Number Systems

When you first started learning to count you started with the number 1. This was the set of Natural Numbers

Then Someone discovered ZERO!

Muhammad ibn Ahmad al Khwarizm from Persia referred to it as “sifr” or empty space.

The Mayans may have discovered it. So also, the Babylonians. So also, India and Egypt.

The Set of WHole Numbers…..get it!

Then came the Set of Integers

Then came the Set of Rational Numbers, Positive

and Negative Fractions

And now the Irrational Numbers

Let’s Keep It Real!

So what can we do with all of these numbers?

How do you operate on these number systems?

Basic OperationsAdd or Subtract

Higher Order OperationsMultiply or Divide

Higher Still!Raise to an exponent – repeated

multiplicationRooting – repeated division

Adding or Subtracting

The items must always

be the same!

Adding or Subtracting Fractions

•Make sure the denominators are the same!

•If not, convert.

•To find a common denominator, multiply OR find a number each denominator will divide into. Change the numerators.

•Keep the denominator and add or subtract the numerators.

•Go on a diet and Reduce!

Adding or Subtracting Integers

• Eliminate extra signs so that there is only one operation sign between each number. (Two negatives become one positive.)

• Collect and Total numbers with the same sign.

• When the signs are the same, add and keep the sign!

• When the signs are different, subtract and keep the sign of the larger number!

)10()2()7(43 )10()2()7(43 )10()2()7(43

Adding or Subtracting Algebraic Terms

• Identify the different types of terms in the expression.

• Collect like terms – make sure to keep beginning signs.

• Add or subtract the COEFFICIENTS and keep the variable.

Things can be different for MULTIPLY and DIVIDE

Things are going to CHANGE!

Multiplying Fractions

• The denominators do not have to be the same!

• Multiply NUMERATORS TOGETHER.

• Multiply DENOMINATORS TOGETHER.

• REDUCE TO LOWEST TERMS! ` `

Dividing Fractions

• The denominators do not have to be the same!

• KEEP the original fraction.

• CHANGE the operation to multiplication..

• FLIP the fraction after the division sign.

• Now MULTIPLY! ` `

Multiplying and Dividing Integers

• COUNT the number of negative signs FIRST to determine the sign of the answer.

• Then, just multiply or divide the integers.

• Use the sign with the number answer. `

Multiplying and Dividing Algebraic Expressions

• Multiply or divide coefficients..

• When multiplying variables, they will change!

• MORE PRACTICE WITH THIS LATER!