A REVISIT TO FRACTIONS AND EXTENSION

Algebraic Fractions

TO UNDERSTAND HOW TO SIMPLIFY, WE NEED TO TAKE A DEEPER LOOK

1. Find the prime factorization of the following numbers. (Make a factor tree if necessary)

45 54 36 96 100 144

LET’S LOOK AT SIMPLIFYING FROM A PERSPECTIVE OF PRIME FACTORIZATION

1. 2. 3.

LET’S LOOK AT IT FROM A PERSPECTIVE OF PRIME FACTORIZATION

Try these on your own to prove you know what you’re doing.

LET’S LOOK AT WHY WE MIGHT BE DOING THIS.

What does this equal?

LET’S LOOK AT SOME HARDER ONES

TRY THESE ON YOUR OWN

NOW, FOR THE NOTATION THAT MAY THROW YOU OFF

Remember, we can rewrite repeated multiplication as exponents

Example

But what is the answer?

LET’S LOOK AT THESE

Written as exponents

What’s the key to dividing variables with exponents?

SUBTRACT THE EXPONENTS

TRY THESE ON YOUR OWN

WHAT ABOUT WHEN WE MIX COEFFICIENTS AND VARIABLES?

Example: Simplify

Simplify the numbers first, then worry about the variables

LET’S LOOK AT ANOTHER ONE

Simplify

LET’S LOOK AT ONE MORE WITH MORE VARIABLES.

Simplify

Isolating each part to see what happens at each level

TRY THESE ON YOUR OWN

Simplify each of the following

WHAT’S THE NEXT LEVEL OF THESE?

When we have to FACTOR!!! Example: Simplify

LET’S TRY A FEW TOGETHER

Simplify:

Simplify:

LET’S DO TWO MORE BEFORE YOU TRY THEM ON YOUR OWN.

Simplify

Simplify

SEE IF YOU CAN DO THESE ON YOUR OWN Simplify

CHALLENGE