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Dr. Towns
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Fractions Signed Numbers


Simplifying Improper Fractions

Fractions that have numerators (tops numbers in fractions) that are equal to or higher than the denominator (the bottom number of a fraction) are called improper fractions.

Answers (sums; differences; quotients; products) that are improper must be simplified.

Ex. 1: 3/4 + 3/4 = 6/4.

The numerator (6) is greater than the denominator (4). Thus, the sum must be simplified into a mixed number (a whole number with a fraction)

Ex. 2: 1 3/4 "one and three fourths" is a mixed number as it has both a whole number (1) and a fraction (3/4).

To simplify an improper fraction you divide the numerator by the denominator

6/4 is simplified by dividing 6 divided by 4, writing the remainder as a fraction (the remainder goes as the numerator, the denominator, or dividend (a number being divided) as the denominator.

Ex. 3: 6/4 is "six divided by four" four will go into six one time with a remainder of 2. The answer would be 1 2/4. (2/4 can be reduced to 1/2) The final answer will be 1 1/2.

Adding Fractions With Common Denominators

Fractions with common demoninators (the bottom number in a fraction) can be added simply by adding the numerator (the top number in a fraction). The denominators stay the same.

Ex. 1: 3/5 + 1/5 = 4/5
Ex. 2: 5/16 + 4/16 = 9/16

When both the numerator and denominator of the sum (the answer) have a common factor, divide both the numerator and denominator by that common factor and reduce the fraction.


Adding Fractions with Different Denominators

To add fractions that have different denominators you must first increase the fractions until they have a common denominator (See Lease Common Denominator). Then add the numerators. The denominator of the sum (answer) will be the same as the denominators of the addends (what was added).

Ex 1: 2/3 + 3/7 = ____
a. The denominators are 3 & 7.
b. The LCD (Least Common Denominator) of 3 & 7 is 21.
c. 2/3 = 14/21 ; 3/7 = 9/21.
d. 14/21 + 9/21 = 23/21.
*this is an improper fraction (where the numerator is equal to or higher than the denominator) and must be simplified (see simplifying improper fractions).
23/21 = "1 2/21"