Adding and Subtracting Fractions
FRACTION: If a and b are real numbers then the expression
is called a fraction. The top number a is called the numerator and the bottom
number b is called the denominator. Division by zero is not allowed, so b ≠ 0
or the result is undefined.
Remember that for addition all fractions must have common
denominators. [The result must be checked to see if it will reduce to simpler form.]
I. Adding fractions with common denominators:
common denominator then add the numerators.
Follow all of the properties for â€œsigned numbersâ€.
II. Adding fractions that do not have common denominators:
Factor the denominators and find the least
common denominator (LCD). Raise both
(or all) fractions to have the LCD, then add
the new numerators.
Equivalent Fractions: If the numerator and denominator are
multiplied by a
common factor the resulting expression is an equivalent fraction that has the same
Multiply fractions: Multiply numerators times numerators and
Add Fractions with Different Denominators:
If the fractions do not have common denominators [Factor the denominators and
find the LCD. ] RAIISE all fractions to have common denominators,
then add the resulting numerators.
→ Another approach to this is to write the
LCD in the denominator with a long
â€œoverbarâ€ -- write the â€œfirst numeratorâ€ then compare its denominator with the
LCD (the other factors will be the â€œmissing factorâ€) which will be multiplied times
→ Next, remember that the â€œsign goes with the number that follows itâ€ and write
the â€œnext signed numeratorâ€ â€“ compare its denominator with the LCD for the
â€œmissing factorâ€ to multiply times that numerator. Repeat for all fractions in the
Learn this well. These steps will also work with algebraic fractions that contain
variables so you will probably want to â€œbookmarkâ€ these pages.
Adding mixed numbers â€“ integers and fractions
One of the problems that students have difficulty with occurs when one of the
â€œaddendsâ€ is an integer. They forget that all integers have a denominator of 1.
III. In algebra some of the factors may be letters, or variables, which must be
treated as â€œprime factorsâ€. They will be left in the result as â€œliteral sumsâ€.