Use this chart to identify key operation words like "sum" and "product" when translating word problems into math expressions.

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

The goal is to translate each verbal expression into an algebraic expression, using the key words provided in the chart at the top.

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🔑 Key Words Recap:

- Addition: Plus, Sum, Total, Increased by, More than → `+`
- Subtraction: Minus, Difference, Subtracted from, Decreased by, Less than → `-`
- Multiplication: Times, Multiplied by, Product of, Twice → `×` or just write together (e.g., `2x`)
- Division: Quotient, Divided by → `÷` or fraction bar

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Now let’s go row by row through the “Now give it a try!” section.

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## ✔ Row 1:

Left Column: "the sum of q and 8"

- “Sum” = addition
- So: `q + 8`

✔ Answer: `q + 8`

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Right Column: "x decreased by 2"

- “Decreased by” = subtraction
- So: `x - 2`

✔ Answer: `x - 2`

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## ✔ Row 2:

Left Column: "the quotient of 9 and c"

- “Quotient” = division
- So: `9 ÷ c` or better written as a fraction: `9/c`

✔ Answer: `9/c`

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Right Column: "5 subtracted from w"

- “Subtracted from” — this is tricky! It means: start with `w`, then subtract 5.
- So: `w - 5`

⚠️ Note: “5 subtracted from w” ≠ “w subtracted from 5”. Order matters!

✔ Answer: `w - 5`

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## ✔ Row 3:

Left Column: "7 times m"

- “Times” = multiplication
- So: `7 × m` or simply `7m`

✔ Answer: `7m`

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Right Column: "6 times the difference of d and 5"

- First, find “the difference of d and 5” → `d - 5`
- Then “6 times” that → `6 × (d - 5)`

✔ Answer: `6(d - 5)`

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## ✔ Row 4:

Left Column: "Twice the sum of j and 4"

- “Sum of j and 4” → `j + 4`
- “Twice” = multiply by 2 → `2 × (j + 4)`

✔ Answer: `2(j + 4)`

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Right Column: "12 divided by p"

- “Divided by” = division
- So: `12 ÷ p` or `12/p`

✔ Answer: `12/p`

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## 📝 Final Answers Table:

| Verbal Expression | Algebraic Expression |
|----------------------------------|----------------------|
| the sum of q and 8 | `q + 8` |
| x decreased by 2 | `x - 2` |
| the quotient of 9 and c | `9/c` |
| 5 subtracted from w | `w - 5` |
| 7 times m | `7m` |
| 6 times the difference of d and 5 | `6(d - 5)` |
| Twice the sum of j and 4 | `2(j + 4)` |
| 12 divided by p | `12/p` |

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✔ All done! You’ve successfully translated each verbal phrase into its correct algebraic expression. Remember to watch for word order — especially with subtraction and division — because “A subtracted from B” is `B - A`, not `A - B`.

Let me know if you’d like to practice more! 🐬