Math worksheet for students to practice converting numerical expressions into verbal statements and vice versa.
Worksheet titled "Describing Expressions" from SplashLearn, featuring two tables for converting between numerical expressions and their verbal descriptions.
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Step-by-step solution for: Write and Interpret Numerical Expressions - Math Worksheets ...
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Show Answer Key & Explanations
Step-by-step solution for: Write and Interpret Numerical Expressions - Math Worksheets ...
Let’s solve both parts of the problem step by step.
---
## Part 1: Describe the numerical expressions
We need to write a verbal statement for each mathematical expression.
Statement: The difference of seventy-eight and thirty-seven.
> *Explanation:* Subtraction is described as “the difference of A and B”.
---
Statement: Eighty-one divided by three.
> *Explanation:* Division is often described as “A divided by B” or “the quotient of A and B”. “Eighty-one divided by three” is clear and standard.
---
Statement: Seven plus twelve minus three.
> *Explanation:* Since there are no parentheses, we read left to right. It’s fine to describe it literally as “seven plus twelve minus three”.
> *Alternative (more precise):* The sum of seven and twelve, decreased by three.
---
Statement: Fourteen divided by the sum of three and four.
> *Explanation:* Parentheses indicate grouping. So we first compute the sum inside, then divide. We must mention “the sum of three and four” to reflect the grouping.
---
Statement: Five times the difference of sixty-seven and forty-three.
> *Explanation:* The parentheses show subtraction happens first. Then multiplication. So we say “five times the difference...”
---
Statement: The product of one hundred sixty-seven and seventy-three, increased by ninety-one.
> *Explanation:* Multiplication comes before addition (order of operations). So we describe the product first, then adding 91.
> *Alternative:* One hundred sixty-seven times seventy-three plus ninety-one — but that’s less descriptive. Better to clarify order.
---
✔ Completed Table 1:
| Expression | Statement |
|------------------|------------------------------------------------|
| 78 – 37 | The difference of seventy-eight and thirty-seven |
| 81 ÷ 3 | Eighty-one divided by three |
| 7 + 12 – 3 | Seven plus twelve minus three |
| 14 ÷ (3 + 4) | Fourteen divided by the sum of three and four |
| 5(67 – 43) | Five times the difference of sixty-seven and forty-three |
| 167 × 73 + 91 | The product of one hundred sixty-seven and seventy-three, increased by ninety-one |
---
## Part 2: Form the numerical expressions for the given statements
Now we translate verbal phrases into math expressions.
Expression: `14 × 8` or `14 * 8`
> *Explanation:* “Times” means multiplication.
---
Expression: `(80 ÷ 4) × 10` or `(1/4 × 80) × 10`
> *Explanation:* “Quarter of 80” = 80 ÷ 4. Then multiply that result by 10. Parentheses ensure correct order.
---
Expression: `(20 × 6) – 9`
> *Explanation:* “Product of 20 and 6” = 20 × 6. “9 less than” means subtract 9 from that product.
---
Expression: `15 + (2 × 13)` or `15 + 26` (but better to show steps)
> *Explanation:* “Double of 13” = 2 × 13. “Added to” means add 15 to that.
---
Expression: `3 × (79 + 18)`
> *Explanation:* “Sum of 79 and 18” = 79 + 18. “Thrice” means multiply by 3. Parentheses are essential.
---
Expression: `50 ÷ (9 – 2)`
> *Explanation:* “Difference between 9 and 2” = 9 – 2. “Quotient of 50 with [that difference]” = 50 divided by (9 – 2).
---
✔ Completed Table 2:
| Statement | Expression |
|------------------------------------------|------------------------|
| 14 times 8 | `14 × 8` |
| Quarter of 80 multiplied by 10 | `(80 ÷ 4) × 10` |
| 9 less than the product of 20 and 6 | `(20 × 6) – 9` |
| 15 added to the double of 13 | `15 + (2 × 13)` |
| Thrice the sum of 79 and 18 | `3 × (79 + 18)` |
| Quotient of 50 with difference between 9 and 2 | `50 ÷ (9 – 2)` |
---
## ✔ Final Answer Summary:
- 78 – 37 → The difference of seventy-eight and thirty-seven
- 81 ÷ 3 → Eighty-one divided by three
- 7 + 12 – 3 → Seven plus twelve minus three
- 14 ÷ (3 + 4) → Fourteen divided by the sum of three and four
- 5(67 – 43) → Five times the difference of sixty-seven and forty-three
- 167 × 73 + 91 → The product of one hundred sixty-seven and seventy-three, increased by ninety-one
- 14 times 8 → `14 × 8`
- Quarter of 80 multiplied by 10 → `(80 ÷ 4) × 10`
- 9 less than the product of 20 and 6 → `(20 × 6) – 9`
- 15 added to the double of 13 → `15 + (2 × 13)`
- Thrice the sum of 79 and 18 → `3 × (79 + 18)`
- Quotient of 50 with difference between 9 and 2 → `50 ÷ (9 – 2)`
Let me know if you’d like these written in a specific format (like LaTeX or worksheet style)!
---
## Part 1: Describe the numerical expressions
We need to write a verbal statement for each mathematical expression.
1. `78 – 37`
Statement: The difference of seventy-eight and thirty-seven.
> *Explanation:* Subtraction is described as “the difference of A and B”.
---
2. `81 ÷ 3`
Statement: Eighty-one divided by three.
> *Explanation:* Division is often described as “A divided by B” or “the quotient of A and B”. “Eighty-one divided by three” is clear and standard.
---
3. `7 + 12 – 3`
Statement: Seven plus twelve minus three.
> *Explanation:* Since there are no parentheses, we read left to right. It’s fine to describe it literally as “seven plus twelve minus three”.
> *Alternative (more precise):* The sum of seven and twelve, decreased by three.
---
4. `14 ÷ (3 + 4)`
Statement: Fourteen divided by the sum of three and four.
> *Explanation:* Parentheses indicate grouping. So we first compute the sum inside, then divide. We must mention “the sum of three and four” to reflect the grouping.
---
5. `5(67 – 43)`
Statement: Five times the difference of sixty-seven and forty-three.
> *Explanation:* The parentheses show subtraction happens first. Then multiplication. So we say “five times the difference...”
---
6. `167 × 73 + 91`
Statement: The product of one hundred sixty-seven and seventy-three, increased by ninety-one.
> *Explanation:* Multiplication comes before addition (order of operations). So we describe the product first, then adding 91.
> *Alternative:* One hundred sixty-seven times seventy-three plus ninety-one — but that’s less descriptive. Better to clarify order.
---
✔ Completed Table 1:
| Expression | Statement |
|------------------|------------------------------------------------|
| 78 – 37 | The difference of seventy-eight and thirty-seven |
| 81 ÷ 3 | Eighty-one divided by three |
| 7 + 12 – 3 | Seven plus twelve minus three |
| 14 ÷ (3 + 4) | Fourteen divided by the sum of three and four |
| 5(67 – 43) | Five times the difference of sixty-seven and forty-three |
| 167 × 73 + 91 | The product of one hundred sixty-seven and seventy-three, increased by ninety-one |
---
## Part 2: Form the numerical expressions for the given statements
Now we translate verbal phrases into math expressions.
1. “14 times 8”
Expression: `14 × 8` or `14 * 8`
> *Explanation:* “Times” means multiplication.
---
2. “Quarter of 80 multiplied by 10”
Expression: `(80 ÷ 4) × 10` or `(1/4 × 80) × 10`
> *Explanation:* “Quarter of 80” = 80 ÷ 4. Then multiply that result by 10. Parentheses ensure correct order.
---
3. “9 less than the product of 20 and 6”
Expression: `(20 × 6) – 9`
> *Explanation:* “Product of 20 and 6” = 20 × 6. “9 less than” means subtract 9 from that product.
---
4. “15 added to the double of 13”
Expression: `15 + (2 × 13)` or `15 + 26` (but better to show steps)
> *Explanation:* “Double of 13” = 2 × 13. “Added to” means add 15 to that.
---
5. “Thrice the sum of 79 and 18”
Expression: `3 × (79 + 18)`
> *Explanation:* “Sum of 79 and 18” = 79 + 18. “Thrice” means multiply by 3. Parentheses are essential.
---
6. “Quotient of 50 with difference between 9 and 2”
Expression: `50 ÷ (9 – 2)`
> *Explanation:* “Difference between 9 and 2” = 9 – 2. “Quotient of 50 with [that difference]” = 50 divided by (9 – 2).
---
✔ Completed Table 2:
| Statement | Expression |
|------------------------------------------|------------------------|
| 14 times 8 | `14 × 8` |
| Quarter of 80 multiplied by 10 | `(80 ÷ 4) × 10` |
| 9 less than the product of 20 and 6 | `(20 × 6) – 9` |
| 15 added to the double of 13 | `15 + (2 × 13)` |
| Thrice the sum of 79 and 18 | `3 × (79 + 18)` |
| Quotient of 50 with difference between 9 and 2 | `50 ÷ (9 – 2)` |
---
## ✔ Final Answer Summary:
Table 1: Descriptions
- 78 – 37 → The difference of seventy-eight and thirty-seven
- 81 ÷ 3 → Eighty-one divided by three
- 7 + 12 – 3 → Seven plus twelve minus three
- 14 ÷ (3 + 4) → Fourteen divided by the sum of three and four
- 5(67 – 43) → Five times the difference of sixty-seven and forty-three
- 167 × 73 + 91 → The product of one hundred sixty-seven and seventy-three, increased by ninety-one
Table 2: Expressions
- 14 times 8 → `14 × 8`
- Quarter of 80 multiplied by 10 → `(80 ÷ 4) × 10`
- 9 less than the product of 20 and 6 → `(20 × 6) – 9`
- 15 added to the double of 13 → `15 + (2 × 13)`
- Thrice the sum of 79 and 18 → `3 × (79 + 18)`
- Quotient of 50 with difference between 9 and 2 → `50 ÷ (9 – 2)`
Let me know if you’d like these written in a specific format (like LaTeX or worksheet style)!
Parent Tip: Review the logic above to help your child master the concept of writing numerical expressions from word problems worksheet.
