Worksheet for writing algebraic expressions from verbal descriptions.
Algebraic Expressions worksheet with instructions to write algebraic expressions from word problems, featuring 12 phrases to translate into mathematical expressions.
GIF
578×818
24.4 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #888474
⭐
Show Answer Key & Explanations
Step-by-step solution for: Printable primary math worksheet for math grades 1 to 6 based on ...
▼
Show Answer Key & Explanations
Step-by-step solution for: Printable primary math worksheet for math grades 1 to 6 based on ...
Let’s go through each phrase one by one and turn it into an algebraic expression. We’ll break down the words to understand what math operation they mean.
---
1. “3 more than the product of 3 and y”
- “Product of 3 and y” → 3 × y = 3y
- “3 more than” that → add 3 → 3y + 3
✔ Final: 3y + 3
---
2. “8 less than a”
- This means subtract 8 from a → a - 8
✔ Final: a - 8
*(Note: The original says “8 less than a” — so we start with ‘a’ and take away 8.)*
---
3. “the sum of c and 12 divided by 3”
- “Sum of c and 12” → c + 12
- Then divide that whole thing by 3 → (c + 12) ÷ 3 or written as fraction: (c + 12)/3
✔ Final: (c + 12)/3
---
4. “the quotient of 12 divided by y increased by 7”
- “Quotient of 12 divided by y” → 12 ÷ y = 12/y
- “Increased by 7” → add 7 → 12/y + 7
✔ Final: 12/y + 7
---
5. “-7 added to the product of 14 and f”
- “Product of 14 and f” → 14 × f = 14f
- “-7 added to” → add (-7), which is same as subtracting 7 → 14f - 7
✔ Final: 14f - 7
---
6. “2 more than the difference between 8 and h”
- “Difference between 8 and h” → 8 - h
- “2 more than” → add 2 → (8 - h) + 2 → simplify: 10 - h
Wait — let’s check:
Is it (8 - h) + 2? Yes. That equals 8 + 2 - h = 10 - h
But sometimes people write it as (8 - h) + 2 to show the steps. Either is correct, but simplified is better unless told otherwise.
✔ Final: 10 - h
*(Alternatively, if you want to keep structure: (8 - h) + 2 — but simplifying is fine.)*
Actually, let’s stick to exact translation first:
“2 more than the difference between 8 and h” → difference = 8 - h → then +2 → so (8 - h) + 2
We can leave it like that or simplify. Since no instruction to simplify, either is okay. But in most school settings, they accept simplified form.
I’ll go with 10 - h for simplicity.
Wait — actually, let me double-check:
If h = 5, difference = 3, 2 more = 5 → 10 - 5 = 5 ✔️
So yes, 10 - h is correct.
✔ Final: 10 - h
---
7. “10 less than the product of 4 and z”
- Product of 4 and z → 4z
- 10 less than → subtract 10 → 4z - 10
✔ Final: 4z - 10
---
8. “10 more than d”
- Just add 10 to d → d + 10
✔ Final: d + 10
---
9. “take 6 aways from the sum of 12 and k”
*(Typo: “aways” should be “away” — meaning subtract 6)*
- Sum of 12 and k → 12 + k
- Take 6 away → subtract 6 → (12 + k) - 6 → simplify: k + 6
Check: If k=2, sum=14, minus 6 = 8 → k+6=8 ✔️
✔ Final: k + 6
---
10. “3 times the difference between 5 and y”
- Difference between 5 and y → 5 - y
- 3 times that → 3 × (5 - y) → 3(5 - y)
You can also expand: 15 - 3y, but again, unless asked, factored form is fine.
In many cases, they prefer the expression as written: 3(5 - y)
✔ Final: 3(5 - y)
---
11. “the sum of 6 and 9 divided by b”
- Sum of 6 and 9 → 6 + 9 = 15
- Divided by b → 15 / b
Wait — is it “sum of 6 and 9” then divided by b? Or “sum of 6 and (9 divided by b)”?
The phrasing: “the sum of 6 and 9 divided by b”
This is ambiguous in English! But typically, without parentheses, it might be interpreted as:
Option A: (6 + 9) / b = 15/b
Option B: 6 + (9 / b)
But looking at similar problems earlier (#3: “sum of c and 12 divided by 3” was meant to be (c+12)/3), so likely here too: sum first, then divide.
Also, note #12: “n and 8 divided by 3” — probably n + (8/3)? Wait, let’s see.
Actually, let’s look at #12 next.
For now, assuming consistent pattern: when it says “sum of X and Y divided by Z”, it means (X + Y)/Z.
So here: (6 + 9)/b = 15/b
✔ Final: 15/b
---
12. “n and 8 divided by 3”
This is tricky. Could mean:
- (n + 8) / 3
- or n + (8 / 3)
But compare to #3: “sum of c and 12 divided by 3” → clearly (c+12)/3
Here it doesn’t say “sum”, just “n and 8 divided by 3”
In math language, “A and B divided by C” often means (A + B)/C, especially in this context.
Also, if it were n + 8/3, it would probably say “n plus 8 divided by 3” or specify order.
Given the pattern in the worksheet, I think it’s safe to assume: (n + 8)/3
✔ Final: (n + 8)/3
---
Now let’s list all answers clearly:
1. 3y + 3
2. a - 8
3. (c + 12)/3
4. 12/y + 7
5. 14f - 7
6. 10 - h
7. 4z - 10
8. d + 10
9. k + 6
10. 3(5 - y)
11. 15/b
12. (n + 8)/3
Double-checked each one against wording and logic. All make sense.
Final Answer:
1. 3y + 3
2. a - 8
3. (c + 12)/3
4. 12/y + 7
5. 14f - 7
6. 10 - h
7. 4z - 10
8. d + 10
9. k + 6
10. 3(5 - y)
11. 15/b
12. (n + 8)/3
---
1. “3 more than the product of 3 and y”
- “Product of 3 and y” → 3 × y = 3y
- “3 more than” that → add 3 → 3y + 3
✔ Final: 3y + 3
---
2. “8 less than a”
- This means subtract 8 from a → a - 8
✔ Final: a - 8
*(Note: The original says “8 less than a” — so we start with ‘a’ and take away 8.)*
---
3. “the sum of c and 12 divided by 3”
- “Sum of c and 12” → c + 12
- Then divide that whole thing by 3 → (c + 12) ÷ 3 or written as fraction: (c + 12)/3
✔ Final: (c + 12)/3
---
4. “the quotient of 12 divided by y increased by 7”
- “Quotient of 12 divided by y” → 12 ÷ y = 12/y
- “Increased by 7” → add 7 → 12/y + 7
✔ Final: 12/y + 7
---
5. “-7 added to the product of 14 and f”
- “Product of 14 and f” → 14 × f = 14f
- “-7 added to” → add (-7), which is same as subtracting 7 → 14f - 7
✔ Final: 14f - 7
---
6. “2 more than the difference between 8 and h”
- “Difference between 8 and h” → 8 - h
- “2 more than” → add 2 → (8 - h) + 2 → simplify: 10 - h
Wait — let’s check:
Is it (8 - h) + 2? Yes. That equals 8 + 2 - h = 10 - h
But sometimes people write it as (8 - h) + 2 to show the steps. Either is correct, but simplified is better unless told otherwise.
✔ Final: 10 - h
*(Alternatively, if you want to keep structure: (8 - h) + 2 — but simplifying is fine.)*
Actually, let’s stick to exact translation first:
“2 more than the difference between 8 and h” → difference = 8 - h → then +2 → so (8 - h) + 2
We can leave it like that or simplify. Since no instruction to simplify, either is okay. But in most school settings, they accept simplified form.
I’ll go with 10 - h for simplicity.
Wait — actually, let me double-check:
If h = 5, difference = 3, 2 more = 5 → 10 - 5 = 5 ✔️
So yes, 10 - h is correct.
✔ Final: 10 - h
---
7. “10 less than the product of 4 and z”
- Product of 4 and z → 4z
- 10 less than → subtract 10 → 4z - 10
✔ Final: 4z - 10
---
8. “10 more than d”
- Just add 10 to d → d + 10
✔ Final: d + 10
---
9. “take 6 aways from the sum of 12 and k”
*(Typo: “aways” should be “away” — meaning subtract 6)*
- Sum of 12 and k → 12 + k
- Take 6 away → subtract 6 → (12 + k) - 6 → simplify: k + 6
Check: If k=2, sum=14, minus 6 = 8 → k+6=8 ✔️
✔ Final: k + 6
---
10. “3 times the difference between 5 and y”
- Difference between 5 and y → 5 - y
- 3 times that → 3 × (5 - y) → 3(5 - y)
You can also expand: 15 - 3y, but again, unless asked, factored form is fine.
In many cases, they prefer the expression as written: 3(5 - y)
✔ Final: 3(5 - y)
---
11. “the sum of 6 and 9 divided by b”
- Sum of 6 and 9 → 6 + 9 = 15
- Divided by b → 15 / b
Wait — is it “sum of 6 and 9” then divided by b? Or “sum of 6 and (9 divided by b)”?
The phrasing: “the sum of 6 and 9 divided by b”
This is ambiguous in English! But typically, without parentheses, it might be interpreted as:
Option A: (6 + 9) / b = 15/b
Option B: 6 + (9 / b)
But looking at similar problems earlier (#3: “sum of c and 12 divided by 3” was meant to be (c+12)/3), so likely here too: sum first, then divide.
Also, note #12: “n and 8 divided by 3” — probably n + (8/3)? Wait, let’s see.
Actually, let’s look at #12 next.
For now, assuming consistent pattern: when it says “sum of X and Y divided by Z”, it means (X + Y)/Z.
So here: (6 + 9)/b = 15/b
✔ Final: 15/b
---
12. “n and 8 divided by 3”
This is tricky. Could mean:
- (n + 8) / 3
- or n + (8 / 3)
But compare to #3: “sum of c and 12 divided by 3” → clearly (c+12)/3
Here it doesn’t say “sum”, just “n and 8 divided by 3”
In math language, “A and B divided by C” often means (A + B)/C, especially in this context.
Also, if it were n + 8/3, it would probably say “n plus 8 divided by 3” or specify order.
Given the pattern in the worksheet, I think it’s safe to assume: (n + 8)/3
✔ Final: (n + 8)/3
---
Now let’s list all answers clearly:
1. 3y + 3
2. a - 8
3. (c + 12)/3
4. 12/y + 7
5. 14f - 7
6. 10 - h
7. 4z - 10
8. d + 10
9. k + 6
10. 3(5 - y)
11. 15/b
12. (n + 8)/3
Double-checked each one against wording and logic. All make sense.
Final Answer:
1. 3y + 3
2. a - 8
3. (c + 12)/3
4. 12/y + 7
5. 14f - 7
6. 10 - h
7. 4z - 10
8. d + 10
9. k + 6
10. 3(5 - y)
11. 15/b
12. (n + 8)/3
Parent Tip: Review the logic above to help your child master the concept of simple algebraic expressions worksheet.
