Problem Analysis:
The task involves identifying whether given mathematical statements are
expressions or
equations. Let's break this down step by step.
#### Definitions:
1.
Expression: A mathematical phrase that combines numbers, variables, and operators but does not contain an equals sign (`=`). It represents a value.
2.
Equation: A mathematical statement that asserts the equality of two expressions, containing an equals sign (`=`).
Part A: Determine Whether Each is an Expression or Equation
We will analyze each statement one by one:
1.
1) \( 4s + 9 \)
- This is a combination of a variable (`s`) and a constant (`9`) with an operator (`+`).
- There is no equals sign.
-
Conclusion: This is an
expression.
2.
2) \( -13 = 2a \)
- This contains an equals sign (`=`), asserting that `-13` is equal to `2a`.
-
Conclusion: This is an
equation.
3.
3) \( 7 = 12 - 8r \)
- This contains an equals sign (`=`), asserting that `7` is equal to `12 - 8r`.
-
Conclusion: This is an
equation.
4.
4) \( \frac{y}{8} + 1 \)
- This is a combination of a variable (`y`), a constant (`1`), and operators (`/`, `+`).
- There is no equals sign.
-
Conclusion: This is an
expression.
5.
5) \( -3(3mn) \)
- This is a combination of constants (`-3`, `3`) and variables (`m`, `n`) with operators (`*`).
- There is no equals sign.
-
Conclusion: This is an
expression.
6.
6) \( b + c = -5 \)
- This contains an equals sign (`=`), asserting that `b + c` is equal to `-5`.
-
Conclusion: This is an
equation.
Part B: Identify Expressions and Equations
#### 1) Which of the following are expressions?
We will analyze each option:
-
a) \( s - 3t \)
- This is a combination of variables (`s`, `t`) with an operator (`-`).
- There is no equals sign.
-
Conclusion: This is an
expression.
-
b) \( p + 6 \)
- This is a combination of a variable (`p`) and a constant (`6`) with an operator (`+`).
- There is no equals sign.
-
Conclusion: This is an
expression.
-
c) \( 9 - \frac{a}{5} \)
- This is a combination of a constant (`9`), a variable (`a`), and operators (`-`, `/`).
- There is no equals sign.
-
Conclusion: This is an
expression.
-
d) \( y - 2 = z \)
- This contains an equals sign (`=`), asserting that `y - 2` is equal to `z`.
-
Conclusion: This is an
equation.
Final Answer for Part B.1:
\[
\boxed{\text{a, b, c}}
\]
#### 2) Which of the following are equations?
We will analyze each option:
-
a) \( -x + 1 = 7 \)
- This contains an equals sign (`=`), asserting that `-x + 1` is equal to `7`.
-
Conclusion: This is an
equation.
-
b) \( 2r - s \)
- This is a combination of variables (`r`, `s`) with an operator (`-`).
- There is no equals sign.
-
Conclusion: This is an
expression.
-
c) \( 8uv \)
- This is a combination of variables (`u`, `v`) with an operator (`*`).
- There is no equals sign.
-
Conclusion: This is an
expression.
-
d) \( 3c = 7d \)
- This contains an equals sign (`=`), asserting that `3c` is equal to `7d`.
-
Conclusion: This is an
equation.
Final Answer for Part B.2:
\[
\boxed{\text{a, d}}
\]
Final Summary:
-
Part A Answers:
1. Expression
2. Equation
3. Equation
4. Expression
5. Expression
6. Equation
-
Part B Answers:
1. Expressions: \( \boxed{\text{a, b, c}} \)
2. Equations: \( \boxed{\text{a, d}} \)
This completes the solution. If you have any further questions, feel free to ask!
Parent Tip: Review the logic above to help your child master the concept of algebraic problems worksheet.
