Decimals
Fractions
The following section reviews the processes of renaming and reducing fractions. These processes are invaluable when you add, subtract, multiply, or divide fractions.
Equivalent fractions
Fractions that name the same number, such as1/2,2/4,3/6,4/8, and5/10, are called equivalent fractions. A simple method to check if fractions are equivalent is to cross multiply and check the products.
Example 1: Is2/4 equivalent to3/6?
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The cross products are the same, so the fractions2/4 and3/6 are equivalent.
Example 2: Is3/4 equivalent to ⅔?
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The cross products are not the same, so the fractions3/4 and ⅔ are not equivalent.
Reducing fractions
When given as a final answer, a fraction should be reduced to lowest terms. Reducing fractions is done by dividing both the numerator and denominator by the largest number that will divide evenly into both.
Example 3: Reduce15/25 to lowest terms.
To reduce15/25 to lowest terms, divide the numerator and denominator by 5.
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Since3/5 cannot be reduced any further, that is, the numerator and denominator cannot both be evenly divided again,3/5 is reduced to lowest terms.
Example 4: Reduce8/40 to lowest terms.
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Enlarging denominators
The denominator of a fraction may be enlarged by multiplying both the numerator and denominator by the same number.
Example 5: Change3/4 to eighths.
To change3/4 to eighths, simply multiply the numerator and denominator by 2.
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Example 6: Express1/2 as tenths.
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