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Rayhana J.

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Variables, Expressions, and Properties

A __Variable__ is a symbol, usually a letter, to represent a number. Example: 4xn. That is called an **algebraic expression**, and when you replace **n **with a number (ex. 10), it becomes a __numerical expression__.

When you ** evaluate **an expression, you find it's numerical value. To avoid confusion, mathmeticians have agreed on a set of rules called

**P**arentheses

**E**xpressions

**M**ultiplication

**D**ivision

**A**ddition

**S**ubtraction

**PEMDAS**

The problem is: 6-(5-3)+10. First, do the parenthesis.

5-3=2. So it becomes: 6-2+10. Then do: 6-2, and it will become 4. So now it is: 4+10. Add. 4+10=14.

Remember, some problems will have all 6 operations. Just follow **PEMDAS **for the right answer

Evaluate an Algebraic Expresion

If **a**=5, **b**=4, and **c**=8

4a-3b+1

This is actually: 4(5)- 3(4)+1 or 4x5-3x4+1

Evaluate 4x5 and 3x4. 20 and 12. Subtract. 20-12= 8. Add the 1. 9. The final answer is nine (9).

Note: N(N) means multiply. (N is a variable for any number)

Equations

A mathematical sentence that contains an **equal **(=) sign is called an ** equation**.

Ex. 7+8=15 3(6)= 18 x+2=5 (x is a **variable**)

Commutative Property

**Properties** are open sentences that are true for any numbers.

**Commutative Property **looks like this.

__Algebra__

a+b=b+a

__Arithmetic__

6+1=1+6

Associative Property

Distributive Property

Identity Property

Transitive Property

Counterexample

Writing Integers

Comparing Integers

Adding Integers

Subtracting Integers

Multiplying Integers with Different Signs

Multiplying Integers with the Same Sign

Writing an Algebraic Expression

Write an Algebraic Equation

Solving Addition Equations

Solving Subtraction Equations

Solving Multiplication Equations

Solving Division Equations

The End of Chapter 1

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