math 2a chapter eight powerpoint presentation fractions and algebra
TRANSCRIPT
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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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