containing, on an average, 670 men each: how many men in the army?

11. If a steamer can run 260 miles a day, how far can it run in 10 days? In 100 days?

12. In a field of corn there are 70 rows, and each row contains 280 hills, and each hill 3 stalks: how many stalks of corn in the field?

LESSON VII.

REVIEW.

1. What will 4 oranges cost, at 5 cents apiece? 2. What will 5 barrels of flour cost, at $9 a barrel?

3. If an orange is worth 5 apples, how many apples are 7 oranges worth?

4. If there are 8 pints in a gallon, how many pints are there in 6 gallons?

5. Two men start from the same place, and travel in opposite directions, one at the rate of 3 miles an hour and the other 4 miles an hour: how far will they be apart in 8 hours?

6. If an orange is worth 2 lemons and a lemon is worth 5 plums, how many plums are worth 6 oranges?

7. If 7 men can do a piece of work in 5 days, how long would it take one man to do it?

8. If 6 men can cut a field of grass in 8 days, how many men will it take to cut it in one day? 9. If 3 pipes fill a cistern in 10 hours, in how many hours will one pipe fill it?

WRITTEN EXERCISES.

1. What is the product of 4894 × 37?
2. What is the product of 5680 × 340?

5. Multiply forty-eight thousand by sixty-five thousand.

6. A freight train consists of 37 cars, and each car contains 9850 pounds of freight: how much freight in the entire train?

7. If 980 pounds of bread will supply the inmates of the State Prison one day, how many pounds will supply them one year, or 365 days?

8. If a sack of salt contain 168 pounds, what will be the weight of 1600 sacks?

9. A merchant bought 18 firkins of butter, each weighing 32 pounds, at 37 cents a pound: what did it cost?

10. A train of 27 cars is loaded with iron; each car contains 48 bars, and each bar weighs 365 pounds; what is the weight of the cargo?

DEFINITIONS, PRINCIPLES, AND RULE.

Art. 33. Multiplication is the process of taking one number as many times as there are units in another.

The Multiplicand is the number taken or multiplied.

I. A.-5.

The Multiplier is the number denoting how many times the multiplicand is taken.

The Product is the number obtained by multiplying.

The multiplicand and multiplier are called the Factors of the product.

Art. 34. The Sign of Multiplication is X, and is read multiplied by. When placed between two numbers, it shows that the number before it is to be multiplied by the number after it. Thus : 63 is read 6 multiplied by 3.

NOTE. Since a change in the order of the factors does not change the product, 6 X 3 may also be read 6 times 3.

Art. 35. Multiplication is a short method of addition. The sum of 5+5 +5 +5 is the same as 4 times 5.

Art. 36. RULE FOR MULTIPLICATION.-1. Write the multiplier under the multiplicand, placing units under units, tens under tens, etc.

2. When the multiplier consists of but one term, begin at the right and multiply successively each term of the multiplicand, writing the right-hand term of each result in the product and adding the left-hand term to the next result.

3. When the multiplier consists of more than one term, multiply the multiplicand successively by each significant term of the multiplier, writing the first term of each partial product under the term of the multiplier which produces it.

4. Add the partial products thus obtained, and the sum will be the true product.

Art. 37. 1. When the multiplier or multiplicand or both end with one or more ciphers, omit the ciphers in the partial products and annex them to the product obtained.

2. Any number may be multiplied by 10, 100, 1000, etc, by annexing to it as many ciphers as there are ciphers in the multiplier.

LESSON VIII.

MENTAL EXERCISES.

Problems combining Addition, Subtraction, and Multiplication.

1. 6 × 7 + 4 + 5 + 8 +7 −6 = how many? 2. 8 x 46 3+2 5+ 6 = how many?

3. A grocer bought 10 barrels of apples, at $4 a barrel, and sold them so as to gain $15: for how much did he sell them?

4. John has 6 marbles, and Willis has 4 times as many less 9, and Charles has as many as both John and Willis: how many marbles has Charles?

5. A lady teacher receives $9 a week, and spends $6 for board and washing: how much can she save in 8 weeks?

6. Two men start from the same place and travel in opposite directions, one at 7 miles an hour and the other at 5 miles an hour: how far will they be apart in 8 hours?

7. Two stages start from the same place and go in the same direction, one at 9 miles an hour and the other at 6 miles an hour: how far will they be apart in 5 hours?

8. When oranges are sold at 7 cents apiece and lemons at 5 cents apiece, how many cents will buy 6 oranges and 8 lemons?

9. If a man earn $8 a week and a boy $3, how much will they both earn in 7 weeks?

10. A pedestrian left a city and walked 9 hours at the rate of 4 miles an hour; he then returned at the rate of 3 miles an hour, but in 4 hours stopped to rest: how far was he from the city? 11. If a man earn $12 a week and spend $7, how much will he save in 9 weeks?

WRITTEN EXERCISES.

1. From 4080 × 26 take 2024 × 16.

2. A grocer bought 275 barrels of flour for $2475, and sold it at $12 a barrel: what did he gain?

3. A clerk receives $125 a month, and his expenses are $68 a month: how much does he lay up each year?

4. An agent sold 48 sets of outline maps, at $16 a set; the maps cost him $10 a set: how much did he make?

5. If a steamer carry, on an average, 75 passengers each trip, how many passengers will it carry in 12 weeks, making 3 trips a week?