NOTE. The teacher should show that the use of the ciphers in forming the partial products would produce the same result.

6. There are 5280 feet in a mile: how many feet in 805 miles?

7. The earth moyes in its orbit at an average rate of 68000 miles in an hour: how far does it move in 24 hours? In 48 hours?

8. If a carriage-wheel revolve 280 times in running a mile, how many times will it revolve in running. 68 miles? 75 miles?

9. A canal-boat was loaded with 245 bales of hay, weighing 280 pounds each: what was the weight of the cargo?

10. There are 480 sheets of paper in a ream: how many sheets are there in 604 reams?

11. If an acre of land produce 380 pounds of cotton, how many pounds will 248 acres produce?

12. A steam-boat makes 145 trips in a season, and carries, on an average, 280 passengers each trip: how many passengers does she carry during the season?

LESSON VI.

New Multiplicand Figure, 9.

MENTAL EXERCISES.

1. Three times 9 are how many? 4 times 9? 6 times 9? 8 times 9? 7 times 9? 9 times 9?

2. How many are 5 times 9? 9 times 5? 7 times 9? 9 times 7? 10 times 9? 9 times 10?

3. How many are 5 times 10? 10 times 5? 7 times 10? 10 times 7? 9 times 10? 10 times 9?

4. A man gave 7 boys 9 rabbits each: how many rabbits did he give them all?

5. If a man earn 10 dollars a week, how much I will he earn in 8 weeks?

6. Jane writes 9 lines each day at school: how many lines does she write in 8 days?

7. Charles receives 9 dollars a month as errandboy: how much will he earn in 10 months?

8. If 7 men can do a piece of work in 9 days, how many men will it take to do the same work in one day?

9. If a quantity of provisions will supply 10 men 9 days, how long will it supply one man?

10. What will 6 barrels of flour cost, at $9 a barrel?

6. There are 3600 seconds in one hour: how many seconds are there in 630 hours?

7. Light moves 192000 miles in a second: how far does it move in one hour?

8. A ship has provisions enough to allow the crew 130 pounds a day for 90 days: how many pounds of provisions are aboard?

9. What will 1700 tons of railroad iron cost at $250 a ton?

10. An army is composed of 54 regiments, 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 bananas 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 1 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 1 day?

9. If 3 pipes fill a cistern in 10 hours, in how many hours will 1 pipe fill it?

WRITTEN EXERCISES.

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

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

6. In a train of 37 cars, each car contains 9850 pounds of freight: how much freight in the 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. (See Multiplication Table, p. 213.)

The Multiplicand is the number taken or multiplied.

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: 6 X 3 is read 6 multiplied by 3.

NOTE. Since a change in the order of the factors does not change the product, 6X3 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.