evaluating expressions and combining like terms
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Evaluating Expressions and Combining Like Terms. R. Portteus. Evaluating Expressions. Vocabulary: Variable – A symbol, usually a letter of the alphabet, such as the letter n, that is used to represent a number. - PowerPoint PPT PresentationTRANSCRIPT
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Evaluating Evaluating Expressions and Expressions and
Combining Like TermsCombining Like Terms
Evaluating Evaluating Expressions and Expressions and
Combining Like TermsCombining Like Terms
R. PortteusR. Portteus
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Evaluating Expressions• Vocabulary:
– Variable – A symbol, usually a letter of the alphabet, such as the letter n, that is used to represent a number.
– Variable expression (A.K.A. - Algebraic Expression) – An expression, such as n – 5, that consists of one or more numbers and variables along with one or more arithmetic operations. (Note: No equal sign)
– Evaluate a Variable Expression – write the expression, substitute a number for each variable, and simplify the result.
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How do you describe a variable expression?
Variable Expression
Meaning Operation
5x, 5·x, (5)(x) (same as x·5)
5 times x Multiplication
5 divided by x
Division
5 + x (same as x + 5)
5 plus x Addition
5 – x 5 minus x subtraction
xx
5,5
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Substitute 4 for n. Simplify
Simplify (means to solve the problem or perform as many of the indicated operations as possible.)
Simplify (means to solve the problem or perform as many of the indicated operations as possible.)
Solution:Solution: Substitute 4 for n. Simplify
Solution:Solution:
Evaluate a Variable Expression
• Example 1: Evaluate each expression when n = 4.a. n + 3
n + 3 = 4 + 3= 7
b. n – 3n – 3 = 4 – 3= 1
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Substitute 8 for x. Simplify
Solution:Solution:
Solution:Solution:
Using parenthesis is the preferred method to show multiplication. Additional ways to show multiplication are 5 · 8 and 5 x 8.
Using parenthesis is the preferred method to show multiplication. Additional ways to show multiplication are 5 · 8 and 5 x 8.
Substitute 8 for x. Simplify
Recall that division problems are also fractions – this problem could be written as:
Recall that division problems are also fractions – this problem could be written as:
44
2; 4
8
4
xx
because
x
Evaluate an Algebraic Expression
• Example 2: Evaluate each expression if x = 8.a. 5x
5x = 5(8)= 40
b. x ÷ 4x ÷ 4 = 8 ÷ 4= 2
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Substitute 4 for x; 6 for y. simplify
Solution:Solution:
Evaluating More Expressions
• Example 3: Evaluate each expression if x = 4, y = 6, and z = 24.a. 5xy
5xy = 5(4)(6)= 120
b.
= 4
Solution:Solution:
y
z
6
24
y
z
Substitute 24 for z; 6 for y. Simplify.
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A
A
A
A
A
A
Now You Try… Evaluate each expression given that
a = 6, b = 12, and c = 3.
1. 4ac2. a ÷ c3. a + b + c4. ba5. b – c6. c ÷ b
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Substitute the value for a = 6 and c = 3 into the problem and multiply
Substitute the value for a = 6 and c = 3 into the problem and multiply
Click to return to “You try it” slide
Click to return to “You try it” slide
You Try #1Evaluate each expression given that
a = 6, b = 12, and c = 3.1. 4ac
4ac = 4(6)(3)= (24)(3)= 72
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Substitute the value for a = 6 and c = 3 into the problem and divide
Substitute the value for a = 6 and c = 3 into the problem and divide
Click to return to “You try it” slide
Click to return to “You try it” slide
You Try #2Evaluate each expression given that
a = 6, b = 12, and c = 3.2. a ÷ c
a ÷ c = 6 ÷ 3= 2
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Substitute the value for a = 6, b=12, and c = 3 into the problem, then add.
Substitute the value for a = 6, b=12, and c = 3 into the problem, then add.
Click to return to “You try it” slide
Click to return to “You try it” slide
You Try #3Evaluate each expression given that
a = 6, b = 12, and c = 3.3. a + b + c
a + b + c = 6 + 12 + 3= 18 + 3= 21
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Substitute the value for b=12 and a = 6 into the problem, then multiply.
Substitute the value for b=12 and a = 6 into the problem, then multiply.
Click to return to “You try it” slide
Click to return to “You try it” slide
You Try #4Evaluate each expression given that
a = 6, b = 12, and c = 3.4. ba
ba = (12)(6)= 72
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Substitute the value for b=12 and a = 3 into the problem, then subtract.
Substitute the value for b=12 and a = 3 into the problem, then subtract.
Click to return to “You try it” slide
Click to return to “You try it” slide
You Try #5Evaluate each expression given that
a = 6, b = 12, and c = 3.5. b - c
b – c = 12 – 3= 9
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Substitute the value for c=3 and b = 12 into the problem, then Divide
Note: It is better to rewrite this division problem as a fraction.
This fraction can now be reduced to its simplest form.
Substitute the value for c=3 and b = 12 into the problem, then Divide
Note: It is better to rewrite this division problem as a fraction.
This fraction can now be reduced to its simplest form.
Divide both numerator and denominator by the GCF = (3) to reduce this fraction.
Divide both numerator and denominator by the GCF = (3) to reduce this fraction.
It is OK to have a fraction as an answer.
It is OK to have a fraction as an answer.
Click to return to “You try it” slide
Click to return to “You try it” slide
You Try #6Evaluate each expression given that
a = 6, b = 12, and c = 3.6. c ÷ b
12
3
b
cbc
4
1
3
3
12
3
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Combining Like Terms• Now that we have seen some algebraic
expressions, we need to know how to simplify them.
• Vocabulary– Like terms: In an expression, like terms are
the terms that have the same variables, raised to the same powers (same exponents).
• i.e. 4x and -3x or 2y2 and –y2
– Coefficient: A constant that multiplies a variable.
• i.e. the 3 in 3a or the -1 in –b
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Combining Like Terms• In algebra we often get very long
expressions, which we need to make simpler. Simpler expressions are easier to solve!
• To simplify an expression we collect like terms. Like terms include letters that are the same and numbers.
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Let’s try one…• Step One: Write the expression.
4x + 5x -2 - 2x + 7• Collect all the terms together which are alike. Remember that
each term comes with an operation (+,-) which goes before it. 4x, 5x, and -2x-2 and 7
• Simplify the variable terms. 4x+5x-2x = 9x-2x = 7x
• Simplify the constant (number) terms.-2+7 = 5
• You have a simplified expression by writing all of the results from simplifying.7x + 5
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Another example…• 10x – 4y + 3x2 + 2x – 2y
3x2
10x, 2x-4y – 2y
• 3x2 + 12x – 6y
Remember you cannot combine
terms with the same variable but
different exponents.
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Now you try…Simplify the following:• 5x + 3y - 6x + 4y + 3z • 3b - 3a - 5c + 4b• 4ab – 2a2b + 5 – ab + ab2 +
2a2b + 4• 5xy – 2yx + 7y + 3x – 4xy + 2x
A
A
A
A
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You Try #1• Simplify the following:1. 5x + 3y - 6x + 4y + 3z
5x, -6x3y, 4y3z-x + 7y + 3z
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You Try #2• Simplify the following:2. 3b - 3a - 5c + 4b
3b, 4b-3a-5c-3a + 7b – 5c
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You Try #3• Simplify the following:3. 4ab – 2a2b + 5 – ab + ab2 + 2a2b + 4
4ab, -ab-2a2b, 2a2b5, 4ab2
3ab + ab2 + 9
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You Try #4• Simplify the following:4. 5xy – 2yx + 7y + 3x – 4xy + 2x
5xy, -2yx, -4xy 7y3x, 2x-xy + 7y + 5x
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Conclusion• A variable or algebraic expression is an
expression that consists of one or more ________ and _________ along with one or more ________ _________. (Note: No _______ sign)
• To evaluate an expression write the _________, substitute a _______ for each variable, and _________ the result.
numbers variables
arithmetic operations
equal
expression number
simplify
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Conclusion Continued…• In an expression, __________ are
the terms that have the same ________, raised to the same ________ (same exponents).
• A coefficient is a number that ________ a variable.
like terms
variables
power
multiplies