Writing Algebraic Expressions

Writing Algebraic Expressions

• Write phrases as algebraic expressions
• Use operations and order symbols to write mathematical sentences
• Write algebraic expressions that can be simplified

Translating Phrases

Algebraic Equations

An algebraic equation is a statement that two expressions have equal value.

Equality is donoted by the phrases:

• equals
• gives
• is/was
• yields
• amounts to
• represents
• is the same as

Order Property for Real Numbers

For any two real numbers a and b, a is less than b if a is to the left of b on the number line.

• a < b means a is to the left of b on a number line.
• a > b means a is to the right of b on a number line

Multiple Choice

 $-3\ \ \ \ \ ?\ \ \ \ \ -4$  

• <

• >

• =

Multiple Choice

 $\frac{15}{3}\ \ \ \ \ ?\ \ \ \ \ 5$  

• <

• >

• =

Multiple Choice

 $-6\ \ \ \ \ ?\ \ \ \ \ 0$  

• <

• >

• =

Equality and Inequality Symbols

Multiple Choice

Write the sentence using mathematical symbols.

"The quotient of y and twice x is the same as the product of 4 and z."

• $\frac{y}{2}x=4z$

• $\frac{y}{2x}=4z$

• $y\cdot2x=4z$

• $y\cdot2x=\frac{4}{z}$

• $2\frac{y}{x}=4z$

Consecutive Integers

• First Integer = x

• Second Integer = x + 1

• Third Integer = x + 2

• ... and so on ...

Consecutive Even Integers

• First Integer = x

• Second Integer = x + 2

• Third Integer = (x + 2) + 2 = x + 4

• Fourth Integer = x + 6

• ... and so on ...

Consecutive Odd Integers

• First Integer = x

• Second Integer = x + 2

• Third Integer = x + 4

• Fourth Integer = x + 6

• ... and so on ...

Union and Intersection of Sets

• Find the Union of two sets

• Find the Intersection of two sets

Intersection of Sets

• The set of all elements common to both sides

• We use the symbol

   $\cap$   to represent "intersection"

• Can be seen using the word "and"

Union of Sets

• The set of elements that belong to either of the sets                           *either meaning one or the other or both

• We use the symbol

   $\cup$   to represent "union"
  

• Can be seen using the word "or"

Multiple Choice

If A = { x | x is an odd number greater than 0 but less than 9} 

and B = {4, 5, 6, 7, 8},
find A $\cap$  B.

• {1, 3, 5, 7}

• {1, 3, 4, 5, 6, 7, 8}

• {5, 7}

• {    }

Multiple Choice

If A = { x | x is an odd number greater than 0 but less than 9} 

and B = {4, 5, 6, 7, 8},
find A $\cup$  B.

• {1, 3, 5, 7}

• {1, 3, 4, 5, 6, 7, 8}

• {5, 7}

• {    }