MATH 2A CHAPTER EIGHT POWERPOINT PRESENTATION

FRACTIONS AND ALGEBRA

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.

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.

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

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.

Algebraic Fractions

• Fractions with variables:

More examples of algebraic fractions:

Multiplying & Dividing Algebraic Fractions

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.

LIST OF MULTIPLES

WHAT A COMPLEX FRACTION LOOKS LIKE

Prime Factors

• Prime Numbers are prime factors:

Adding and Subtracting Algebraic Fractions

Proportions

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

Other Proportions

EQUATIONS WITH FRACTIONS

More Equations With Fractions

ALGEBRA EQUATIONS

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.

RATIONAL EXPRESSIONS!!!