80. From 8311, subtract the difference between 8131 and 2654.

81. From a tract of land containing 10000 acres, the owner sold to A 4750 acres, and to B 875 acres less than to A: how many acres had he left?

EXAMPLES COMBINING ADDITION AND SUBTRACTION.

82. From 153 yards of cloth, I sold 27 yards to A, and 48 yards to B: how much remains?

83. From 43021, subtract the sum of 3798 and 30247.

84. A man worth $19000 lost at one time $3427, and at another $1946: how much had he remaining? 85. A had 640 acres of land; he bought 266 acres, and then sold 512 acres: how many acres had he then?

86. From the difference between 10001 and 667, take the sum of 2347 and 5169.

87. A bought 463 barrels of flour; B bought 95 barrels less than A: how many barrels did both buy?

88. C and D commenced business with $3000 each; C lost $281, D gained $513: how much more is D now worth than C?

89. To the sum of 7749 and 5928, add their dif ference.

90. A man gave to one of his sons $3521, to the next $94 less than to the first, to the third $147 more than to the second, to the fourth $99 less than to the third: how much did he give to all?

91. From the sum of 9327 and 4683, subtract their difference.

92. A had $3958, B $1463; A lost $1365, B gained $1165: which then had the most, and how much?

QUESTIONS FOR REVIEW.

What is Subtraction? The Minuend?

The Subtrahend? The

Difference, or Remainder? What the sign of Subtraction? What called? What does it mean? What show? Of what denomination are the Minuend and Sub rahend? The Remainder? What is meant by same denomination? Give examples.

How write numbers for subtraction? Where begin to subtract? Why? (Teacher explain.) When any figure in the subtrahend exceeds the one above it, how proceed? How does taking 1-from the next higher figure in the minuend affect that figure? What is necessary in continuing the subtraction? Give the Rule for Subtraction. What is the method of proof? What order should be observed in solving examples?

What is arithmetic? A number? A unit? How many fundamental rules are there? What are they? What is notation? What two methods of notation? What is used in each? Which is the most convenient for use? Write all the numbers from 90

to 110 by each method. What is numeration? How many figures in a period? What two values have figures? Define each. Give the rules for numeration and notation.

What is Addition? The sum, or amount? What numbers can be added? What is a problem? A solution? An operation? The conclusion? A rule?

MULTIPLICATION.

34. Multiplication is the process, of taking one number as many times as there are units in another.

35. The Multiplicand is the number taken.

36. The Multiplier is the number denoting how many times the Multiplicand is taken.

37, The Product is the result obtained.

NOTE.-The Multiplicand and Multiplier are called Factors.

38. The Sign of Multiplication is X. Placed be tween two numbers, it denotes that they are to be multiplied together.

Thus, 4×3=12, read 4 multiplied by 3 equals 12.

MENTAL EXERCISES.

EXAMPLE. At four cents apiece, what will twe lemons cost?

SOLUTION.-If one lemon costs four cents, two lemons will cost two times four cents, which are eight cents.

CONCLUSION.-Therefore, at four cents apiece two lemons will cost eight cents.

1. John bought 2 pears at 3 cents apiece: how much did they cost?

2. At 6 cents a pound, what cost 2 pounds of beef? 3. What is the cost of 3 yards of cloth at 3 dollars a yard?

4. If one barrel of apples cost 4 dollars, what cost 3 barrels?

5. How many are four times 3 books?

6. If one pound of iron costs 5 cents, what is the cost of 3 pounds?

7. If a farmer gets 5 pounds of wool from one sheep, how much does he get from 4 sheep?

8. If Henry goes to school 5 days each week, how many days will he go in 5 weeks?

9. Frank can throw a stone 6 yards, his father can throw one 5 times as far: how far can he throw?

10. Susan had 5 peaches, Mary had seven times as many as Susan: how many had Mary? ·

11. In one mile there are 8 furlongs, how many furlongs in 6 miles?

12. In one peck there are eight quarts, how many quarts in seven pecks?

13. How many are 7 times 7 bushels?

14. There are 7 days in one week, how many days in 9 weeks?

15. If one barrel of flour costs 10 dollars, how much wil 6 barrels cost?

16. If one cannon ball weighs 8 pounds, what is the weight of nine such balls?

17. What is the weight of eight packages of tea, if each weighs 11 pounds?

18. If one pound of rice costs 12 cents, what is the cost of 7 pounds?

19. What cost 12 pair of boots at $5 a pair?

20. Bought 12 pounds of starch at 8 cents a pound: what was the cost?

21. Samuel had five cents, his mother gave him three more, and his father gave him five times as many as he then had: how many did his father give him?

39. MODEL SOLUTIONS.

EXAMPLE.-What is the product of 659 multiplied

by 7?

SOLUTION.-Write the multiplier under the multiplicand, placing units under units, and draw a line beneath.

Hund's.

OPERATION.

Tens.

Units.

Begin at the right hand to multiply. 7 times 9 units are 63 units=6 tens and 3 units; write the 3 units in the units' place, and add the 6 tens to the product of tens. 7 times 5 tens are 35 tens, +6 tens are 41 6 5 9 Multiplicand. tens, 4 hundreds and 1 ten; write the 1 7 Multiplier. ten in the tens' place, and add the 4 hundreds to the product of hundreds. 7 times 461 3 Product. 6 hundreds are 42 hundreds, +4 hundreds

are 46 hundreds, 4 thousands and 6 hundreds; write the 6 hundreds in the hundreds' place, and the 4 thousands in the place of thousands.

CONCLUSION.-Therefore, the product of 659 multiplied by 7

is 4613.