Translating Word Phrases Into Algebraic Expressions - Free Printable
Educational worksheet: Translating Word Phrases Into Algebraic Expressions. Download and print for classroom or home learning activities.
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Step-by-step solution for: Translating Word Phrases Into Algebraic Expressions
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Show Answer Key & Explanations
Step-by-step solution for: Translating Word Phrases Into Algebraic Expressions
Let’s go step by step to understand how to translate word phrases into algebraic expressions using the table provided.
We’re going to look at each phrase one at a time, find the key words, match them to the operation, and then write the correct algebraic expression.
---
1. “A number plus three”
- Key word: “plus” → that means addition (+)
- “A number” = x (we use x for the unknown)
- So: x + 3
✔ Translation: x + 3
---
2. “Ten more than a number”
- Key phrase: “more than” → also means addition
- But note: “ten more than a number” means you start with the number and add ten.
- So: x + 10
✔ Translation: x + 10
---
3. “The sum of a number and five”
- Key phrase: “the sum of” → addition
- Sum of x and 5 → x + 5
✔ Translation: x + 5
---
4. “The total of six and some number”
- “Total of” → addition
- Six and some number → 6 + x (or x + 6 — same thing)
✔ Translation: 6 + x
---
5. “A number increased by two”
- “Increased by” → addition
- x increased by 2 → x + 2
✔ Translation: x + 2
---
6. “Eleven added to a number”
- “Added to” → addition
- Eleven added to x → x + 11
✔ Translation: x + 11
---
7. “A number minus seven”
- “Minus” → subtraction (-)
- x - 7
✔ Translation: x - 7
---
8. “Four less than a number”
- “Less than” → subtraction, BUT order matters!
- “Four less than a number” means: take the number and subtract four → x - 4
⚠️ Don’t write 4 - x — that would be “a number less than four”
✔ Translation: x - 4
---
9. “The difference of a number and three”
- “Difference of” → subtraction
- Difference of x and 3 → x - 3
✔ Translation: x - 3
---
10. “Nine less a number”
- “Less” here means subtraction — but again, check order.
- “Nine less a number” → 9 - x
✔ Translation: 9 - x
---
11. “A number decreased by twelve”
- “Decreased by” → subtraction
- x decreased by 12 → x - 12
✔ Translation: x - 12
---
12. “Six subtracted from a number”
- “Subtracted from” → subtraction, and order matters!
- Six subtracted from x → x - 6
✔ Translation: x - 6
---
13. “Eight times a number”
- “Times” → multiplication (×)
- 8 × x → we write it as 8x
✔ Translation: 8x
---
14. “The product of fourteen and a number”
- “Product of” → multiplication
- 14 × x → 14x
✔ Translation: 14x
---
15. “Twice a number; double a number”
- “Twice” or “double” → multiply by 2
- 2 × x → 2x
✔ Translation: 2x
---
16. “A number multiplied by negative six”
- Multiply x by -6 → -6x
✔ Translation: –6x
---
17. “Three fourths of a number”
- “Of” often means multiplication in math
- Three fourths = 3/4
- So: (3/4) × x → written as ³⁄₄x
✔ Translation: ³⁄₄x
---
18. “The quotient of a number and seven”
- “Quotient of” → division (÷)
- Quotient of x and 7 → x ÷ 7 → written as x/7
✔ Translation: x/7
---
19. “Ten divided by a number”
- “Divided by” → division
- 10 ÷ x → written as 10/x
✔ Translation: 10/x
---
20. “The ratio of a number to fifteen”
- “Ratio of A to B” → A ÷ B
- So: x ÷ 15 → x/15
✔ Translation: x/15
---
21. “The square of a number; a number squared”
- “Square” or “squared” → raise to power 2
- x²
✔ Translation: x²
---
22. “The cube of a number; a number cubed”
- “Cube” or “cubed” → raise to power 3
- x³
✔ Translation: x³
---
23. “Seven less than a number equals ten.”
- This is an equation (has “equals”)
- “Seven less than a number” → x - 7
- Equals ten → = 10
- So: x - 7 = 10
✔ Translation: x – 7 = 10
---
24. “Three times a number is negative six.”
- “Three times a number” → 3x
- “Is” → equals (=)
- Negative six → -6
- So: 3x = -6
✔ Translation: 3x = –6
---
25. “Eight is the same as twice a number.”
- “Eight is” → 8 =
- “Twice a number” → 2x
- So: 8 = 2x
✔ Translation: 8 = 2x
---
26. “Twelve added to a number yields five.”
- “Twelve added to a number” → x + 12
- “Yields” → equals (=)
- Five → 5
- So: x + 12 = 5
✔ Translation: x + 12 = 5
---
27. “Nine less a number amounts to twenty.”
- “Nine less a number” → 9 - x
- “Amounts to” → equals (=)
- Twenty → 20
- So: 9 - x = 20
✔ Translation: 9 – x = 20
---
All translations are now complete and checked against the rules in the table.
Final Answer:
x + 3
x + 10
x + 5
6 + x
x + 2
x + 11
x - 7
x - 4
x - 3
9 - x
x - 12
x - 6
8x
14x
2x
–6x
³⁄₄x
x/7
10/x
x/15
x²
x³
x – 7 = 10
3x = –6
8 = 2x
x + 12 = 5
9 – x = 20
We’re going to look at each phrase one at a time, find the key words, match them to the operation, and then write the correct algebraic expression.
---
1. “A number plus three”
- Key word: “plus” → that means addition (+)
- “A number” = x (we use x for the unknown)
- So: x + 3
✔ Translation: x + 3
---
2. “Ten more than a number”
- Key phrase: “more than” → also means addition
- But note: “ten more than a number” means you start with the number and add ten.
- So: x + 10
✔ Translation: x + 10
---
3. “The sum of a number and five”
- Key phrase: “the sum of” → addition
- Sum of x and 5 → x + 5
✔ Translation: x + 5
---
4. “The total of six and some number”
- “Total of” → addition
- Six and some number → 6 + x (or x + 6 — same thing)
✔ Translation: 6 + x
---
5. “A number increased by two”
- “Increased by” → addition
- x increased by 2 → x + 2
✔ Translation: x + 2
---
6. “Eleven added to a number”
- “Added to” → addition
- Eleven added to x → x + 11
✔ Translation: x + 11
---
7. “A number minus seven”
- “Minus” → subtraction (-)
- x - 7
✔ Translation: x - 7
---
8. “Four less than a number”
- “Less than” → subtraction, BUT order matters!
- “Four less than a number” means: take the number and subtract four → x - 4
⚠️ Don’t write 4 - x — that would be “a number less than four”
✔ Translation: x - 4
---
9. “The difference of a number and three”
- “Difference of” → subtraction
- Difference of x and 3 → x - 3
✔ Translation: x - 3
---
10. “Nine less a number”
- “Less” here means subtraction — but again, check order.
- “Nine less a number” → 9 - x
✔ Translation: 9 - x
---
11. “A number decreased by twelve”
- “Decreased by” → subtraction
- x decreased by 12 → x - 12
✔ Translation: x - 12
---
12. “Six subtracted from a number”
- “Subtracted from” → subtraction, and order matters!
- Six subtracted from x → x - 6
✔ Translation: x - 6
---
13. “Eight times a number”
- “Times” → multiplication (×)
- 8 × x → we write it as 8x
✔ Translation: 8x
---
14. “The product of fourteen and a number”
- “Product of” → multiplication
- 14 × x → 14x
✔ Translation: 14x
---
15. “Twice a number; double a number”
- “Twice” or “double” → multiply by 2
- 2 × x → 2x
✔ Translation: 2x
---
16. “A number multiplied by negative six”
- Multiply x by -6 → -6x
✔ Translation: –6x
---
17. “Three fourths of a number”
- “Of” often means multiplication in math
- Three fourths = 3/4
- So: (3/4) × x → written as ³⁄₄x
✔ Translation: ³⁄₄x
---
18. “The quotient of a number and seven”
- “Quotient of” → division (÷)
- Quotient of x and 7 → x ÷ 7 → written as x/7
✔ Translation: x/7
---
19. “Ten divided by a number”
- “Divided by” → division
- 10 ÷ x → written as 10/x
✔ Translation: 10/x
---
20. “The ratio of a number to fifteen”
- “Ratio of A to B” → A ÷ B
- So: x ÷ 15 → x/15
✔ Translation: x/15
---
21. “The square of a number; a number squared”
- “Square” or “squared” → raise to power 2
- x²
✔ Translation: x²
---
22. “The cube of a number; a number cubed”
- “Cube” or “cubed” → raise to power 3
- x³
✔ Translation: x³
---
23. “Seven less than a number equals ten.”
- This is an equation (has “equals”)
- “Seven less than a number” → x - 7
- Equals ten → = 10
- So: x - 7 = 10
✔ Translation: x – 7 = 10
---
24. “Three times a number is negative six.”
- “Three times a number” → 3x
- “Is” → equals (=)
- Negative six → -6
- So: 3x = -6
✔ Translation: 3x = –6
---
25. “Eight is the same as twice a number.”
- “Eight is” → 8 =
- “Twice a number” → 2x
- So: 8 = 2x
✔ Translation: 8 = 2x
---
26. “Twelve added to a number yields five.”
- “Twelve added to a number” → x + 12
- “Yields” → equals (=)
- Five → 5
- So: x + 12 = 5
✔ Translation: x + 12 = 5
---
27. “Nine less a number amounts to twenty.”
- “Nine less a number” → 9 - x
- “Amounts to” → equals (=)
- Twenty → 20
- So: 9 - x = 20
✔ Translation: 9 – x = 20
---
All translations are now complete and checked against the rules in the table.
Final Answer:
x + 3
x + 10
x + 5
6 + x
x + 2
x + 11
x - 7
x - 4
x - 3
9 - x
x - 12
x - 6
8x
14x
2x
–6x
³⁄₄x
x/7
10/x
x/15
x²
x³
x – 7 = 10
3x = –6
8 = 2x
x + 12 = 5
9 – x = 20
Parent Tip: Review the logic above to help your child master the concept of translate verbal expressions into algebraic expressions worksheet.
