WRITING AND EVALUATING ALGEBRAIC EXPRESSIONS

Algebra Review Unit

ALGEBRA MAGIC

1. Think of a number – shh! Don’t tell me!

2. Double it in your head.

3. Add 6.

4. Divide by 2.

5. Subtract the original number from your new number – shh! Let me guess the number you ended up with…..

DID YOU GET…

3I bet you’re wondering how I knew that!

Let’s use some algebra to find out!

LET’S TRANSLATE OUR WORDS INTO ALGEBRA

1. Think of a number.

2. Double it in your head.

3. Add 6.

4. Divide by 2.

5. Subtract the original number from your new number.

Let’s call our number n

n + n = 2n

2n + 6 2n + 6 simplifies to: n + 3 2

n + 3 – n simplifies to: 3

WORDS ALGEBRA

LET’S REVIEW SOME IMPORTANT VOCABULARY WORDS

A variable is a symbol that represents one or more numbers. Examples of variables are:

n number of studentst time in minutesx may represent any number for any reason

A term is a number, variable or the product of a number and variable(s). Examples of terms are:

3x z2ab 5y3

A coefficient is the numeric factor of your term.

An algebraic expression is a mathematical phrase with at least one variable. Examples of algebraic expressions are:

3m 4t + 122x - 3 n + 8

TERM COEFFICIENT

3x 3

2ab 2

5y3 5

z 1

ALGEBRAIC EXPRESSIONS CAN REPRESENT WORD PHRASES

WORD PHRASE ALGEBRAIC EXPRESSION

a temperature of t degrees increased by

5 degreest + 5

five cats fewer than c cats

c - 5

the product of 5 and n tickets

5n

a dinner bill of d dollars divided among

five friends

d5

KEY WORDS AND PHRASES USED TO DESCRIBE MATHEMATICAL

OPERATIONS

OPERATION KEY WORDS OR PHRASES

Addition summore than

increased bytotal

added to

Subtraction difference less than

fewer thandecreased by

OPERATION KEY WORDS OR

PHRASES

Multiplication product times

multiplied byper

each

Division quotient ofdivided by

WRITE AN ALGEBRAIC EXPRESSION FOR EACH WORD

PHRASE

swimming m meters per minute for 3 minutes

12 heartbeats more than x heartbeats

a price p decreased by 16

the quotient of q and 6

3m

x + 12

p - 16

q6

The cost of a package of markers is d dollars. Write an algebraic expression for the total cost in dollars of 7 packages of markers.

WORDS:NUMBER OF PACKAGES TIMES COST PER PACKAGE

Let d = cost per package

An algebraic expression for the total cost in dollars is

7d

Nine students will purchase b books each. Write an algebraic expression for the total number of books the students will buy.

WORDS:NUMBER OF STUDENTS TIMES # OF BOOKS

PURCHASED EACH

Let b = # of books purchased each

An algebraic expression for the total number of books

is 9b

What is the cost of one pen if a package of 12 pens costs d dollars?

WORDS:COST PER PACKAGE DIVIDED BY # OF PENS IN

PACKAGE

Let d = cost per package

An algebraic expression for the total cost in dollars is

d

12

WE CAN ALSO WRITE WORD PHRASES FROM ALGEBRAIC

EXPRESSIONS

Write three different word phrases for x + 2 a number plus 2 a number increased by 2 two more than a number

Write three different word phrases for c - 50 a number minus 50 a number decreased by 50 50 less than a number

STEPS FOR EVALUATING ALGEBRAIC EXPRESSIONS

1. Replace the variables with the values that have been given.

2. Follow the rules for the order of operations. Example: Evaluate 50 – 3x when x = 7a. write the expression

50 – 3xb. replace the variable with its given value

50 – 3(7)c. multiply

50 – 21d. subtract 29

EVALUATE THESE ALGEBRAIC EXPRESSIONS

8x + 2let x = 3

9n let n = 4 6

10ab – 15let a = 2let b = 5

8(3) + 224 + 226

9(4) 636 = 6

6

10(2)(5) – 15 20(5) – 15100 – 1585