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Algebraic Fractions.

Review pages

97 and 98.

198. PROBLEMS IN DIVISION WITH A FRACTION FOR A

DIVISOR.

EXAMPLE I.

See page 101, Rule II, and Observation.

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EXAMPLE II.
See page 101, Rule II, and Observation.

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ас

Let a = 7, x = 10, b = 2, and c = 3; then

bx

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a

I. Find the quotient and verify as above.

b

1
1. x =
3. a =

5. xy =
6

2 4. b

6. yz + d

y

X

a

с

с

2. y =

a

II. Find the quotient and verify as above.

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I. Reduce to improper fractions and verify as above.

2
a
1. x +

3. b +

5. 3+
y

2
2
2. y +
4. ct

6. x +

3

a

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Geometry.

200. CONSTRUCTION PROBLEMS. TRIANGLES.

с

a

b

1. Draw a triangle. Make the side ab 3 inches long. Make the angle a, 45°. Make the angle b, 45°. Prove your work by measuring the angle c which should 'be an angle of degrees.

Observe that if two angles of any triangle and the length of the included side * are given, the triangle may be drawn.

2. Draw a triangle making one of the angles 40°, another 60°, and the included side 5 inches long. The third angle should measure degrees. Prove your work by measuring the third angle.

Measure the sides carefully and observe that the longest side is opposite the largest angle and the shortest side opposite the smallest angle.

3. Draw several triangles of different shapes and sizes. Convince yourself by measurement with the protractor that the sum of the three angles of any triangle is degrees.

4. Draw several triangles of different shapes and sizes. Convince yourself by measurement with a ruler that the sum of two sides of any triangle is greater than the third side of the same triangle.

5. Attempt to draw a triangle whose sides are 6 inches, 37 inches, and 24 inches.

*The “included side" is the side between the two given angles.

201. MISCELLANEOUS REVIEW.

1. If $ of a cord of wood cost $4.50 how much will 27 cords cost at the same rate ?

2. If 24 tons of coal cost $12.60, how much will 17} tons cost at the same rate ?

3. A man owned 7 acres of land; he sold 23 acres. What fractional part of his land did he sell ?

4. The sum of two fractions is 1 1 ; one of the fractions is . What is the other fraction?

5. The product of two fractions is t'; one of the fractions is . What is the other fraction?

6. If a furnace consumes of a ton of coal a day, in how many days will 54 tons be consumed ?

7. How many pounds of sugar at 4¢ a pound must be given for 277 pounds of butter at 234 a pound?

8. How many pounds of coffee at 333¢ a pound must be given for 15} dozen eggs at 20¢ a dozen ?

9. Which is the greater fraction for y? 10. Multiplying both terms of a fraction by the same number does not change the value of the fraction. Does adding the same number to both terms of a fraction change the value ?

11. Dividing both terms of a fraction by the same number does not change the value of the fraction. Does subtracting the same number from both terms of a fraction change the value?

12. Change tí to a fraction whose denominator is 46. 13. Change in to a fraction whose denominator is 15.

FRACTIONS.

202. To CHANGE DECIMALS TO COMMON FRACTIONS AND

COMMON FRACTIONS TO DECIMALS.

EXAMPLE I.

Change .36 to a common fraction in its lowest terms. *

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(a) Find the sum of the eight decimals.
(b) Find the sum of the eight common fractions.

EXAMPLE II.

Change š to a decimal. Operation.

Explanation. 8)3.000

3 over 8 means 3 divided by 8. We therefore .375 annex zeros to the numerator 3, and perform the

division. One eighth of 30 tenths is 3 tenths with a remainder of 6 tenths, etc.

Reduce to decimals.

1. 1
3. 움
5.

7.
2. do
4. do
6. 37

8. 43
(c) Find the sum of the eight decimals.

* The numerator of .36 is 36; its denominator is 100, and the decimal is 36 hundredths.

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