Question

think about what you know about expressions. fill in each box. use words, numbers, and pictures. show as many ideas as you can.

word	in my own words	examples
like terms
term
variable

2 for each expression, circle any like terms and list any variables.

a. $-2.5x + 3.9 + 1.7x$

b. $1\frac{1}{2} + t + \frac{2}{3}s$

c. $15k + \frac{2}{5}k - 3m$

Explanation:

Part 1: Defining Terms (Table Completion)

Word	In My Own Words	Examples
like terms	Terms with the same variable (or no variable) and same exponent on the variable.	\( 2x \) and \( 3x \); \( 4 \) and \( 7 \); \( 5y^2 \) and \( 9y^2 \)
term	A single part of an expression, separated by + or −.	In \( 3x + 2 \), the terms are \( 3x \) and \( 2 \); in \( 4y - 7z + 1 \), terms are \( 4y \), \( -7z \), \( 1 \)
variable	A letter representing an unknown or changing value.	\( x \) in \( 2x \); \( t \) in \( 5t + 3 \); \( s \) in \( \frac{2}{3}s \)

Part 2: Analyzing Expressions

a. \( -2.5x + 3.9 + 1.7x \)

• Like Terms: \( -2.5x \) and \( 1.7x \) (both have variable \( x \) with exponent 1)
• Variables: \( x \)

b. \( 1\frac{1}{2} + t + \frac{2}{3}s \)

• Like Terms: None (terms are \( 1\frac{1}{2} \) (constant), \( t \) (variable \( t \)), \( \frac{2}{3}s \) (variable \( s \))—no shared variables)
• Variables: \( t \), \( s \)

c. \( 15k + \frac{2}{5}k - 3m \)

• Like Terms: \( 15k \) and \( \frac{2}{5}k \) (both have variable \( k \) with exponent 1)
• Variables: \( k \), \( m \)

Final Answers (Expression Analysis)

a. Like terms: \( \boldsymbol{-2.5x} \) and \( \boldsymbol{1.7x} \); Variables: \( \boldsymbol{x} \)
b. Like terms: None; Variables: \( \boldsymbol{t} \), \( \boldsymbol{s} \)
c. Like terms: \( \boldsymbol{15k} \) and \( \boldsymbol{\frac{2}{5}k} \); Variables: \( \boldsymbol{k} \), \( \boldsymbol{m} \)

Answer:

Part 1: Defining Terms (Table Completion)

Word	In My Own Words	Examples
like terms	Terms with the same variable (or no variable) and same exponent on the variable.	\( 2x \) and \( 3x \); \( 4 \) and \( 7 \); \( 5y^2 \) and \( 9y^2 \)
term	A single part of an expression, separated by + or −.	In \( 3x + 2 \), the terms are \( 3x \) and \( 2 \); in \( 4y - 7z + 1 \), terms are \( 4y \), \( -7z \), \( 1 \)
variable	A letter representing an unknown or changing value.	\( x \) in \( 2x \); \( t \) in \( 5t + 3 \); \( s \) in \( \frac{2}{3}s \)

Part 2: Analyzing Expressions

a. \( -2.5x + 3.9 + 1.7x \)

• Like Terms: \( -2.5x \) and \( 1.7x \) (both have variable \( x \) with exponent 1)
• Variables: \( x \)

b. \( 1\frac{1}{2} + t + \frac{2}{3}s \)

• Like Terms: None (terms are \( 1\frac{1}{2} \) (constant), \( t \) (variable \( t \)), \( \frac{2}{3}s \) (variable \( s \))—no shared variables)
• Variables: \( t \), \( s \)

c. \( 15k + \frac{2}{5}k - 3m \)

• Like Terms: \( 15k \) and \( \frac{2}{5}k \) (both have variable \( k \) with exponent 1)
• Variables: \( k \), \( m \)

Final Answers (Expression Analysis)

a. Like terms: \( \boldsymbol{-2.5x} \) and \( \boldsymbol{1.7x} \); Variables: \( \boldsymbol{x} \)
b. Like terms: None; Variables: \( \boldsymbol{t} \), \( \boldsymbol{s} \)
c. Like terms: \( \boldsymbol{15k} \) and \( \boldsymbol{\frac{2}{5}k} \); Variables: \( \boldsymbol{k} \), \( \boldsymbol{m} \)