Chapter 01 – Section 01
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Transcript of Chapter 01 – Section 01
Chapter 01 – Section 01
Variables and Expressions
© William James Calhoun
To translate verbal expressions into mathematical expressions and vice versa.
This section is the basics of the basics.
Terms to become familiar with:
• variables – symbol used to express an unspecified number
• algebraic expressions – one or more numbers and variables along with one or more arithmetic operations
• factors – quantities that are being multiplied
• product – the result of factors being multiplied
© William James Calhoun
EXAMPLE 1α: Write an algebraic expression for each verbal expression.a. three times a number x subtracted from 24
b. 5 greater than half of a number t
EX1EX1ββ
© William James Calhoun
EXAMPLE 1β: Write an algebraic expression for each verbal expression.a. m increased by 5
b. the difference of x and 9
c. 7 times the product of x and t
© William James Calhoun
EXAMPLE 2α: Write a verbal expression for each algebraic expression.a. (3 + b) ÷ y
b. 5y + 10x
EX2EX2ββ
© William James Calhoun
EXAMPLE 2β: Write a verbal expression for each algebraic expression.a. 9t
b. 8 + a
c. 7 – 3y
© William James Calhoun
More terms you will need to become familiar with:
• power – an expression with a superscript representing a number multiplied by itself a certain number of times
Examples of powers: 54 and x3
• base – the number or variable that is multiplied
• exponent – the superscript number that signifies the number of times multiplication should occur
45 = 4 * 4 * 4 * 4 * 4
four is multiplied by itself five times
{ = 1024
© William James Calhoun
EXAMPLE 3α: Write a power that represents the number of smallest squares in the large square.
EX3EX3ββ
Count the number of squares along one side.
There are 8 squares in each row.
Count the number of squares along the other side.
There are 8 squares in each column.
To find the number of smallest squares, you would multiply 8 * 8.
8 * 8 can be written as a power by 1) writing the base, 8, once2) writing the number of times multiplied, 2,
once superscripted
Answer:
82
© William James Calhoun
EXAMPLE 3β: Write a power that represents the number of smallest squares in the large square.
© William James Calhoun
EXAMPLE 4α: Evaluate 34.
EX4EX4ββ
Method 1Write the problem out in long form.3 * 3 * 3 * 3Multiply in small steps.3 * 3 = 99 * 3 = 2727 * 3 = 81
Method 2Use your calculator.Hit the “3” key.Hit the power key – “^” or “yx”.Hit the “4” key.Hit the “=“ key.Answer: 81.
© William James Calhoun
EXAMPLE 4β: Evaluate each expression.
a. 35 b. 53
© William James Calhoun
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