Step-by-Step Reasoning:
1.
Understand the Definitions:
*
Expression: A mathematical phrase that contains numbers, variables, and operations (like $+$, $-$, $\times$, $\div$). It does *not* have an equal sign ($=$). Think of it like a phrase in English (e.g., "the red ball"). Examples: $2x + 5$, $7 - y$.
*
Equation: A mathematical sentence that states two expressions are equal. It *must* have an equal sign ($=$). Think of it like a complete sentence (e.g., "The red ball is mine"). Examples: $2x + 5 = 10$, $y = 7$.
2.
Analyze Part A (Identify each item):
*
1) $4x + 9$: There is no equal sign. It is just a combination of terms. $\rightarrow$
Expression
*
2) $-13 = 2a$: There is an equal sign connecting $-13$ and $2a$. $\rightarrow$
Equation
*
3) $7 = 12 - 8v$: There is an equal sign connecting $7$ and $12 - 8v$. $\rightarrow$
Equation
*
4) $\frac{y}{8} + 1$: There is no equal sign. $\rightarrow$
Expression
*
5) $-3(3mn)$: There is no equal sign. It represents multiplication. $\rightarrow$
Expression
*
6) $b + c = -5$: There is an equal sign. $\rightarrow$
Equation
3.
Analyze Part B, Question 1 (Which are expressions?):
* Look for items *without* an equal sign.
* a) $s - 3t$: No equal sign. (Expression)
* b) $p + 6$: No equal sign. (Expression)
* c) $9 - \frac{d}{5}$: No equal sign. (Expression)
* d) $y - 2 = z$: Has an equal sign. (Equation)
*
Result: a, b, and c are expressions.
4.
Analyze Part B, Question 2 (Which are equations?):
* Look for items *with* an equal sign.
* a) $-x + 1 = 7$: Has an equal sign. (Equation)
* b) $2r - s$: No equal sign. (Expression)
* c) $8uv$: No equal sign. (Expression)
* d) $3c = 7d$: Has an equal sign. (Equation)
*
Result: a and d are equations.
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Final Answer:
A) Determine whether each is an expression or equation:
1) Expression
2) Equation
3) Equation
4) Expression
5) Expression
6) Equation
B) 1) Which of the following are expressions?
a) $s - 3t$
b) $p + 6$
c) $9 - \frac{d}{5}$
B) 2) Which of the following are equations?
a) $-x + 1 = 7$
d) $3c = 7d$
Parent Tip: Review the logic above to help your child master the concept of equation worksheet.
