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19. Four hundred ninety and six thousand twenty-four ten-thousandths.

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REDUCTION OF FRACTIONS

Reduction is the process of changing the form of a number without changing its value.

1. Divide both terms of the fraction by 2. How does compare in value with?

2. Multiply both terms of the fraction by 2. How compare in value with ? How may we obtain & or

does

from?

Multiplying or dividing both terms of a fraction by the same number does not change its value.

Changing a fraction to higher terms.

1. Explain why a fraction is expressed in smaller fractional units when it is changed to higher terms.

2. Explain why changing a fraction to higher terms does not change the value of the fraction.

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Changing a fraction to lower terms or to lowest terms.

1. Explain why a fraction is expressed in larger fractional units when it is changed to lower terms. Explain also why changing a fraction to lower terms does not change its value.

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A fraction is expressed in its lowest terms when the numerator and the denominator are prime to each other.

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to lowest terms.

Since dividing both terms of a fraction by the same number does not change its value, we may reject by cancellation all the factors common to both terms, leaving the factors 7 and 9. Hence, 1= 3.

Or we may, in one step, divide both terms of the fraction by their g. c. d., 6.

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Cancel all the factors common to both numerator and denominator. Or, divide both numerator and denominator by their greatest common divisor.

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Changing a mixed number to an improper fraction, or an improper fraction to a mixed number.

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In small numbers the work may be done mentally, only

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Every fraction is an indicated division.
Change to integers or mixed numbers:

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