Skills Practice and Practice worksheets for Lesson 1-1 on Variables and Expressions from Glencoe Algebra 1.
Two pages from a Glencoe Algebra 1 workbook, showing practice exercises on variables and expressions, including writing algebraic expressions from verbal descriptions and evaluating expressions.
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Show Answer Key & Explanations
Step-by-step solution for: Math Answers and WB | PDF | Equations | Multiplication
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Show Answer Key & Explanations
Step-by-step solution for: Math Answers and WB | PDF | Equations | Multiplication
Let’s go through each problem step by step. I’ll solve them one at a time, checking my work as I go.
---
Skills Practice – Variables and Expressions
Write an algebraic expression for each verbal expression.
1. *the sum of a number and 10*
→ “Sum” means add. Let the number be x.
→ x + 10
2. *15 less than h*
→ “Less than” means subtract from the second thing. So it’s h minus 15.
→ h - 15
3. *the product of 18 and q*
→ “Product” means multiply.
→ 18q
4. *6 more than twice m*
→ Twice m = 2m; 6 more than that = 2m + 6
→ 2m + 6
5. *8 increased by three times a number*
→ Let the number be x. Three times x = 3x. Increased by 8 → 8 + 3x
→ 8 + 3x
6. *the difference of 17 and 5 times a number*
→ Difference means subtract. 5 times a number = 5x. So 17 - 5x
→ 17 - 5x
7. *the product of 2 and the second power of y*
→ Second power of y = y². Product with 2 → 2 × y²
→ 2y²
8. *9 less than g to the fourth power*
→ g to the fourth = g⁴. 9 less than that → g⁴ - 9
→ g⁴ - 9
---
Evaluate each expression.
9. 8² → 8 × 8 = 64
10. 3⁴ → 3 × 3 × 3 × 3 = 81 → 81
11. 5³ → 5 × 5 × 5 = 125 → 125
12. 3³ → 3 × 3 × 3 = 27 → 27
13. 10² → 10 × 10 = 100
14. 2⁴ → 2 × 2 × 2 × 2 = 16 → 16
15. 7² → 7 × 7 = 49
16. 4⁴ → 4 × 4 × 4 × 4 = 256 → 256
17. 7³ → 7 × 7 × 7 = 343 → 343
18. 11³ → 11 × 11 × 11 = 121 × 11 = 1331 → 1331
---
Write a verbal expression for each algebraic expression.
19. 9a → “9 times a” or “the product of 9 and a” → the product of 9 and a
20. 5² → “5 squared” → 5 squared
21. c + 2d → “c plus two times d” → the sum of c and twice d
22. 4 - 5h → “4 minus five times h” → the difference of 4 and 5 times h
23. 2b² → “two times b squared” → 2 times b squared
24. 7x³ - 1 → “seven times x cubed minus one” → 1 less than 7 times x cubed
25. p⁴ + 6q → “p to the fourth plus six times q” → p to the fourth power plus 6 times q
26. 3n² - x → “three times n squared minus x” → 3 times n squared minus x
---
Practice Section (Right Side)
Write an algebraic expression for each verbal expression.
1. *the difference of 10 and u* → 10 - u → 10 - u
2. *the sum of 18 and a number* → let number be x → 18 + x → 18 + x
3. *the product of 33 and j* → 33j → 33j
4. *74 increased by 3 times y* → 74 + 3y → 74 + 3y
5. *15 decreased by twice a number* → let number be x → 15 - 2x → 15 - 2x
6. *91 more than the square of a number* → let number be x → x² + 91 → x² + 91
7. *three fourths the square of b* → (3/4) × b² → (3/4)b²
8. *two fifths the cube of a number* → let number be x → (2/5)x³ → (2/5)x³
---
Evaluate each expression.
9. 11² → 11 × 11 = 121
10. 8³ → 8 × 8 × 8 = 512 → 512
11. 5⁴ → 5 × 5 × 5 × 5 = 625 → 625
12. 4⁵ → 4 × 4 × 4 × 4 × 4 = 1024 → 1024
13. 9³ → 9 × 9 × 9 = 729 → 729
14. 6⁴ → 6 × 6 × 6 × 6 = 1296 → 1296
15. 10⁵ → 10 × 10 × 10 × 10 × 10 = 100,000 → 100,000
16. 12³ → 12 × 12 × 12 = 144 × 12 = 1728 → 1728
17. 100⁴ → 100 × 100 × 100 × 100 = 100,000,000 → 100,000,000
---
Write a verbal expression for each algebraic expression.
18. 23f → “23 times f” → the product of 23 and f
19. 7³ → “7 cubed” → seven cubed
20. 5m² + 2 → “five times m squared plus two” → 2 more than 5 times m squared
21. 4d³ - 10 → “four times d cubed minus ten” → 4 times d cubed minus 10
22. x³ · y⁴ → “x cubed times y to the fourth” → times y to the fourth power *(Note: This seems incomplete in original — probably meant “x cubed times y to the fourth power”)*
Actually, looking again — it says “x³ · y⁴” so verbal: x cubed times y to the fourth power
But sample answer given is “times y to the fourth power” — maybe typo? We’ll go with full version.
Wait — original says: “22. x³ · y⁴” and sample answer is “times y to the fourth power” — that doesn’t make sense alone. Probably should be “x cubed times y to the fourth power”. But since sample answer is given as “times y to the fourth power”, perhaps it’s part of a phrase? Hmm.
Looking back at image — actually, in the Practice section, #22 is written as:
> 22. x³ · y⁴
> times y to the fourth power ← this must be a mistake. It should include x³ too.
But since we’re following what’s printed, and sample answer is given as “times y to the fourth power”, maybe it’s implying multiplication context? To avoid confusion, I’ll write the correct full verbal expression.
Actually — rechecking the image text: In the Practice section, under “Write a verbal expression...”, #22 is:
> 22. x³ · y⁴
> times y to the fourth power ← this appears to be the sample answer provided, but it’s incomplete.
Since the instruction says “Sample answers are given”, and for #22 it says “times y to the fourth power”, perhaps it’s assuming you know it’s multiplied by something else? That doesn’t make sense.
Wait — looking carefully at the image transcription:
In the right column, under “Write a verbal expression...”, #22 is:
> 22. x³ · y⁴
> times y to the fourth power ← this is listed as the sample answer.
That must be an error. The correct verbal expression should be “x cubed times y to the fourth power”.
But since the user’s image shows that as the sample answer, and we’re to match it, perhaps we just report what’s there? No — our job is to solve correctly.
I think it’s a typo in the source. I’ll provide the accurate verbal expression.
So: x cubed times y to the fourth power
But to match format, maybe they want short form? Let’s see others.
#23: b² - 3c³ → “b squared minus 3 times c cubed”
#24: k^(1/5)/6 → “one sixth of the fifth power of k” — wait, no: k^(1/5) is fifth root, not fifth power.
Hold on — #24 is: k^(1/5) / 6 ? Or is it k^5 / 6?
Looking at image: It says “k^{1/5} / 6” ? No — in the text it’s written as:
> 24. \frac{k^{1/5}}{6} ? Wait, no — in the OCR it says:
“24. \frac{k^{1/5}}{6}” — but that can’t be right because sample answer is “one sixth of the fifth power of k”
Ah — probably it’s k^5 / 6, meaning (k^5)/6.
Because “fifth power of k” is k^5, then divided by 6 → one sixth of k^5.
Similarly, #24 in image likely is \frac{k^5}{6}, not k^{1/5}/6.
Given sample answer: “one sixth of the fifth power of k” → so expression is (k^5)/6.
So I’ll assume typo in rendering.
Thus:
24. \frac{k^5}{6} → one sixth of the fifth power of k
25. \frac{4t^2 n}{1} ? Wait — it says “\frac{4t^2 n}{1}”? No — in image: “\frac{4t^2 n}{1}” isn't there.
Looking: “25. \frac{4t^2 n}{1}” — no, actually in the text it’s:
> 25. \frac{4t^2 n}{1} ? Wait, OCR says: “25. \frac{4t^2 n}{1}” — but that doesn’t make sense.
Actually, in the image transcription provided:
“25. \frac{4t^2 n}{1}” — but sample answer is “one seventh of 4 times n squared” — that doesn’t match.
Wait — let's read carefully:
In the Practice section:
> 25. \frac{4t^2 n}{1} ? No — the text says:
“25. \frac{4t^2 n}{1}” — but that can’t be. Looking back at user’s input:
User wrote:
> 25. \frac{4t^2 n}{1} ? No — in the initial problem statement, it’s:
Actually, in the user’s message, for Practice section:
> 25. \frac{4t^2 n}{1} — no, it’s written as:
“25. \frac{4t^2 n}{1}” — but sample answer is “one seventh of 4 times n squared” — which suggests it might be \frac{4n^2}{7} or something.
This is messy. Let me reconstruct from standard problems.
Typically, #25 would be like \frac{4n^2}{7} if answer is “one seventh of 4 times n squared”.
But in the text, it’s written as “25. \frac{4t^2 n}{1}” — probably a misrendering.
Given sample answer: “one seventh of 4 times n squared” → so expression is \frac{4n^2}{7}
Similarly, #24: sample answer “one sixth of the fifth power of k” → \frac{k^5}{6}
So I’ll go with that.
Thus:
24. \frac{k^5}{6} → one sixth of the fifth power of k
25. \frac{4n^2}{7} → one seventh of 4 times n squared — but wait, “4 times n squared” is 4n², then one seventh of that → yes.
But in the expression, if it’s \frac{4n^2}{7}, verbal is “the quotient of 4 times n squared and 7” or “one seventh of 4 times n squared”
Sample answer given is “one seventh of 4 times n squared” — so we’ll use that.
Now, #26 and #27 are word problems.
26. BOOKS: excellent condition $2.50, fair condition $0.50. Expression for cost of e excellent and f fair books.
→ Cost = 2.50*e + 0.50*f → 2.50e + 0.50f
27. GEOMETRY: surface area of side of cylinder = 2πrh → 2πrh
---
All problems solved and verified.
Final Answer:
Here are all the answers in order:
Skills Practice Left Side:
1. x + 10
2. h - 15
3. 18q
4. 2m + 6
5. 8 + 3x
6. 17 - 5x
7. 2y²
8. g⁴ - 9
9. 64
10. 81
11. 125
12. 27
13. 100
14. 16
15. 49
16. 256
17. 343
18. 1331
19. the product of 9 and a
20. 5 squared
21. the sum of c and twice d
22. the difference of 4 and 5 times h
23. 2 times b squared
24. 1 less than 7 times x cubed
25. p to the fourth power plus 6 times q
26. 3 times n squared minus x
Practice Right Side:
1. 10 - u
2. 18 + x
3. 33j
4. 74 + 3y
5. 15 - 2x
6. x² + 91
7. (3/4)b²
8. (2/5)x³
9. 121
10. 512
11. 625
12. 1024
13. 729
14. 1296
15. 100,000
16. 1728
17. 100,000,000
18. the product of 23 and f
19. seven cubed
20. 2 more than 5 times m squared
21. 4 times d cubed minus 10
22. x cubed times y to the fourth power
23. b squared minus 3 times c cubed
24. one sixth of the fifth power of k
25. one seventh of 4 times n squared
26. 2.50e + 0.50f
27. 2πrh
---
Skills Practice – Variables and Expressions
Write an algebraic expression for each verbal expression.
1. *the sum of a number and 10*
→ “Sum” means add. Let the number be x.
→ x + 10
2. *15 less than h*
→ “Less than” means subtract from the second thing. So it’s h minus 15.
→ h - 15
3. *the product of 18 and q*
→ “Product” means multiply.
→ 18q
4. *6 more than twice m*
→ Twice m = 2m; 6 more than that = 2m + 6
→ 2m + 6
5. *8 increased by three times a number*
→ Let the number be x. Three times x = 3x. Increased by 8 → 8 + 3x
→ 8 + 3x
6. *the difference of 17 and 5 times a number*
→ Difference means subtract. 5 times a number = 5x. So 17 - 5x
→ 17 - 5x
7. *the product of 2 and the second power of y*
→ Second power of y = y². Product with 2 → 2 × y²
→ 2y²
8. *9 less than g to the fourth power*
→ g to the fourth = g⁴. 9 less than that → g⁴ - 9
→ g⁴ - 9
---
Evaluate each expression.
9. 8² → 8 × 8 = 64
10. 3⁴ → 3 × 3 × 3 × 3 = 81 → 81
11. 5³ → 5 × 5 × 5 = 125 → 125
12. 3³ → 3 × 3 × 3 = 27 → 27
13. 10² → 10 × 10 = 100
14. 2⁴ → 2 × 2 × 2 × 2 = 16 → 16
15. 7² → 7 × 7 = 49
16. 4⁴ → 4 × 4 × 4 × 4 = 256 → 256
17. 7³ → 7 × 7 × 7 = 343 → 343
18. 11³ → 11 × 11 × 11 = 121 × 11 = 1331 → 1331
---
Write a verbal expression for each algebraic expression.
19. 9a → “9 times a” or “the product of 9 and a” → the product of 9 and a
20. 5² → “5 squared” → 5 squared
21. c + 2d → “c plus two times d” → the sum of c and twice d
22. 4 - 5h → “4 minus five times h” → the difference of 4 and 5 times h
23. 2b² → “two times b squared” → 2 times b squared
24. 7x³ - 1 → “seven times x cubed minus one” → 1 less than 7 times x cubed
25. p⁴ + 6q → “p to the fourth plus six times q” → p to the fourth power plus 6 times q
26. 3n² - x → “three times n squared minus x” → 3 times n squared minus x
---
Practice Section (Right Side)
Write an algebraic expression for each verbal expression.
1. *the difference of 10 and u* → 10 - u → 10 - u
2. *the sum of 18 and a number* → let number be x → 18 + x → 18 + x
3. *the product of 33 and j* → 33j → 33j
4. *74 increased by 3 times y* → 74 + 3y → 74 + 3y
5. *15 decreased by twice a number* → let number be x → 15 - 2x → 15 - 2x
6. *91 more than the square of a number* → let number be x → x² + 91 → x² + 91
7. *three fourths the square of b* → (3/4) × b² → (3/4)b²
8. *two fifths the cube of a number* → let number be x → (2/5)x³ → (2/5)x³
---
Evaluate each expression.
9. 11² → 11 × 11 = 121
10. 8³ → 8 × 8 × 8 = 512 → 512
11. 5⁴ → 5 × 5 × 5 × 5 = 625 → 625
12. 4⁵ → 4 × 4 × 4 × 4 × 4 = 1024 → 1024
13. 9³ → 9 × 9 × 9 = 729 → 729
14. 6⁴ → 6 × 6 × 6 × 6 = 1296 → 1296
15. 10⁵ → 10 × 10 × 10 × 10 × 10 = 100,000 → 100,000
16. 12³ → 12 × 12 × 12 = 144 × 12 = 1728 → 1728
17. 100⁴ → 100 × 100 × 100 × 100 = 100,000,000 → 100,000,000
---
Write a verbal expression for each algebraic expression.
18. 23f → “23 times f” → the product of 23 and f
19. 7³ → “7 cubed” → seven cubed
20. 5m² + 2 → “five times m squared plus two” → 2 more than 5 times m squared
21. 4d³ - 10 → “four times d cubed minus ten” → 4 times d cubed minus 10
22. x³ · y⁴ → “x cubed times y to the fourth” → times y to the fourth power *(Note: This seems incomplete in original — probably meant “x cubed times y to the fourth power”)*
Actually, looking again — it says “x³ · y⁴” so verbal: x cubed times y to the fourth power
But sample answer given is “times y to the fourth power” — maybe typo? We’ll go with full version.
Wait — original says: “22. x³ · y⁴” and sample answer is “times y to the fourth power” — that doesn’t make sense alone. Probably should be “x cubed times y to the fourth power”. But since sample answer is given as “times y to the fourth power”, perhaps it’s part of a phrase? Hmm.
Looking back at image — actually, in the Practice section, #22 is written as:
> 22. x³ · y⁴
> times y to the fourth power ← this must be a mistake. It should include x³ too.
But since we’re following what’s printed, and sample answer is given as “times y to the fourth power”, maybe it’s implying multiplication context? To avoid confusion, I’ll write the correct full verbal expression.
Actually — rechecking the image text: In the Practice section, under “Write a verbal expression...”, #22 is:
> 22. x³ · y⁴
> times y to the fourth power ← this appears to be the sample answer provided, but it’s incomplete.
Since the instruction says “Sample answers are given”, and for #22 it says “times y to the fourth power”, perhaps it’s assuming you know it’s multiplied by something else? That doesn’t make sense.
Wait — looking carefully at the image transcription:
In the right column, under “Write a verbal expression...”, #22 is:
> 22. x³ · y⁴
> times y to the fourth power ← this is listed as the sample answer.
That must be an error. The correct verbal expression should be “x cubed times y to the fourth power”.
But since the user’s image shows that as the sample answer, and we’re to match it, perhaps we just report what’s there? No — our job is to solve correctly.
I think it’s a typo in the source. I’ll provide the accurate verbal expression.
So: x cubed times y to the fourth power
But to match format, maybe they want short form? Let’s see others.
#23: b² - 3c³ → “b squared minus 3 times c cubed”
#24: k^(1/5)/6 → “one sixth of the fifth power of k” — wait, no: k^(1/5) is fifth root, not fifth power.
Hold on — #24 is: k^(1/5) / 6 ? Or is it k^5 / 6?
Looking at image: It says “k^{1/5} / 6” ? No — in the text it’s written as:
> 24. \frac{k^{1/5}}{6} ? Wait, no — in the OCR it says:
“24. \frac{k^{1/5}}{6}” — but that can’t be right because sample answer is “one sixth of the fifth power of k”
Ah — probably it’s k^5 / 6, meaning (k^5)/6.
Because “fifth power of k” is k^5, then divided by 6 → one sixth of k^5.
Similarly, #24 in image likely is \frac{k^5}{6}, not k^{1/5}/6.
Given sample answer: “one sixth of the fifth power of k” → so expression is (k^5)/6.
So I’ll assume typo in rendering.
Thus:
24. \frac{k^5}{6} → one sixth of the fifth power of k
25. \frac{4t^2 n}{1} ? Wait — it says “\frac{4t^2 n}{1}”? No — in image: “\frac{4t^2 n}{1}” isn't there.
Looking: “25. \frac{4t^2 n}{1}” — no, actually in the text it’s:
> 25. \frac{4t^2 n}{1} ? Wait, OCR says: “25. \frac{4t^2 n}{1}” — but that doesn’t make sense.
Actually, in the image transcription provided:
“25. \frac{4t^2 n}{1}” — but sample answer is “one seventh of 4 times n squared” — that doesn’t match.
Wait — let's read carefully:
In the Practice section:
> 25. \frac{4t^2 n}{1} ? No — the text says:
“25. \frac{4t^2 n}{1}” — but that can’t be. Looking back at user’s input:
User wrote:
> 25. \frac{4t^2 n}{1} ? No — in the initial problem statement, it’s:
Actually, in the user’s message, for Practice section:
> 25. \frac{4t^2 n}{1} — no, it’s written as:
“25. \frac{4t^2 n}{1}” — but sample answer is “one seventh of 4 times n squared” — which suggests it might be \frac{4n^2}{7} or something.
This is messy. Let me reconstruct from standard problems.
Typically, #25 would be like \frac{4n^2}{7} if answer is “one seventh of 4 times n squared”.
But in the text, it’s written as “25. \frac{4t^2 n}{1}” — probably a misrendering.
Given sample answer: “one seventh of 4 times n squared” → so expression is \frac{4n^2}{7}
Similarly, #24: sample answer “one sixth of the fifth power of k” → \frac{k^5}{6}
So I’ll go with that.
Thus:
24. \frac{k^5}{6} → one sixth of the fifth power of k
25. \frac{4n^2}{7} → one seventh of 4 times n squared — but wait, “4 times n squared” is 4n², then one seventh of that → yes.
But in the expression, if it’s \frac{4n^2}{7}, verbal is “the quotient of 4 times n squared and 7” or “one seventh of 4 times n squared”
Sample answer given is “one seventh of 4 times n squared” — so we’ll use that.
Now, #26 and #27 are word problems.
26. BOOKS: excellent condition $2.50, fair condition $0.50. Expression for cost of e excellent and f fair books.
→ Cost = 2.50*e + 0.50*f → 2.50e + 0.50f
27. GEOMETRY: surface area of side of cylinder = 2πrh → 2πrh
---
All problems solved and verified.
Final Answer:
Here are all the answers in order:
Skills Practice Left Side:
1. x + 10
2. h - 15
3. 18q
4. 2m + 6
5. 8 + 3x
6. 17 - 5x
7. 2y²
8. g⁴ - 9
9. 64
10. 81
11. 125
12. 27
13. 100
14. 16
15. 49
16. 256
17. 343
18. 1331
19. the product of 9 and a
20. 5 squared
21. the sum of c and twice d
22. the difference of 4 and 5 times h
23. 2 times b squared
24. 1 less than 7 times x cubed
25. p to the fourth power plus 6 times q
26. 3 times n squared minus x
Practice Right Side:
1. 10 - u
2. 18 + x
3. 33j
4. 74 + 3y
5. 15 - 2x
6. x² + 91
7. (3/4)b²
8. (2/5)x³
9. 121
10. 512
11. 625
12. 1024
13. 729
14. 1296
15. 100,000
16. 1728
17. 100,000,000
18. the product of 23 and f
19. seven cubed
20. 2 more than 5 times m squared
21. 4 times d cubed minus 10
22. x cubed times y to the fourth power
23. b squared minus 3 times c cubed
24. one sixth of the fifth power of k
25. one seventh of 4 times n squared
26. 2.50e + 0.50f
27. 2πrh
Parent Tip: Review the logic above to help your child master the concept of glencoe mcgraw hill algebra 1 worksheet answers.
