# Properties of fractions - reducing, multiplication, addition, division, subtraction

Fractions are numbers written with a numerator and a denominator; the denominator tells how many parts one whole is being separated into, and the numerator tells how many of those parts are being considered.

EX: The fraction 2/5 means one whole is divided into 5 parts and 2 of those parts are being considered.

### Properties of fractions - reducing, multiplication, addition, division, subtraction, table

 REDUCING of fractions Divide the numerator (top) and denominator (bottom) by the same number (essentially dividing by 1, which does not change the value), thereby renaming it to an equivalent fraction in lower terms; this process may be repeated EX: 20/32 ÷ 4/4 = 5/8 MULTIPLICATION of fractions • Common denominators are not needed: 1. Multiply the numerators and multiply the denominators, then reduce the answer to lowest terms 2. Or reduce any numerator with any denominator and then multiply the numerators and multiply the denominators ADDITION of fractions • Change to equivalent fractions with a common denominator 1. Find the least common denominator by determining the least number that can be divided evenly (no remainders) by all of the numbers in the denominators EX: 3, 4, and 6 divide evenly into 12 2. Multiply the numerator and denominator of each fraction so that the fraction value has not changed but the common denominator has been obtained 3. Add the numerators and keep the same denominator because the addition of fractions is counting equal parts DIVISION of fractions • Common denominators are not needed 1. Change division to multiplication by the reciprocal; that is, flip the fraction after the division sign and change the division sign to a multiplication sign 2. Now follow the steps for multiplication of fractions, as indicated above SUBTRACTION of fractions • Change to equivalent fractions with a common denominator EX: To evaluate 7/9 - 1/3, follow these steps: 1. Find the least common denominator by determining 2. Multiply the numerator and denominator by the same number so that the fraction value has not changed but the common denominator has been obtained 3. Subtract the numerators and keep the same denominator because the subtraction of fractions is finding the difference between equal parts  