Download Simplify Algebraic Expressions

Main Idea and New Vocabulary
NGSSS
Example 1: Identify Parts of an Expression
Example 2: Simplify Algebraic Expressions
Example 3: Simplify Algebraic Expressions
Example 4: Real-World Example
Five-Minute Check
• Simplify algebraic expressions.
• term
• coefficient
• like terms
• constant
MA.912.A.3.1 Solve linear equations in one
variable that include simplifying algebraic
expressions.
MA.912.A.3.2 Identify and apply the
distributive, associative, and commutative
properties of real numbers and the properties
of equality.
Identify Parts of an Expression
Identify the terms, like terms, coefficients, and
constants in the expression 3x – 5 + 2x – x.
3x – 5 + 2x – x = 3x + (–5) + 2x + (–1x)
Answer:
• terms: 3x, –5, 2x, and –x
• like terms: 3x, 2x, and –x
• coefficients: 3, 2, and –1
• constant: –5
Rewrite the
expression.
Identify the terms, like terms, coefficients, and
constants in the expression n – 4 + 7n – 6n.
A. terms: n, –4, 7n, –6n; terms: like terms: n and
7n; coefficients: 1, 7, and –6; constant: –4
B. terms: n, –4, 7n, –6n; like terms: n, 7n, and
–6n; coefficients: 1, 7, and –6; constant: –4
C. terms: n, 4, 7n, 6n; like terms: n, 7n, and –6n;
coefficients: 1, –4, 7, and –6; constant: –4
D. terms: n, 4, 7n, 6n; like terms: n, 7n, and –6n;
coefficients: 1, –4, 7, and –6; constant: none
Simplify Algebraic Expressions
Write the expression 6n – n in simplest form.
6n and n are like terms.
6n – n = 6n – 1n
Identity Property; n = 1n
= (6 – 1)n
Distributive Property
= 5n
Simplify.
Answer: 5n
Write the expression 10w + w in simplest form.
A. 10w
B. 11w
C. 10w + 1
D. 10 + w
Simplify Algebraic Expressions
Write the expression 8z + z – 5 – 9z + 2 in
simplest form.
8z, z, and –9z are like terms.
–5 and 2 are also like terms.
8z + z – 5 – 9z + 2
= 8z + z + (–5) + (–9z) + 2
Definition of
subtraction
= 8z + z + (–9z) + (–5) + 2
Commutative
Property
= [8 + 1 + (–9)]z + (–5) + 2
Distributive Property
Simplify Algebraic Expressions
= 0z + (–3)
Simplify.
= 0 + (–3) or –3
0z = 0 • z or 0
Answer: –3
Write the expression 4t + 3 – t + 7 in simplest form.
A. 5t + 10
B. 4t – 4
C. 3t + 10
D. 3t – 4
GROCERIES Manfred buys some boxes of cereal
for $4.85 each and the same number of bags of
pretzels for $2.90 each. Write an expression in
simplest form that represents the total amount
spent.
4.85x + 2.90x = (4.85 + 2.90)x
= 7.75x
Distributive Property
Simplify.
Answer: The expression $7.75x represents the
total amount spent.
MOVIES Each person in a group buys a movie
ticket for $7.50 and a tub of popcorn for $3.80.
Write an expression in simplest form that
represents the total amount spent.
A. $11.30
B. $11.30x
C. $7.50x + $3.80
D. $7.50 + $3.80 + x
Identify the terms, like terms, coefficients, and
constants in the expression 8y – 3 + y.
A. terms: 8y, –3, y; like terms: 8y, y;
coefficients: 8, 1; constant: –3
B. terms: 8y, –3, y; like terms: 8y, y;
coefficients: 8, –3, 1; constant: none
C. terms: 8y; –3; like terms: 8, –3;
coefficients: 8, 1; constant: –3
D. terms: 8, –3, 1; like terms: 8y, y;
coefficients: 8, 1; constant: none
Identify the terms, like terms, coefficients, and
constants in the expression –22m – 2n + 1.
A. terms: –22, n, 1; no like terms;
coefficients: –22, –2; constant: 1
B. terms: –22m, –2n, 1; no like terms;
coefficients: –22, –2, 1; constant: none
C. terms: –22m, –2n, 1; no like terms;
coefficients: –22, –2; constant: 1
D. terms: –22m, –2n, 1; like terms: –22m, –2n;
coefficients: –22, –2; constant: 1
Write the expression 7k + 9k in simplest form.
A. 2k
B. 16k
C. 16 + 2k
D. 7k + 9k
Write the expression 14h – 3 – 11h in simplest form.
A. 0
B. –3h – 3
C. 3h – 3
D. 25h – 3
Sara has x number of apples, 3 times as many
oranges as apples, and 2 peaches. Write an
expression in simplest form that represents the
total number of fruits.
A. 3x + 2
B. 4x + 2
C. 5x
D. 7x + 2
Which expression represents
the perimeter of the triangle?
A. 5x + 1
B. 3x
C. 2x – 1
D. 6x