2. What does the line between the terms of a fraction mean?

3. What does the denominator of a fraction show?

1. What is a proper fraction? An improper fraction? Give two examples of proper fractions. Give two of improper fractions. What is a mixed number? Give an example.

2.

3. How is a fraction reduced to higher terms? To lower terms? Give an example of each.

4. If the numerator is increased, what effect will it have on the value of a fraction? If the denominator is increased?

5. What is the effect on the value of a fraction if the numerator is decreased? If the denominator is decreased?

1.

EXERCISE III.

What effect would it have on the value of a fraction to divide the numerator? To divide the denominator?

2. What effect would it have on the value of a fraction to multiply the numerator? To multiply the denominator?

3. If we multiply both numerator and denominator of a fraction by 17 and then divide each product by 13, would it produce a change in the value of the fraction?

1. Change

2. Change

EXERCISE IV.

to a fraction whose denominator is 96.
to a fraction whose denominator is 105.

3. Reduce to lowest terms.

4.

5.

6.

7.

8.

9.

10.

100

5. Five lengths of shafting weigh respectively 3394, 4091, 3871, 4188, and 3573 pounds.

723 pounds. What is their total weight?

1. Two boats are a mile (5280 feet) apart. They row

towards each other, one at the rate of 323 other at the rate of 31117 feet per minute. they at the end of two minutes?

feet per minute, the

How far apart are

Ans. 40107 feet.

2. A dynamo requires 37 horse-power to drive it. If it loses 17 horse-power what horse-power does it furnish?

Ans. 35 horse-power.

3. Supposing a Grove cell to have an electromotive force of 19%, how much greater is its electromotive force than that of a Daniell cell if the latter has 13? Ans.. 45

1. What is the cost of 22 thousand bricks at $11 per thousand? Ans. $267.31 +

2.

What distance can a vessel sail in 37 hours, going at the

rate of 5 miles per hour?

3. If 11 men can do a piece of work in 47 would it take 3 men to do it if each works at the

4. A stone crusher yields on the average 237 cubic feet of broken stone per hour. If the average weight of the broken stone per cubic foot is 93 pounds, what weight of stone will the crusher yield in 173 hours? Ans. 39658 pounds.

EXERCISE x.

1. How is the denominator of a decimal fraction expressed?

2. How is a fraction changed to a decimal?

Give an

9.

9,843,218.431716.000814.335

847 from .923

438.58719 from 1,229.68227

114.00076 from 203

A square foot of "wrought iron plate weighs 25.176 pounds. The same size plate in cast iron weighs 23.466. What is the difference in weight per square foot of the two plates? Ans. 1.710 pounds.

10. A single-acting pump with 12-inch cylinder and 14-inch stroke delivers 68.544 gallons per minute. A similar pump with 16-inch stroke delivers 78.336 gallons per minute. How much more per minute does the latter deliver? Ans. 9.792 gallons.

Multiply

1. .075 by 13

2. .947 by .0016

EXERCISE XII.

3. 4001.876 by 1.00003

4. A square foot of wrought iron plate, of an inch in thickness, weighs 22.659 pounds. How much will 17 square feet weigh? Ans. 402.19725 pounds. 5. A three-inch pipe weighs 7.536 pounds per linear foot. What will 740.75 feet weigh? Ans. 5582.292 pounds.

Divide

1. .00468 by .013

EXERCISE XIII.

2. 43.287 by 10.103

3. .48179 by 37.2

4. The weight of 750 rivets (2 by inches), is 191.1

pounds. What is the weight of a single rivet?

Ans. .2548 pound.

MISCELLANEOUS PROBLEMS,

1. The revolutions per minute of an engine were as follows: 40, 45, 40, 46, 38.67, 38.5, 38.6. What was the average number of revolutions per minute? Ans. 40.9671 +

2. An investigation of the value of tan as fuel showed that a pound of wet tan evaporated .893 pound of water (from 212° F.) A pound of dry tan was found to evaporate 2.319 pounds. How much more water did the tan evaporate when dry? Ans. 1.426 pounds.

3. In the case of an air compressor, the amount of air in cubic feet passing through the valves per hour is as follows: 111.864, 125.844, 118.632, 132.534, 116.434, 115.818, and 117.74. What is the average number of cubic feet? Ans. 119.838 cubic feet. 4. An engine makes 113.9 revolutions per minute. How many revolutions will it make in 2.5 hours (60 minutes each)? Ans. 17085 revolutions.

5. The specific gravity of cast copper is 8.94. That of cast iron is 7.207. How much greater is the specific gravity of cast copper than that of cast iron? Ans. 1.733

6. A locomotive has a total coal capacity of 8,000 pounds. After using 2 tons (2000 pounds each) how many pounds remain ? Ans. 2250 pounds. 7. One kind of lubricating oil costs $.90 per gallon. Another kind costs $.43. What is the total difference in price of 7 gallons of each? Ans. $3.465. 8. A steam pump delivers 26.44 gallons per stroke. A gallon weighs 8.355 pounds. What weight of water will it deliver in 117 strokes? Ans. 25846.0254 lbs.

9. The external diameter of a tube is 12 inches. The iron is .24 of an inch thick, what is the internal diameter?

10.

Boston.

Ans. 11.52 inches.

It is 11:07 A. M. in Chicago when it is 12:12 P. M. in
What is the difference in time between the two places?
Ans. 1 hour 5 minutes.

11. The number of watts is equal to the number of amperes multiplied by the number of volts. There are 746 watts in a horse-power. How many amperes are required to furnish 161 horse-power, the number of volts being 500?

Ans. 24.618 amperes.