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**MATH 2A CHAPTER EIGHT POWERPOINT PRESENTATION**

FRACTIONS AND ALGEBRA

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**LEARNING TARGETS AFTER YOU COMPLETE THIS CHAPTER YOU WILL BE ABLE TO:**

WRITE FRACTIONS IN THE SIMPLEST FORM. MULTIPLY, DIVIDE, ADD, AND SUBTRACT ALGEBRAIC FRACTIONS. SIMPLIFY COMPLEX FRACTIONS. FIND THE LEAST COMMON MULTIPLE (LCM). SOLVE PROPORTIONS. SOLVE EQUATIONS WITH ALGEBRAIC FRACTIONS.

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**FRACTIONS AS RATIONAL NUMBERS**

RATIONAL NUMBERS – ANY NUMBER THAT IS EXPRESSED AS AN INTEGER OR AS A RATIO BETWEEN TWO INTEGERS WHEN ZERO DOES NOT SERVE AS THE DENOMINATOR. SIMPLEST FORM – A FRACTION REDUCED TO LOWEST TERMS. ALGEBRAIC FRACTION – A SINGLE ALGEBRAIC TERM DIVIDED BY A SINGLE ALGEBRAIC TERM. RATIONAL EXPRESSION – AN ALGEBRAIC EXPRESSION DIVIDED BY ANOTHER ALGEBRAIC EXPRESSION.

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**What that looks like!! All of these fractions are rational numbers!!**

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Simplest Form When you have a fraction like 6/12 – it can be reduced to one-half, if you have 6/8 – it can be reduced to three-fourths. You must always show fractions in their simplest form. If you have a fraction like 12/4 – it can be reduced to three. If you have a fraction like 22/5 – it can be reduced to 4 and 2/5.

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Algebraic Fractions Fractions with variables:

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**More examples of algebraic fractions:**

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**Multiplying & Dividing Algebraic Fractions**

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**COMPLEX FRACTIONS AND LCM**

COMPLEX FRACTIONS – A FRACTION IN WHICH THE NUMERATOR, THE DENOMINATOR, OR BOTH ARE FRACTIONS. LEAST COMMON MULTIPLE – THE SMALLEST NUMBER THAT TWO OR MORE NUMBERS CAN DIVIDE INTO WITHOUT LEAVING A DENOMINATOR.

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LIST OF MULTIPLES

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**WHAT A COMPLEX FRACTION LOOKS LIKE**

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Prime Factors Prime Numbers are prime factors:

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**Adding and Subtracting Algebraic Fractions**

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Proportions A proportion states both sides of an equation are equal.

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Other Proportions

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**EQUATIONS WITH FRACTIONS**

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**More Equations With Fractions**

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ALGEBRA EQUATIONS

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**DENOMINATORS AND ZERO ANYTHING MULTIPLIED BY ZERO = 0**

UNDEFINED – A TERM USED WITHOUT A SPECIFIC MATHEMATICAL DEFINITION. DIVISION BY ZERO IN UNDEFINED. DENOMINATORS IN ALGEBRAIC EXPRESSIONS MUST NEVER BE ZERO.

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RATIONAL EXPRESSIONS!!!

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