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Reduce a Fraction:
Factor the numerator and denominator.
Cancel out like factors.
Example: 15/35 = (3*5)/ (7*5) = 3/7
Equivalent Fractions:
If two fractions are equivalent, then the product of the means equals the product of the extremes. (ie) The cross products are equal.
Example: 4/5 = 8/10 because 4 * 10 = 5 * 8
Addition and Subtraction of Two Fractions:
Find a common denominator, a number that is a multiple of both denominators. (You can use the product of both denominators for the common denominator, although this may not be the lowest common denominator.)
Express each fraction as an equivalent faction with the new denominator.
Add or subtract the numerators of the equivalent fractions and put that over the common denominator.
Reduce the fraction by factoring the numerator and the denominator and then canceling out like factors.
Multiplication of Two Fractions:
If possible, cancel out like factors of the numerators and denominators.
Multiply the numerators and put that product over the product of the denominators.
Division of Two Fractions:
Invert the divisor (second fraction) and proceed as in multiplication.
Express a Fraction with a New Denominator:
Divide the denominator of the faction into a new denominator.
Multiply the result by the numerator of the fraction and put the product over the new denominator.
Example: Write 2/3 as an equivalent fraction with the denominator of 12.
12/3 = 4. Multiply 4 by 2, the numerator of the fraction. Put the product, 8, over the new denominator to get 8/12.