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(1) What is the product of and? Of .1 and .1?

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1. In multiplying .1 by .1, how many decimal places are there in the multiplicand and the multiplier together? How many are there in the product?

(2) What is the product of and expressed decimally? Of 1 and 180?

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2. Compare the number of decimal places in the product with the number in the multiplicand and multiplier together, in multiplying .1 by .01. In multiplying .3 by .03.

II

At the rate of 14.75 miles per hour, how far can a steamboat travel in three hours? In 4.5 hours?

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In the multiplication of decimals, a number of places should be pointed off in the product equal to the sum of those in the multiplicand and the multiplier.

It is sometimes necessary to prefix one or more ciphers to make the required number of decimal places. Illustration: .04 x .2 = .008.

[With pencil.]

1. Multiply: .024 by 3; 2.21 by 4; 24.2 by .3; 3.21 by .2. 2. What is the weight of 4 loads of hay having an average weight of 1.42 tons?

3. A passenger train traveling at the rate of 45.5 miles per hour makes a trip in 2.5 hours. What is the distance covered?

4. A fast freight traveling at the rate of 35.8 miles per hour covers what distance in 1.5 hours?

5. An engine is to pull, besides its tender, 24 freight cars having an average weight of 34.25 tons. The tender weighs 25 tons. Find the weight of the load pulled by the engine.

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68. Division of a Decimal by an Integer

1. What is of $8.64? Of $6.048?

2. How many places are pointed off in the quotient in finding of $8.64? In finding of $6.048?

How many miles are there in 3 of 9.75 miles? In of 6.039 miles?

9.75 mi. ÷ 3 ?

3.25 mi. 39.75 mi.

=

6.039 mi.÷3

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=

2.013 mi. 36.039 mi.

?

of 9.75 mi. = 3.25 mi.

of 6.039 mi.

=

2.013 mi.

EXERCISES FOR SKILL

103

3. How many places are pointed off in the quotient in finding of 9.75 miles? In finding of 6.039 miles? Explain why."

In dividing a decimal by an integer, point off in the quotient a number of decimal places equal to the number in the dividend.

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22. In a 3-hour airship race, the winner rode 436.5 miles. What was his average rate of speed per hour?

23. In a 6-day bicycle race, the winner rode 2731.2 miles. Find the average number of miles covered per day.

24. A passenger train travels 962.88 miles in 24 hours. Find the average number of miles per hour.

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1. Traveling at the rate of a mile in 3.5 minutes, how long does it take a motor-boat to make a five-mile trip?

2. Around a lake the distances between the stations at which the motor-boat stops are: from the first to the second, 2.25 miles; from the second to the third, 1.75 miles; from the third to the fourth, .625 miles, from the fourth back to the first, 2.375 miles. What is the total distance covered in making the trip around the lake?

3. At the rate of $.035 per mile for gasoline, how much does the gasoline cost for one trip around the lake?

RUNNING AN AUTOMOBILE

105

4. Twelve-trip tickets are sold at the rate of $.375 per trip. How much should be charged for one such ticket?

5. Single tickets are sold at 50¢ apiece. How much is saved on a trip by a customer who uses a twelve-trip ticket?

6. On one excursion 6 passengers buy single-fare tickets, and 3 pay their fares from their twelve-trip tickets. What is the value of the fares received?

7. Find the value of the fares for a day when 18 cash fares are collected at 50¢ apiece, and 24 tickets at $.375 apiece.

8. What is the difference in the value of 20 cash fares at 50¢ each and the same number of tickets at $.375 each?

71. Running an Automobile

[With pencil.]

In many cities large automobiles are used to show strangers the sights of interest.

1. A sight-seeing automobile travels 38.2 miles in the morning, 55.2 miles in the afternoon, and 26.6 miles in the evening. What is the entire distance covered during the day?

2. What is the difference in the distance covered in 3 hours, traveling at the rate of 18.2 miles an hour, and that covered in the same time at the rate of 14.5 miles an hour? (Find two ways of solving this problem; then choose the easier way.)

3. At the rate of $1.25 a passenger, how much more is received from a load of 24 passengers than from a load of 18?

4. With an expense of $.035 per mile for gasoline, how much does the gasoline cost for a trip 20 miles long? For one 60 miles long?

*5. How much more than the cost of the gasoline used is received in fares on a 30-mile trip when 20 passengers are carried at $.75 a passenger and the gasoline costs $.045 per mile?

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