Search | Evaluating Algebraic Expression | Page 1 | Weekly Sort - Free Printable

Let’s solve each expression one by one, using the given values for the variables. We’ll follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division left to right, Addition/Subtraction left to right).

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1. $(a - (-8) \cdot (-3)) \div 7 = a$
Given: $a = 4$, $b = 0$ → but b is not used here.

First, compute inside parentheses:
- $(-8) \cdot (-3) = 24$
- So: $a - 24 = 4 - 24 = -20$
- Then divide by 7: $-20 \div 7 = -\frac{20}{7}$

Wait — that doesn’t look like it equals “a” unless we’re solving for something? But the problem says “evaluate each expression using the values given.” And it shows “= a” at the end — that might be a typo or mislabeling. Let me check the original image again mentally.

Actually, looking back — in the worksheet, each problem has an expression and then below it, variable assignments. The “= a” etc. are probably just labels for the answer box, NOT part of the equation. So we ignore the “= a”, “= n”, etc. — they’re just placeholders for where you write your answer.

So let’s re-solve #1 correctly:

Expression: $(a - (-8) \cdot (-3)) \div 7$

With $a = 4$:

Step 1: Multiply: $(-8) \cdot (-3) = 24$

Step 2: Subtract from a: $4 - 24 = -20$

Step 3: Divide by 7: $-20 ÷ 7 = -\frac{20}{7} ≈ -2.857...$

But maybe we leave as fraction? Or did I misread?

Wait — perhaps the expression is meant to be evaluated numerically, and the “= a” is just labeling the answer space. So yes, answer is $-\frac{20}{7}$.

But let’s double-check all problems carefully.

Actually, let’s go one by one with full care.

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Problem 1:
$(a - (-8) \cdot (-3)) \div 7$
$a = 4$

→ $(-8) × (-3) = +24$
→ $a - 24 = 4 - 24 = -20$
→ $-20 ÷ 7 = -\frac{20}{7}$

✔ Final for #1: $-\frac{20}{7}$

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Problem 2:
$6 + 3 - 2 - (-8 - b)$
$b = 8$

First, simplify inside parentheses:
$-8 - b = -8 - 8 = -16$

Now plug in:
$6 + 3 - 2 - (-16)$

Remember: minus a negative = plus positive
So: $6 + 3 - 2 + 16$

Left to right:
6 + 3 = 9
9 - 2 = 7
7 + 16 = 23

✔ Final for #2: 23

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Problem 3:
$5 \times [1 + (5 + 6 + a)]$
$a = -6$

Inside innermost parentheses:
$5 + 6 + (-6) = 5 + 6 - 6 = 5$

Then: $1 + 5 = 6$

Then multiply: $5 × 6 = 30$

✔ Final for #3: 30

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Problem 4:
$e + (-2) ÷ [4 + (4 - 3)] - 4$
$e = -5$

First, innermost: $4 - 3 = 1$

Then: $4 + 1 = 5$

Now division: $(-2) ÷ 5 = -\frac{2}{5}$

Now expression becomes:
$e + (-\frac{2}{5}) - 4 = -5 - \frac{2}{5} - 4$

Combine integers: $-5 - 4 = -9$

Then: $-9 - \frac{2}{5} = -\frac{45}{5} - \frac{2}{5} = -\frac{47}{5}$

✔ Final for #4: $-\frac{47}{5}$ or $-9.4$

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Problem 5:
$10 + (6 + (a - a)) - a + 9$
$a = 3$

Note: $a - a = 0$ always.

So: $6 + 0 = 6$

Then: $10 + 6 - a + 9 = 16 - a + 9$

Since $a = 3$: $16 - 3 + 9 = 13 + 9 = 22$

✔ Final for #5: 22

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Problem 6:
$(2 - (-3) + (10) \cdot 3) + 5$
$n = 4$, $v = -2$ → neither used? Wait, expression has no n or v. Maybe typo? Just evaluate as is.

Compute step by step:

First: $2 - (-3) = 2 + 3 = 5$

Then: $10 · 3 = 30$

Add them: $5 + 30 = 35$

Then +5: $35 + 5 = 40$

✔ Final for #6: 40

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Problem 7:
$v + (-2) + (-3)$
$v = -2$

Plug in: $-2 + (-2) + (-3) = -2 -2 -3 = -7$

✔ Final for #7: -7

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Problem 8:
$(-7) + ((9 - (4 - 3)) \cdot 7)$
$z = 10$ → not used.

Innermost: $4 - 3 = 1$

Then: $9 - 1 = 8$

Then: $8 · 7 = 56$

Then: $-7 + 56 = 49$

✔ Final for #8: 49

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Problem 9:
$e - 7 + v - ((y - 7))$
$e = -5$, $v = -2$, $y = 10$

First, compute inside parentheses: $y - 7 = 10 - 7 = 3$

So expression: $e - 7 + v - 3$

Plug in: $-5 - 7 + (-2) - 3$

Left to right:

-5 -7 = -12
-12 + (-2) = -14
-14 - 3 = -17

✔ Final for #9: -17

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Problem 10:
$(n - 6 + 2) + (c^2 + c) - 2$
$n = 4$, $c = 6$

First part: $n - 6 + 2 = 4 - 6 + 2 = 0$

Second part: $c^2 + c = 6^2 + 6 = 36 + 6 = 42$

Now combine: $0 + 42 - 2 = 40$

✔ Final for #10: 40

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Now let’s list all answers clearly:

1. $-\frac{20}{7}$
2. 23
3. 30
4. $-\frac{47}{5}$
5. 22
6. 40
7. -7
8. 49
9. -17
10. 40

I’ll present them in order as requested.

Final Answer:
1. -20/7
2. 23
3. 30
4. -47/5
5. 22
6. 40
7. -7
8. 49
9. -17
10. 40