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Translating Expression
Chapter 1, Lesson 1
Objectives
• Translate verbal expressions into
numerical expressions.
• Write numerical expressions from verbal
expressions.
• Translate numerical expressions into
verbal expressions.
• Write verbal expressions from numerical
expressions.
Numerical Expressions
• Two or more numbers joined by operations
such as addition, subtraction, multiplication
and division.
• NO EQUALS SIGN IS USED!!!!!!
• Constants—Terms used in mathematics for
any number without a variable.
• Parentheses can also be used.
Variable Expressions
• Variable—a letter of the
alphabet that represents
unknown values.
• Coefficient—Number
attached to variable.
• Variable Expressions—
mathematical statements
that contains one or more
variables and/or
numbers.
• Like Terms—terms
that have identical
variable parts.
• Unlike Terms—terms
that have different
variable parts
• NO EQUALS SIGN IS
USED!!!!
Addition
• More Than
– Three more than a
number
• Sum of
– Two minus the sum of
a number and 20
– “of” with an operation
BEFORE it means
parentheses.
– 2 – (n + 20)
• Increased by
– A number increased by
negative eight
– y + (-8)
– Quantity of
– What is the quantity of the
boxes?
• Total of
• What is the total of the
sale?
• Plus
– Six plus a number
Subtraction
• Difference Of
– Three plus the
difference of a number
and 20.
(x – 20)
• Decreased by
– Negative two
decreased by a
number
-2 - n
• Less than
– Seven less than a
number
p–7
• Minus
– Three minus a
negative number.
3 – (-n)
Multiplication
• Times
• Two times a number
» 2n
• The Product Of
• Three plus the product of 6 and a number x.
» 3 + (6n)
• Multiplied By
• A number multiplied by negative eleven
» -11n
Multiplication Sign Change
• We no longer use “x” for multiplication.
• Since “x” is a variable and “x” means
multiplication, it will get confusing.
• Therefore we represent multiplication with:
– •
– Putting everything side by side (separating
numbers with parentheses. 3(4)xyz
Division
• The quotient of…
• The quotient of six times a number and three plus
a number
• Divided by
• Seven divided by a number
Just So You Know…
Write an algebraic expression for five less than a
number c.
The words less than suggest subtraction.
a number c
less
five
c
–
5
Answer: Thus, the algebraic expression is
.
Write an algebraic expression for the sum of 9 and 2
times the number d.
Sum implies add, and times implies multiply.
Answer: The expression can be written as
.
Write an algebraic expression for two thirds of the
original volume v.
The word of implies multiply.
Answer: The expression can be written as
Write an algebraic expression for each
verbal expression.
a. nine more than a number h
Answer:
b. the difference of 6 and 4 times a number x
Answer:
c. one half the size of the original perimeter p
Answer:
Exponents
Write the product of
algebraically.
Answer:
to the seventh power
Write the sum of 11 and x to the third power
algebraically.
Answer:
Write each expression algebraically.
a. the difference of 12 and x squared
Answer:
b. the quotient of 6 and x to the fifth power
Answer:
Write a verbal expression for
.
Answer: the quotient of 8 times x squared and 5
Write a verbal expression for
.
Answer: the difference of y to the fifth power and
16 times y
Write a verbal expression for each
algebraic expression.
a.
Answer: 7 times a to the fourth power
b.
Answer: the sum of x squared and 3
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Order of Operations
Chapter 1, Lesson 2
Objectives
1. Evaluate and simplify expressions using
substitution and order of operations.
2. Evaluate powers and exponents.
3. Learn how to convert decimals to
fractions and fractions to decimals using
a Casio calculator.
Order of Operations
WHEN TO USE
1. To simplify numerical
expressions
• Parentheses
2. To simplify verbal
expressions
• Multiply/Divide from
left to right
3. To simplify same-side
like terms
• Add/Subtract from left
to right
• Exponents
Parentheses
• In Algebra I, parentheses is ALWAYS
first!!!!!!!!!!!
• (3 + 4) = 7 (order of operations)
• 3(x + 2) = 3x + 6 (distributive property)
Exponents
Evaluate .
Use 3 as a factor 4 times.
Answer:
Multiply.
Evaluate
.
Use 8 as a factor 2 times.
Answer:
Multiply.
Evaluate each expression.
a.
Answer: 625
b.
Answer: 32
Other Operations
• Multiply/Divide FROM LEFT TO RIGHT!!!
• Add/Subtract FROM LEFT TO RIGHT!!!
Evaluate
.
Multiply 2 and 3.
Add 6 and 4.
Answer:
Subtract 10 and 6.
Evaluate
Evaluate powers.
Divide 48 by 8.
Multiply 6 and 3.
Answer:
Add 18 and 5.
Evaluate each expression.
a.
Answer: 23
b.
Answer: 7
Evaluate
.
Evaluate inside grouping symbols.
Multiply.
Answer:
Multiply.
Evaluate
.
Evaluate innermost
expression first.
Evaluate expression in
grouping symbol.
Evaluate power.
Answer:
Multiply.
Evaluate each expression.
a.
Answer: 88
b.
Answer: 3
Evaluate
Evaluate the power in
the numerator.
Multiply 6 and 2 in
the numerator.
Subtract 32 and 12 in
the numerator.
Evaluate the power in
the denominator.
Multiply 5 and 3 in
the denominator.
Answer:
Subtract from left to right
in the denominator. Then
simplify.
Evaluate
Answer: 1
Solve
Original equation
Add 8 and 2 in the numerator.
Subtract 5 and 3 in the denominator.
Evaluate the power in the denominator.
Simplify.
Answer:
Divide.
Answer: 6
Simplify
The fraction bar indicates division.
However, you cannot combine
-39b and 65 (Unlike terms)
Therefore, you have to split the
fraction ONLY when there is
ADDITION OR SUBTRACTION on
top!!!
-3b + 5
Simplify
Answer:
Substitution
• When a variable stands alone and is equal
to a constant, another variable or
expression, then wherever I see the
variable that stands alone, I can substitute
whatever it is equal to in for the variable
that stands alone.
Evaluate
Replace x with 4, y with 3
and z with 2.
Evaluate .
Subtract 16 and 3.
Evaluate
.
Multiply 2 and 13.
Answer:
Add.
Replace y with 12.
Answer:
Simplify.
Answer: 10
Evaluate
Answer: 28
.
Architecture Each of the four sides of the Great
Pyramid at Giza, Egypt, is a triangle. The base of
each triangle originally measured 230 meters. The
height of each triangle originally measured 187
meters. The area of any triangle is one-half the
product of the length of the base b and the height h.
Write an expression that represents the area of one
side of the Great Pyramid.
one half of the product of length of base and height
Answer:
Find the area of one side of the Great Pyramid.
Evaluate
Multiply 230 by 187.
.
Divide 43,010 by 2.
Answer: The area of one side of the Great
Pyramid is 21,505 .
Find the area of a triangle with a base of 123 feet and
a height of 62 feet.
Answer:
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Distributive Property
Objectives
• Use the distributive property to simplify
expressions.
• Simplify expressions by combining like
terms.
• Determine if expressions are simplified or
not.
Distributive Property
If the value of a is
positive, then the
following can be done.
If the value of “a” is
negative, then the
following can be done.
– If a(b + c), then ab + ac.
– If –a(b – c), then –ab + ac.
– If a(b – c), then ab – ac.
– If –a(-b + c), then ab – ac.
– If a(-b + c), then –ab + ac.
– If –a(-b – c), then ab + ac
– If a(-b – c), then –ab - ac.
– -a(b + c), then –ab – ac
using the Distributive Property.
Then evaluate.
Distributive Property.
Multiply.
Answer:
Add.
using the Distributive Property.
Then evaluate.
Answer:
using the Distributive Property.
Then evaluate.
Distributive Property.
Multiply.
Answer:
Subtract.
using the Distributive Property.
Then evaluate.
Answer:
Terms
Like & Unlike Terms
Like Terms
Unlike Terms
Simplify & Simplified
• Simplify – Combine Your Like Terms
• Perform as many of the indicated operations as
possible
• Simplified
• Your are done when only unlike terms remain
Rewrite
Then simplify.
using the Distributive Property.
Distributive Property
Answer:
Multiply.
Rewrite
Then simplify.
using the Distributive Property.
Distributive
Property
Answer:
Multiply.
Rewrite each product using the Distributive Property.
Then simplify.
a.
Answer:
b.
Answer:
Simplify
.
Distributive Property
Answer:
Substitution
Simplify
.
Distributive Property
Answer:
Substitution
Simplify each expression.
a.
Answer: 5x
b.
Answer:
Distributive Property
Multiply.
Commutative (+)
Associative (+)
Distributive Property
Answer:
Substitution
Answer:
Use the expression three times the sum of 3x and 2y
added to five times the sum of x and 4y.
Write an algebraic expression for the verbal expression.
three times the sum
of 3x and 2y
Answer:
added to
five times the sum
of x and 4y
Cars Find what the total cost of the Morris family
operating two cars would have been in 1985, if they
drove the first car 18,000 miles and the second car
16,000 miles.
USA TODAY Snapshots®
Use the Distributive Property to
write and evaluate an expression.
Distributive
Property
Multiply.
Add.
Answer: It would have cost them $7820.
Cars Find what the total cost of the Morris family
operating two cars would have been in 1995, if they
drove the first car 18,000 miles and the second car
16,000 miles.
USA TODAY Snapshots®
Answer: $13,940
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