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

Fill in the Blanks

Translate the phrase to an algebraic expression. Use the variable x to represent each unknown number.

"5 decreased by a number"

Fill in the Blanks

Translate the phrase to an algebraic expression. Use the variable x to represent each unknown number.

"The quotient of a number and 12."

Fill in the Blanks

Translate the phrase to an algebraic expression.

"The sum of 4 and twice y"

Fill in the Blanks

Translate the phrase to an algebraic expression.

"x less than the product of y and z"

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

Fill in the Blanks

Write the sentence as an equation:

"The sum of x and 9 is 24."

Fill in the Blanks

Write each sentence as an equation.

"Three times the sum of 5 and y amounts to 9."

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

Fill in the Blanks

Write the sentence using mathematical symbols.

"The difference of 7 and a number is less than 42."

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."

• $\frac{y}{2}x=4z$

• $\frac{y}{2x}=4z$

• $y\cdot2x=4z$

• $y\cdot2x=\frac{4}{z}$

• $2\frac{y}{x}=4z$

Fill in the Blanks

Write each as an algebraic expression.

"A vending machine contains x quarters. Write an expression for the value of the quarters."

Fill in the Blanks

Write each as an algebraic expression.

"The number of grams of fat in x pieces of bread if each piece of bread contains 2 grams of fat."

Fill in the Blanks

Two numbers have a sum of 20. If one number is x, represent the other number as an expression in x.

Fill in the Blanks

The older sister is 8 years older than her younger sister. If the age of the younger sister is x, represent the age of the older sister as an expression in x.

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 ...

Fill in the Blanks

If x is the first of two consecutive integers, represent the second integer as an expression in x.

Fill in the Blanks

Write the following as an algebraic expressions. Then simplify.

"The sum of three consecutive odd integers, if x is the first consecutive integer."

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}

• {    }