Identifying Parts in An Algebraic Expression: Worksheet 7.1 | PDF - Free Printable
Educational worksheet: Identifying Parts in An Algebraic Expression: Worksheet 7.1 | PDF. Download and print for classroom or home learning activities.
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Step-by-step solution for: Identifying Parts in An Algebraic Expression: Worksheet 7.1 | PDF
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Step-by-step solution for: Identifying Parts in An Algebraic Expression: Worksheet 7.1 | PDF
Here are the solutions to the problems on the worksheet, worked out step by step.
1. Identify the constant term in the expression: $2x + y + 3z + 5$
* Step-by-step: A constant term is a number that stands alone and does not have a variable (like $x$, $y$, or $z$) attached to it. In this list of terms ($2x$, $y$, $3z$, and $5$), the only one without a letter is $5$.
* Answer: $5$
2. Identify the like terms in the expression: $-12x + 15y - 17x + 16y$
* Step-by-step: Like terms are terms that have exactly the same variable part.
* Look for terms with $x$: We have $-12x$ and $-17x$. These match.
* Look for terms with $y$: We have $15y$ and $16y$. These match.
* Answer: The pairs of like terms are $-12x$ and $-17x$, and $15y$ and $16y$.
3. Identify the coefficient of term $g^2$ in the expression: $2f + 9g + 4g^2 - 3h$
* Step-by-step: The coefficient is the number multiplied by the variable. Find the term with $g^2$, which is $4g^2$. The number in front of $g^2$ is $4$.
* Answer: $4$
4. Identify the term with coefficient $-3$ in the expression: $9a^3 + 4b^2 - 3c + 11$
* Step-by-step: Look through the expression for a number $-3$ attached to a variable. We see $-3c$. The entire term includes the variable.
* Answer: $-3c$
5. Identify the highest degree/order of the expression: $11x + 9x^3 - 8y + 5$
* Step-by-step: The degree is determined by the highest exponent (power) on any variable in the expression.
* $11x$ has an exponent of $1$ ($x^1$).
* $9x^3$ has an exponent of $3$.
* $-8y$ has an exponent of $1$ ($y^1$).
* $5$ has an exponent of $0$.
* The highest number among these exponents is $3$.
* Answer: $3$
6. Identify the constant term in the expression: $3x + 45y + 13z + 43$
* Step-by-step: Look for the number that does not have a variable ($x, y, z$) next to it. That number is $43$.
* Answer: $43$
7. Identify the like terms in the expression: $6a + 4b + 2b + 8a$
* Step-by-step: Group the terms with the same letters.
* Terms with $a$: $6a$ and $8a$.
* Terms with $b$: $4b$ and $2b$.
* Answer: The pairs of like terms are $6a$ and $8a$, and $4b$ and $2b$.
8. Identify the unlike terms in the expression: $3a + 11b + 3c + 4a + 3b$
* Step-by-step: "Unlike terms" usually refers to terms that cannot be combined because their variables are different. Looking at the whole expression, we have variables $a$, $b$, and $c$. Any term with $a$ is unlike any term with $b$ or $c$. For example, $3a$ and $11b$ are unlike terms. $11b$ and $3c$ are unlike terms.
* Answer: Examples of unlike terms include $3a$ and $11b$, or $11b$ and $3c$. (Generally, terms with different variables are unlike).
9. Identify the coefficient of second term in the expression: $3x^2 + 7y^3 + 2x + 9y - 5y^2$
* Step-by-step: Count the terms from left to right.
1. First term: $3x^2$
2. Second term: $+ 7y^3$
The coefficient is the number part of that second term.
* Answer: $7$
10. Identify the term whose coefficient is $-12$ in the expression: $98x - 12xy^2 - 15xy^2$
* Step-by-step: Look for the number $-12$ in the expression. It appears in the middle: $-12xy^2$. The "term" includes the variables attached to it.
* Answer: $-12xy^2$
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Final Answer:
1. 5
2. $-12x$ and $-17x$; $15y$ and $16y$
3. 4
4. $-3c$
5. 3
6. 43
7. $6a$ and $8a$; $4b$ and $2b$
8. Terms with different variables (e.g., $3a$ and $11b$)
9. 7
10. $-12xy^2$
1. Identify the constant term in the expression: $2x + y + 3z + 5$
* Step-by-step: A constant term is a number that stands alone and does not have a variable (like $x$, $y$, or $z$) attached to it. In this list of terms ($2x$, $y$, $3z$, and $5$), the only one without a letter is $5$.
* Answer: $5$
2. Identify the like terms in the expression: $-12x + 15y - 17x + 16y$
* Step-by-step: Like terms are terms that have exactly the same variable part.
* Look for terms with $x$: We have $-12x$ and $-17x$. These match.
* Look for terms with $y$: We have $15y$ and $16y$. These match.
* Answer: The pairs of like terms are $-12x$ and $-17x$, and $15y$ and $16y$.
3. Identify the coefficient of term $g^2$ in the expression: $2f + 9g + 4g^2 - 3h$
* Step-by-step: The coefficient is the number multiplied by the variable. Find the term with $g^2$, which is $4g^2$. The number in front of $g^2$ is $4$.
* Answer: $4$
4. Identify the term with coefficient $-3$ in the expression: $9a^3 + 4b^2 - 3c + 11$
* Step-by-step: Look through the expression for a number $-3$ attached to a variable. We see $-3c$. The entire term includes the variable.
* Answer: $-3c$
5. Identify the highest degree/order of the expression: $11x + 9x^3 - 8y + 5$
* Step-by-step: The degree is determined by the highest exponent (power) on any variable in the expression.
* $11x$ has an exponent of $1$ ($x^1$).
* $9x^3$ has an exponent of $3$.
* $-8y$ has an exponent of $1$ ($y^1$).
* $5$ has an exponent of $0$.
* The highest number among these exponents is $3$.
* Answer: $3$
6. Identify the constant term in the expression: $3x + 45y + 13z + 43$
* Step-by-step: Look for the number that does not have a variable ($x, y, z$) next to it. That number is $43$.
* Answer: $43$
7. Identify the like terms in the expression: $6a + 4b + 2b + 8a$
* Step-by-step: Group the terms with the same letters.
* Terms with $a$: $6a$ and $8a$.
* Terms with $b$: $4b$ and $2b$.
* Answer: The pairs of like terms are $6a$ and $8a$, and $4b$ and $2b$.
8. Identify the unlike terms in the expression: $3a + 11b + 3c + 4a + 3b$
* Step-by-step: "Unlike terms" usually refers to terms that cannot be combined because their variables are different. Looking at the whole expression, we have variables $a$, $b$, and $c$. Any term with $a$ is unlike any term with $b$ or $c$. For example, $3a$ and $11b$ are unlike terms. $11b$ and $3c$ are unlike terms.
* Answer: Examples of unlike terms include $3a$ and $11b$, or $11b$ and $3c$. (Generally, terms with different variables are unlike).
9. Identify the coefficient of second term in the expression: $3x^2 + 7y^3 + 2x + 9y - 5y^2$
* Step-by-step: Count the terms from left to right.
1. First term: $3x^2$
2. Second term: $+ 7y^3$
The coefficient is the number part of that second term.
* Answer: $7$
10. Identify the term whose coefficient is $-12$ in the expression: $98x - 12xy^2 - 15xy^2$
* Step-by-step: Look for the number $-12$ in the expression. It appears in the middle: $-12xy^2$. The "term" includes the variables attached to it.
* Answer: $-12xy^2$
──────────────────────────────────────
Final Answer:
1. 5
2. $-12x$ and $-17x$; $15y$ and $16y$
3. 4
4. $-3c$
5. 3
6. 43
7. $6a$ and $8a$; $4b$ and $2b$
8. Terms with different variables (e.g., $3a$ and $11b$)
9. 7
10. $-12xy^2$
Parent Tip: Review the logic above to help your child master the concept of parts of an expression worksheet.
![Identify Parts Of An Expression Worksheet [PDF] (6.RP.A.1): 6th ...](/images2/parts-of-an-expression-worksheet/parts-of-an-expression-worksheet-29.png)
