Question

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

Step 1: Identify Like Terms

Like terms are terms with the same variable (or constant terms). Here, $-2.5x$ and $1.7x$ have the variable $x$, so they are like terms. The term $3.9$ is a constant (no variable).

Step 2: List Variables

The only variable present in the expression is $x$.

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

Step 1: Identify Like Terms

There are no like terms here because $1\frac{1}{2}$ is a constant, $t$ has variable $t$, and $\frac{2}{3}s$ has variable $s$. All terms have different "types" (constant, $t$, $s$), so no like terms.

Step 2: List Variables

The variables present are $t$ and $s$.

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

Step 1: Identify Like Terms

The terms $15k$ and $\frac{2}{5}k$ have the variable $k$, so they are like terms. The term $-3m$ has variable $m$ (different from $k$), so it is not a like term with the $k$-terms.

Step 2: List Variables

The variables present are $k$ and $m$.

Final Answers (Summary)

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

Answer:

Part a: $-2.5x + 3.9 + 1.7x$

Step 1: Identify Like Terms

Like terms are terms with the same variable (or constant terms). Here, $-2.5x$ and $1.7x$ have the variable $x$, so they are like terms. The term $3.9$ is a constant (no variable).

Step 2: List Variables

The only variable present in the expression is $x$.

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

Step 1: Identify Like Terms

There are no like terms here because $1\frac{1}{2}$ is a constant, $t$ has variable $t$, and $\frac{2}{3}s$ has variable $s$. All terms have different "types" (constant, $t$, $s$), so no like terms.

Step 2: List Variables

The variables present are $t$ and $s$.

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

Step 1: Identify Like Terms

The terms $15k$ and $\frac{2}{5}k$ have the variable $k$, so they are like terms. The term $-3m$ has variable $m$ (different from $k$), so it is not a like term with the $k$-terms.

Step 2: List Variables

The variables present are $k$ and $m$.

Final Answers (Summary)

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