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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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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:

Keep the common denominator then add the numerators. Follow all of the properties for â€œsigned numbersâ€.

Example:

II. Adding fractions that do not have common denominators:

Example:

Factor the denominators and find the least common denominator (LCD). Raise both (or all) fractions to have the LCD, then add the new numerators.

Example:

Equivalent Fractions: If the numerator and denominator are multiplied by a common factor the resulting expression is an equivalent fraction that has the same numerical value.

Multiply fractions: Multiply numerators times numerators and denominators times denominators.

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,

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 the numerator.

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 sum.

Learn this well. These steps will also work with algebraic fractions that contain variables so you will probably want to â€œbookmarkâ€ these pages.

Example:

## 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.

Example 2:

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€.