This worksheet helps students translate word phrases into numerical expressions and solve them.

Sure! Let’s solve the worksheet step by step.

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## Part 1: Write the numerical expressions

We need to translate each word phrase into a mathematical expression.

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a. The sum of 21 and 4, doubled.

- First, find the sum of 21 and 4 → `21 + 4`
- Then, double it → multiply by 2

✔ Expression: `2 × (21 + 4)`

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b. 5 times the sum of 7 and 23.

- Sum of 7 and 23 → `7 + 23`
- 5 times that sum → multiply by 5

✔ Expression: `5 × (7 + 23)`

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c. Triple the sum of 45 and 55.

- Sum of 45 and 55 → `45 + 55`
- Triple it → multiply by 3

✔ Expression: `3 × (45 + 55)`

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d. The sum of 3 fifteens and 4 twos.

- “3 fifteens” = 3 × 15
- “4 twos” = 4 × 2
- Sum them → add together

✔ Expression: `(3 × 15) + (4 × 2)`

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e. 2 times the difference between 49.5 – 37.5.

- Difference between 49.5 and 37.5 → `49.5 - 37.5`
- 2 times that difference → multiply by 2

✔ Expression: `2 × (49.5 - 37.5)`

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f. The difference between 9 thirty-sevens and 8 thirty-sevens.

- “9 thirty-sevens” = 9 × 37
- “8 thirty-sevens” = 8 × 37
- Difference → subtract

✔ Expression: `(9 × 37) - (8 × 37)`

*(Note: You could also factor this as `(9 - 8) × 37`, but the question asks for the expression as written.)*

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## Part 2: Write the numerical expressions in words, then solve.

We’ll write a verbal description of each expression, then compute the answer.

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a. Expression: `10 × (3.5 + 12.5)`

🔹 Words:
*Ten times the sum of three and a half and twelve and a half.*

🔹 Solution:
First, inside parentheses:
`3.5 + 12.5 = 16`
Then:
`10 × 16 = 160`

✔ Solution: 160

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b. Expression: `(88 - 78) × 11`

🔹 Words:
*The difference between eighty-eight and seventy-eight, multiplied by eleven.*

🔹 Solution:
Inside parentheses:
`88 - 78 = 10`
Then:
`10 × 11 = 110`

✔ Solution: 110

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c. Expression: `(51 + 49) × 26`

*(Note: This appears twice in your image — probably a typo. We’ll solve it once.)*

🔹 Words:
*The sum of fifty-one and forty-nine, multiplied by twenty-six.*

🔹 Solution:
Inside parentheses:
`51 + 49 = 100`
Then:
`100 × 26 = 2600`

✔ Solution: 2600

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## ✔ Final Answers Summary:

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Part 1: Numerical Expressions

a. `2 × (21 + 4)`
b. `5 × (7 + 23)`
c. `3 × (45 + 55)`
d. `(3 × 15) + (4 × 2)`
e. `2 × (49.5 - 37.5)`
f. `(9 × 37) - (8 × 37)`

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Part 2: Words and Solutions

| Expression | Words | Solution |
|--------------------|-----------------------------------------------------------------------|----------|
| a. `10 × (3.5 + 12.5)` | Ten times the sum of three and a half and twelve and a half. | 160 |
| b. `(88 - 78) × 11` | The difference between eighty-eight and seventy-eight, times eleven. | 110 |
| c. `(51 + 49) × 26` | The sum of fifty-one and forty-nine, multiplied by twenty-six. | 2600 |

*(Note: The second "c" in your table is likely a duplicate.)*

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Let me know if you’d like these explained even more simply or with diagrams! 😊