Here's the complete solution to the worksheet “Writing Algebraic Expressions”, with clear explanations for each problem.
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Part 1: Write an expression for each phrase
1) Six less than a number
- “A number” → let’s call it `x`
- “Six less than” → means subtract 6 from the number
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✔ Expression: `x - 6`
> 💡 Note: “Less than” reverses the order. “Six less than x” is `x - 6`, not `6 - x`.
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2) The sum of 10 times a number and two
- “A number” → `x`
- “10 times a number” → `10x`
- “Sum of ... and two” → add 2
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✔ Expression: `10x + 2`
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3) The quotient of 20 divided by y, increased by seven
- “Quotient of 20 divided by y” → `20 ÷ y` or `20/y`
- “Increased by seven” → add 7
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✔ Expression: `20/y + 7`
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4) The product of 4 and a number, divided by 2
- “A number” → `x`
- “Product of 4 and a number” → `4x`
- “Divided by 2” → divide the whole product by 2
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✔ Expression: `(4x)/2` (which simplifies to `2x`, but unless asked to simplify, leave as is)
> 📝 *Note: You can also write it as `4x ÷ 2` — same meaning.*
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5) The difference of ten and six, multiplied by a number
- “Difference of ten and six” → `10 - 6 = 4`
- “Multiplied by a number” → multiply that result by `x`
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✔ Expression: `(10 - 6) * x` or simply `4x`
> 💡 Since 10 - 6 is a fixed value, you could simplify to `4x`, but writing `(10 - 6)x` shows your work clearly.
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Part 2: Write a phrase for each expression
6) `2x - 6`
- `2x` → “twice a number” or “two times a number”
- `- 6` → “minus six” or “decreased by six”
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✔ Phrase: “Two times a number, decreased by six”
*(or “Six less than twice a number”)*
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7) `5(6 + x)`
- Inside parentheses: `6 + x` → “six plus a number”
- Multiply by 5 → “five times the sum of six and a number”
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✔ Phrase: “Five times the sum of six and a number”
> 💡 Important: The parentheses mean you must add first, then multiply — so “sum” is key.
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8) `(2 + x) - 8`
- `2 + x` → “two plus a number”
- Then subtract 8 → “minus eight”
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✔ Phrase: “The sum of two and a number, decreased by eight”
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9) `(2 + x)/5`
- Numerator: `2 + x` → “the sum of two and a number”
- Denominator: `/5` → “divided by five”
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✔ Phrase: “The sum of two and a number, divided by five”
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10) `20/x + 7`
- `20/x` → “twenty divided by a number” or “the quotient of twenty and a number”
- `+ 7` → “increased by seven”
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✔ Phrase: “The quotient of twenty and a number, increased by seven”
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✔ Final Answer Summary:
Part 1: Expressions
1) `x - 6`
2) `10x + 2`
3) `20/y + 7`
4) `(4x)/2`
5) `(10 - 6)x` or `4x`
Part 2: Phrases
6) Two times a number, decreased by six
7) Five times the sum of six and a number
8) The sum of two and a number, decreased by eight
9) The sum of two and a number, divided by five
10) The quotient of twenty and a number, increased by seven
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