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34. A merchant bought 140 boys' suits at $6.75 a suit. He sold of them at $9.50 a suit and the remainder at $8.50 a suit. How much did he gain?

of it,

35. Four men purchased an oil property, the first paying for .3 of it, the second for .375 of it, the third for and the fourth the remainder, which was $3000. much did the property cost them?

How

36. A merchant bought 975 pounds of sugar for $48.75.

He sold of it at $.055 a pound,

the remainder at $.065 a pound.

of it at $.06 a pound, and Find his gain.

37. I invested .4 of my money in a farm and deposited .75

of the remainder in a bank.

If the amount paid for the

farm was $300 less than the amount deposited in the bank,

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PRACTICAL MEASUREMENTS

LENGTH AND SURFACE

TO THE TEACHER. Secure a 50-foot tape measure and have pupils make as many actual measurements as possible.

1. Find the dimensions of the school ground.

2. If your school is in the city, measure the length and width of some square near your school, or if in the country, some field.

3. Measure of a mile along a street or a public road. Compare a mile with a rod; with a yard; with a foot.

After some practice in actual measurements, the pupils should be able to give quite accurate estimates of short distances.

4. Have the pupils estimate the length and the height of the schoolroom; the height of the school building; the length and the width of the playground, etc.

5. Have each pupil draw on the blackboard, without the aid of a rule, an inch, a foot, a yard.

6. Show by diagram the number of square inches in a square foot.

7. Show by diagram the number of square feet in a square yard.

8. Draw a square rod on a scale of 3 inches to 1 yard.

9. Show by a diagram, on a scale of 1 inch to the yard, the number of square yards or square feet in a square rod. 160 square rods of land is called an acre.

A

square mile of land is called a section of land.

10. How many yards are there in the perimeter of a field a mile square?

NOTE.

The perimeter of a figure is the line that bounds it, or the sum of its sides.

11. Name the different units of long measure and the different units of surface measure.

12. What is the shape of the figure that represents a square inch? a square foot? a square yard? a square rod?

13. Draw two figures of different dimensions to represent How do you show that 160 square rods equals

an acre.

each surface?

14. What unit of surface measure is not a square unit? 15. Have each pupil draw a unit surface, without the aid of a rule, to show a square inch, a square foot, a square yard. Learn this table of surface or square measure:

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1. 3 sq. ft. 48 sq. in. to square inches.
2. 4 A. 35 sq. rd. to square rods.
3. 125 sq. rd. to a decimal of an acre.
4. .375 of an acre to square rods.

5. 4 A. to square feet.

6. sq. ft. to square inches. 7. 4.5 sq. rd. to square inches. 8. 21 sq. mi. to square rods. 9. 1800 sq. rd. to acres, etc. 10. 1584 sq. in. to square feet, etc.

11. 6.75 A. to square feet.

12. Mr. Jamison's farm contains 125 A. 120.8 sq. rd. Three fourths of it is purchased at $312.50 per acre, to be laid out in town lots. Find the number of acres sold and the amount received from the sale.

LINES AND ANGLES

1. Observe the two lines. How do they compare in direction?

Parallel lines are lines that cannot meet however far they may be extended.

An angle is the difference in direction of two lines that meet. When two lines meet each other forming a square corner, they form a right angle; thus, L

Lines drawn at right angles to each other are perpendicular; thus, AB and BD in the cut are

A

D

perpendicular to each other.

B

2. Draw a circle and divide it into 4 equal parts by diameters perpendicular to each other.

3. How many angles are there at the center of the circle? What is each angle called? The circumference of a circle is the perimeter or distance around it. The circumference of a circle is measured in degrees; every circum

ference, whether large or small, is divided into 360 degrees (written 360°).

of a circle is 90°. Observe that the angle between two lines that meet at a point is measured by the part of the circumference cut by the lines extended.

4. How do you explain that of circumference A contains as many degrees as of circumference B?

5. Observe the figure. Show that the curved lines are simply parts of circumferences of circles B that could be formed about the

point B. How do you show that

30%

30°

A

B

-90° -909

30°

30°

30°

30°

each curved line measures an angle of 30°? Show the an

gles on the figure.

6. Show that an angle is the difference in direction of two lines that meet at a point and that the angle remains the same, however far the lines may be extended.

Angular Measure

Angles are measured by an instrument called a protractor. When the center O of the

protractor is placed at the vertex of the angle to be measured, the size of the angle may be seen on the scale between the lines that A

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B

form the angle. Thus, BOC is an angle of 30°, and AOC is an angle of 150°.

Every circumference contains 360 degrees (360°), each degree, 60 minutes (60′), and each minute, 60 seconds (60'').

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