Let's solve each problem step by step by translating the verbal expressions into algebraic expressions.
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1a. The difference of 89g and 10, cubed
- "Difference" means subtraction: $ 89g - 10 $
- "Cubed" means raise to the power of 3
✔ Expression:
$$
(89g - 10)^3
$$
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2a. The difference of 10g and 29, cubed
- Difference: $ 10g - 29 $
- Cubed: raise to the 3rd power
✔ Expression:
$$
(10g - 29)^3
$$
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3a. The quantity 8 plus 7y, divided by 8
- "Quantity" implies grouping: $ 8 + 7y $
- Divided by 8: divide the whole expression by 8
✔ Expression:
$$
\frac{8 + 7y}{8}
$$
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4a. The quantity 4 minus 6r, divided by 4
- Quantity: $ 4 - 6r $
- Divided by 4
✔ Expression:
$$
\frac{4 - 6r}{4}
$$
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5a. 7 divided by the difference of c and 3
- Difference of $ c $ and 3: $ c - 3 $
- 7 divided by that: $ \frac{7}{c - 3} $
✔ Expression:
$$
\frac{7}{c - 3}
$$
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6a. The difference of 33d and 6, squared
- Difference: $ 33d - 6 $
- Squared: raise to the 2nd power
✔ Expression:
$$
(33d - 6)^2
$$
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7a. The sum of 69 and 8a
- Sum means addition: $ 69 + 8a $
✔ Expression:
$$
69 + 8a
$$
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8a. The quantity h minus 8, divided by 65
- Quantity: $ h - 8 $
- Divided by 65
✔ Expression:
$$
\frac{h - 8}{65}
$$
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9a. 7 divided by the quantity 9 plus m
- Quantity: $ 9 + m $
- 7 divided by that: $ \frac{7}{9 + m} $
✔ Expression:
$$
\frac{7}{9 + m}
$$
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✔ Final Answers:
| Problem | Expression |
|--------|------------|
| 1a | $(89g - 10)^3$ |
| 2a | $(10g - 29)^3$ |
| 3a | $\frac{8 + 7y}{8}$ |
| 4a | $\frac{4 - 6r}{4}$ |
| 5a | $\frac{7}{c - 3}$ |
| 6a | $(33d - 6)^2$ |
| 7a | $69 + 8a$ |
| 8a | $\frac{h - 8}{65}$ |
| 9a | $\frac{7}{9 + m}$ |
These are the correct algebraic expressions based on the verbal descriptions. Let me know if you'd like an explanation of any specific one!
Parent Tip: Review the logic above to help your child master the concept of variable expression worksheet.
