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In examples 4-13 change the given complex fractions to simplest

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14. If of an acre of land is worth $72-3, what is the value. of 3 acres at the same rate?

15. There are 5 yards in a rod. How many rods in 1401 yards?

16. At $6 a ton how many tons of coal can be bought for $778?

136. In division, if the divisor contains a common fraction that cannot easily be reduced to a decimal, it is sometimes helpful to multiply both dividend and divisor by the denominator of the fraction, thus making both dividend and divisor integers, or simple decimals; e.g.:

.0211).416

Multiplying both dividend and divisor by 3, and then dividing,

Written

19.5 Quotient

.064)1.248.0

137. In the following examples find the quotients correct to two

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COMPARATIVE STUDY OF DECIMALS AND COMMON FRACTIONS

138. A fraction that is expressed by writing the numerator above and the denominator below a line is a common fraction; e.g., . (See § 9 for definition of decimal fractions.)

49

All decimal fractions may be expressed as common fractions without reducing them; e.g. .010411846. What common fractions can be expressed as decimals without reducing them?

139. When a decimal fraction is expressed without its denominator, by using the decimal point, it is said to be expressed in the decimal form.

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In like manner tell the meanings of the following decimals:

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140. A decimal may be reduced to a common fraction in simplest form by expressing it as a common fraction and reducing lowest terms: e.g. .8585617; 13.8138 = 13;

50 1 1

to

= 100

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163/
100 3

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141. Written. Reduce the following decimals to common fractions or mixed numbers in simplest form :

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142. Since a fraction is an expression of division, a common fraction may be reduced to a decimal by dividing its numerator by its denominator.

Before dividing, place a decimal point after the dividend. Annex ciphers as they are needed; e.g.

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144. A fraction in lowest terms whose denominator contains other prime factors than 2 and 5 cannot be reduced to an exact

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Such a fraction may be reduced to a decimal of nearly the same value by carrying the division to a certain number of decimal places, thus:

Reduce to a decimal of four places.

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A COMMON FRACTION AT THE END OF A DECIMAL

145. .21.2+(of 16, or, or .05). .2+.05.25.

In a similar manner we may show that,

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