Writing algebraic expressions worksheets | Worsheets library - Free Printable

Explanation:
We need to write algebraic expressions for each phrase. Let’s go one by one, carefully translating the words into math.

1. Eleven decreased by k
“Decreased by” means subtraction. So:
→ 11 − k

2. p increased by 9
“Increased by” means addition:
→ p + 9

3. Sixteen multiplied by a number h
“Multiplied by” means × (or just write next to each other):
→ 16h

4. 1 less than twelve
This is a number, not involving a variable — but still an expression:
→ 12 − 1 = 11
However, since the instruction says “write an expression using a variable”, and this one has no variable, it's likely just a simple numeric expression. Still, we follow the wording: “1 less than twelve” → 12 − 1. But wait—let’s double-check the list: #4 says “1 less than twelve”, no variable mentioned. The worksheet allows some without variables (e.g., #15 is “Thrice a number p” → uses p). So we write as is:
→ 12 − 1
But usually in such worksheets, they expect simplified form only if asked. Since it says “write an expression”, and no simplification instruction, we can leave as 12 − 1. However, many teachers expect simplified constants. Let’s hold and compare with others.

Wait — actually, looking again: #12 is “The sum of 5 and k” → 5 + k (not simplified further). So for consistency, we should *not* simplify numeric-only expressions unless told. But #4 has no variable — still, the task says “using a variable” in the intro: “Write an expression using a variable to represent each situation.” Hmm — that suggests *all* should involve a variable. But #4 says “1 less than twelve” — maybe it's a typo or exception. Let’s assume we follow the phrase literally.

But let’s check all items:
- #1: has k ✔
- #2: p ✔
- #3: h ✔
- #4: no variable ❓
- #5: m ✔
- #6: e ✔
- #7: c ✔
- #8: x ✔
- #9: m ✔
- #10: f ✔
- #11: y ✔
- #12: k ✔
- #13: g ✔
- #14: b ✔
- #15: p ✔

Only #4 lacks a variable. Possibly it's meant to be “1 less than a number” or something — but as written, it's “1 less than twelve”. In many worksheets, they include a few numeric-only for variety. We’ll write 12 − 1, though it’s unusual. Alternatively, maybe it's a trick: “twelve” is fixed, so expression is just 11 — but again, expression, not value.

Let me verify standard practice: In pre-algebra, “1 less than twelve” is written as 12 − 1, and sometimes simplified to 11 if asked for value. Since the instruction is “write an expression”, and others are symbolic, I think safest is to write 12 − 1. But let’s see official answer patterns — actually, looking at similar worksheets online, they often keep it as 12 − 1 even if numeric. However, I recall K5 Learning (the source) usually expects simplified numeric answers when no variable is present. Let’s assume they want 11 for #4.

But wait — the header says “Grade 5 Pre-Algebra Worksheet” and “Write an expression using a variable”. So #4 may be an error, but we must answer as given. To be safe, I will write 12 − 1, and later if needed adjust. Let’s continue and come back.

5. Sixteen less than m
“Less than” reverses order: m − 16

6. 8 divided by e
→ 8 ÷ e or 8/e

7. The product of 6 and c
→ 6c

8. Eighty-five less than x
→ x − 85

9. Two more than m
→ m + 2

10. Three-fourths of f
→ (3/4)f or ¾f

11. y diminished by 9
“Diminished by” = subtracted: y − 9

12. The sum of 5 and k
→ 5 + k

13. g less than 8
Again, “less than” reverses: 8 − g

14. The quotient of b and 3
→ b ÷ 3 or b/3

15. Thrice a number p
“Thrice” = three times: 3p

Now revisit #4: “1 less than twelve”
If we strictly follow “using a variable", this is odd. But perhaps it's a mistake, and they meant “1 less than a number” — but we must answer what’s written. In real K5 worksheets, I’ve seen #4 as “1 less than t” etc. Given the pattern, and to avoid overcomplicating, I’ll treat it as numeric expression: 12 − 1, but since it’s just a constant, and others are symbolic, maybe they accept 11. However, the instruction says “expression”, and 11 is a numerical expression too. Both are valid, but simpler is better for grade 5.

Let me decide: For consistency with grade-level expectations, and because all others use variables, but #4 is the only exception, I will write 12 − 1 — and if simplification is expected, teacher would ask. But many answer keys show simplified constants. Let’s search memory: K5 Learning answer key for this exact worksheet shows #4 as 12 − 1? Actually, I can’t access, but logically, since #13 is “g less than 8” → 8 − g (not g − 8), order matters. So for #4, “1 less than twelve” = 12 − 1.

Yes. Final decisions:

1. 11 − k
2. p + 9
3. 16h
4. 12 − 1
5. m − 16
6. 8/e
7. 6c
8. x − 85
9. m + 2
10. (3/4)f
11. y − 9
12. 5 + k
13. 8 − g
14. b/3
15. 3p

We can write fractions as 3/4 f or \frac{3}{4}f — but for grade 5, “3/4 f” or “¾f” is fine. In plain text, use (3/4)f.

Also, division can be written with ÷ or / — / is cleaner.

Now verify each:
- #1: eleven decreased by k → 11 − k ✔
- #2: p increased by 9 → p + 9 ✔
- #3: 16 × h → 16h ✔
- #4: 1 less than 12 → 12 − 1 ✔ (though could be 11, but expression form preferred)
- #5: 16 less than m → m − 16 ✔
- #6: 8 divided by e → 8/e ✔
- #7: product of 6 and c → 6c ✔
- #8: 85 less than x → x − 85 ✔
- #9: two more than m → m + 2 ✔
- #10: three-fourths of f → (3/4)f ✔
- #11: y diminished by 9 → y − 9 ✔
- #12: sum of 5 and k → 5 + k ✔
- #13: g less than 8 → 8 − g ✔ (critical: not g − 8)
- #14: quotient of b and 3 → b/3 ✔
- #15: thrice p → 3p ✔

All correct.

Final Answer:
1. 11 − k
2. p + 9
3. 16h
4. 12 − 1
5. m − 16
6. 8/e
7. 6c
8. x − 85
9. m + 2
10. (3/4)f
11. y − 9
12. 5 + k
13. 8 − g
14. b/3
15. 3p