Pre-Algebra Expressions worksheet for evaluating algebraic expressions with the variable y = 82.

Explanation:
We are given 10 expressions to evaluate, and we know that y = 82.
For each expression, we substitute 82 for y, then follow the order of operations (parentheses first, then division).

Let’s go one by one:

1. (y + 49) ÷ 71
→ (82 + 49) ÷ 71 = 131 ÷ 71
→ 131 ÷ 71 = 131/71 or as a decimal ≈ 1.845…
But since this is pre-algebra and likely expects exact values (possibly simplified fraction or whole number), let’s keep it as a fraction unless it divides evenly.
Check: 71 × 1 = 71, 71 × 2 = 142 > 131 → not whole. So answer is 131/71.
Wait — but maybe the worksheet expects decimal? Let's double-check all — maybe some are whole numbers.

Hold on — let’s check if any simplify nicely. Maybe I made a mistake: the problem says “Show your work” and uses division symbol “÷”, so likely expects exact results — possibly fractions or whole numbers.

Let’s compute each carefully:

1. (y + 49) ÷ 71 = (82 + 49) ÷ 71 = 131 ÷ 71
→ 131 and 71 share no common factors (71 is prime, 71×1=71, 71×2=142 >131), so 131/71

2. (y + 83) ÷ 40 = (82 + 83) ÷ 40 = 165 ÷ 40
Simplify: divide numerator and denominator by 5 → 33 ÷ 8 = 33/8 or 4.125

3. (y + 54) ÷ 54 = (82 + 54) ÷ 54 = 136 ÷ 54
Simplify: divide by 2 → 68/27
68 and 27 share no common factor (27 = 3³, 68 = 4×17), so 68/27

4. (y + 42) ÷ 22 = (82 + 42) ÷ 22 = 124 ÷ 22
Simplify: divide by 2 → 62/11
62 and 11 share no factor (11 is prime, 11×5=55, 11×6=66), so 62/11

5. 51 ÷ (y + 44) = 51 ÷ (82 + 44) = 51 ÷ 126
Simplify: divide numerator and denominator by 3 → 17/42
So 17/42

6. (y + 69) ÷ 21 = (82 + 69) ÷ 21 = 151 ÷ 21
151 is prime? Let’s check: divisible by 3? 1+5+1=7 → no. 5? no. 7? 7×21=147, 7×22=154 → no. 11? 11×13=143, 11×14=154 → no. So 151/21 → 151/21

7. 93 ÷ (y + 42) = 93 ÷ (82 + 42) = 93 ÷ 124
Simplify: both divisible by... gcd(93,124)?
93 = 3×31, 124 = 4×31 → yes! Both have 31.
So 93 ÷ 124 = (3×31)/(4×31) = 3/4

8. (y + 98) ÷ 8 = (82 + 98) ÷ 8 = 180 ÷ 8 = 22.5 → or as fraction: 180/8 = simplify by 4 → 45/2
So 45/2 or 22.5 — but fraction preferred in pre-algebra? Let's use simplified fraction: 45/2

9. 14 ÷ (y + 57) = 14 ÷ (82 + 57) = 14 ÷ 139
139 is prime, doesn’t divide 14 → 14/139

10. (y + 63) ÷ 14 = (82 + 63) ÷ 14 = 145 ÷ 14
Simplify: 145 = 5×29, 14 = 2×7 → no common factors → 145/14

Wait — but let me double-check #8: 82 + 98 = 180, yes. 180 ÷ 8 = 22.5 = 45/2 ✔️
#7: 82 + 42 = 124, 93 ÷ 124 = 3/4 ✔️ (since 93 = 3×31, 124 = 4×31)

But hold on — maybe the worksheet expects *decimal answers* rounded? Unlikely — it says “show your work”, and it's pre-algebra, often fractions are acceptable.

However, let me re-read the instruction: “Use the known variable to evaluate each expression. Show your work. (Division, Addition and Parentheses)”

It doesn’t specify format, but in many such worksheets, if it divides evenly, write whole number; otherwise, simplified fraction.

Let’s verify which ones are whole numbers:

- #1: 131/71 → no
- #2: 165/40 = 33/8 = 4.125 → no
- #3: 136/54 = 68/27 ≈ 2.518 → no
- #4: 124/22 = 62/11 ≈ 5.636 → no
- #5: 51/126 = 17/42 ≈ 0.405 → no
- #6: 151/21 ≈ 7.19 → no
- #7: 93/124 = 3/4 = 0.75 → fraction
- #8: 180/8 = 22.5 = 45/2
- #9: 14/139 ≈ 0.1007
- #10: 145/14 ≈ 10.357

None are whole numbers — that’s okay.

But wait — did I misread any? Let’s double-check #10: y = 82, y + 63 = 145, 145 ÷ 14 = 10 remainder 5 → 10 5/14 = 145/14 ✔

Now, perhaps the problem expects answers as simplified fractions (lowest terms). Let’s list them all in simplified fraction form:

1. 131/71
2. 33/8
3. 68/27
4. 62/11
5. 17/42
6. 151/21
7. 3/4
8. 45/2
9. 14/139
10. 145/14

All are simplified.

But before finalizing, let me verify #3 again: y + 54 = 82 + 54 = 136; 136 ÷ 54. GCD of 136 and 54?
54 = 2×3³, 136 = 8×17 = 2³×17 → common factor 2 → 136/54 = 68/27 ✔

#4: 124 and 22 → GCD = 2 → 62/11 ✔

#5: 51 and 126 → GCD = 3 → 17/42 ✔

#7: 93 and 124 → GCD = 31 → 3/4 ✔

Everything checks out.

Final Answer:
1. 131/71
2. 33/8
3. 68/27
4. 62/11
5. 17/42
6. 151/21
7. 3/4
8. 45/2
9. 14/139
10. 145/14