# Adding and Subtracting Polynomial Fractions Multiplying and dividing monomials Slideshow 6, Mathematics Room 307, Mr. Sasaki Multiplication and division drill Learn what a monomial is Recall what happens when we multiply something by something else or itself Recall what happens when we divide something by something else or itself Practice multiplying and dividing monomials Objectives What is a monomial? A monomial is a polynomial

that contains only one term and a coefficient (even 1). Is this a monomial? Monomials Is this a monomial? Yes! Is this a monomial? No! Is this a monomial? Yes! Basically, a monomial is a polynomial without any addition or subtraction operators. When we multiply monomials,

we combine each monomial to make one, single monomial. Lets Monomials have a look Example Multiply by . Here are two monomials, a = and b. In the simplest case, we just write them together. Algebraic expressions in their simplest form do not contain x or symbols, this is why it is important to remove them. Example Simplify . = Dividing

Monomials When written as a fraction, this is thought of as one number, one term. This is why this is simplified in algebra. Numbers follow rules that you should be familiar with by now, lets have a look. Example 2 Simplify 4 2 . 4 2 2 = 8 2 Multiplying Monomials When we have different unknowns (like and ),

we just write them next to each other. When we divide, the same applies however we write the first unknown at the top and last at the bottom. Example 2 Simplify 4 2 . 4 2 2 = 2 2 Multiplying Monomials Try the short worksheet! When we divide two different unknowns (like

and ), we just write them the first above the second. Answers 2 432 8 6 8 3 30 2 2 2

7 2 2 5 2 2 + You can see here that its much easier to read this as a set of fractions! When terms are the same as each other, they combine as one term in a different way. Example Simplify . x

= Simplify . + In algebra, we never Similar write . Also, . We never Terms write . 2 3=( ) ( ) = = 5 Division works in the opposite way. Example

Simplify . Similar 4 2= Terms = 2 So when we multiply powers of the same term, the power is added and when we divide, the power is subtracted. Try to remember this! Lets try some general examples. Note: 0 means

Example 0 We never write . Simplify . =2 Example Simplify . = 8 6 Multiplying and Dividing Monomials Try the last worksheet! Answers

52 217 7 2 7 2 9 9 4 303 1 5

272 4 8 2 2 or 2 2 353