke of oxen for $120. How much more did he give for the horses than for the oxen?

22. A merchant having 6755 yards of cloth, sold 2532 yards. How many yards had he remaining? 23. A father having 3652 acres of land, gave his son 1230

How many acres had he left? 24. A vintner had 38756 gallons of wine, and sold during the year, 34243 gallons. How much remained unsold?

25. The circulation of a newspaper in 1875 was 38293 copies, and in 1876, 37180. What was the decrease?

acres.

CASE II.

64. When any figure of the subtrahend has a greater value than the corresponding figure of the minuend.

1. A gentleman bought a coat at $40, and a vest at $9; he

gave the merchant a hundred-dollar bill. How much change ought he to receive?

ANALYSIS.—Since he paid $40 for a coat and $9 for a vest, for both he paid the sum of $40 and $9, or $49. And since he gave the merchant $100, he should receive the difference between $100 and $49. $100-$10=960; $60—$9=$51. Therefore he should receive $51.

2. A boy saw 15 birds on a tree, and 9 of them flew away. How many remained?

3. John is 16 years old, and James is 8. How much older than James is John?

4. A jeweler bought a watch for $75, and sold it for $100. How much did he gain by the operation?

5. A grocer bought a quantity of sugar for $36, and retailed the same for $50. How much did he gain by the sale?

6. A boy had 34 marbles, and gave away 9 of them. How many

had he left? 7. A lady bought a chair for $3, and a table for $5; she gave a twenty-dollar bill to the cabinet-maker. How much change ought she to receive?

8. A man set out to walk 50 miles; he walked 20 miles the first day, and 19 the second day. How many miles were left for him to walk?

9. A man bought a cow for $35, and sold her for $43, after keeping her 4 weeks at an expense of $2 per week. How much lid he gain?

10. A man who earned $60 a month, paid $25 a month for his board, and $15 a month for other expenses.

How much did he save per month?

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