Write an algebraic expression for each phrase.

To solve the problem, we need to translate each phrase into an algebraic expression. Let's go through each one step by step:

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1. A number \( g \) added to sixty-three

- Phrase: "A number \( g \) added to sixty-three"
- Translation: This means we are adding 63 to the variable \( g \).
- Expression: \( g + 63 \)

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2. The quotient of seven and a number \( x \)

- Phrase: "The quotient of seven and a number \( x \)"
- Translation: The quotient means division. We divide 7 by the variable \( x \).
- Expression: \( \frac{7}{x} \)

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3. Ten less than a number \( v \)

- Phrase: "Ten less than a number \( v \)"
- Translation: "Less than" means subtraction. We subtract 10 from the variable \( v \).
- Expression: \( v - 10 \)

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4. The difference between thirteen and a number \( k \)

- Phrase: "The difference between thirteen and a number \( k \)"
- Translation: The difference means subtraction. We subtract \( k \) from 13.
- Expression: \( 13 - k \)

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5. A number \( q \) increased by seventy-two

- Phrase: "A number \( q \) increased by seventy-two"
- Translation: "Increased by" means addition. We add 72 to the variable \( q \).
- Expression: \( q + 72 \)

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6. The total of eleven and a number \( m \)

- Phrase: "The total of eleven and a number \( m \)"
- Translation: "Total" means addition. We add 11 to the variable \( m \).
- Expression: \( 11 + m \)

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7. Ninety-seven subtracted from a number \( r \)

- Phrase: "Ninety-seven subtracted from a number \( r \)"
- Translation: We subtract 97 from the variable \( r \).
- Expression: \( r - 97 \)

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8. The product of a number \( d \) and sixty-one

- Phrase: "The product of a number \( d \) and sixty-one"
- Translation: "Product" means multiplication. We multiply \( d \) by 61.
- Expression: \( 61d \) or \( d \cdot 61 \)

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9. The sum of thirty-nine and a number \( f \)

- Phrase: "The sum of thirty-nine and a number \( f \)"
- Translation: "Sum" means addition. We add 39 to the variable \( f \).
- Expression: \( 39 + f \)

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10. Twenty-three added to a number \( j \)

- Phrase: "Twenty-three added to a number \( j \)"
- Translation: We add 23 to the variable \( j \).
- Expression: \( j + 23 \)

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11. Twelve divided by a number \( c \)

- Phrase: "Twelve divided by a number \( c \)"
- Translation: We divide 12 by the variable \( c \).
- Expression: \( \frac{12}{c} \)

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12. A number \( y \) multiplied by eighty-five

- Phrase: "A number \( y \) multiplied by eighty-five"
- Translation: We multiply \( y \) by 85.
- Expression: \( 85y \) or \( y \cdot 85 \)

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13. A number \( w \) decreased by fifty-eight

- Phrase: "A number \( w \) decreased by fifty-eight"
- Translation: "Decreased by" means subtraction. We subtract 58 from the variable \( w \).
- Expression: \( w - 58 \)

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14. A number \( b \) minus fifty-eight

- Phrase: "A number \( b \) minus fifty-eight"
- Translation: We subtract 58 from the variable \( b \).
- Expression: \( b - 58 \)

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15. Forty-six more than a number \( z \)

- Phrase: "Forty-six more than a number \( z \)"
- Translation: "More than" means addition. We add 46 to the variable \( z \).
- Expression: \( z + 46 \)

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16. A number \( h \) divided by thirty-one

- Phrase: "A number \( h \) divided by thirty-one"
- Translation: We divide the variable \( h \) by 31.
- Expression: \( \frac{h}{31} \)

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17. The sum of a number \( n \) and forty-nine

- Phrase: "The sum of a number \( n \) and forty-nine"
- Translation: We add 49 to the variable \( n \).
- Expression: \( n + 49 \)

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18. The quotient of a number \( S \) and forty-two

- Phrase: "The quotient of a number \( S \) and forty-two"
- Translation: We divide the variable \( S \) by 42.
- Expression: \( \frac{S}{42} \)

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19. The product of forty and a number \( t \)

- Phrase: "The product of forty and a number \( t \)"
- Translation: We multiply 40 by the variable \( t \).
- Expression: \( 40t \) or \( t \cdot 40 \)

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20. A number \( c \) added to twenty-three

- Phrase: "A number \( c \) added to twenty-three"
- Translation: We add the variable \( c \) to 23.
- Expression: \( c + 23 \)

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Final Answer

Here are all the algebraic expressions:

1. \( g + 63 \)
2. \( \frac{7}{x} \)
3. \( v - 10 \)
4. \( 13 - k \)
5. \( q + 72 \)
6. \( 11 + m \)
7. \( r - 97 \)
8. \( 61d \)
9. \( 39 + f \)
10. \( j + 23 \)
11. \( \frac{12}{c} \)
12. \( 85y \)
13. \( w - 58 \)
14. \( b - 58 \)
15. \( z + 46 \)
16. \( \frac{h}{31} \)
17. \( n + 49 \)
18. \( \frac{S}{42} \)
19. \( 40t \)
20. \( c + 23 \)

\boxed{
\begin{aligned}
1. & \ g + 63 \\
2. & \ \frac{7}{x} \\
3. & \ v - 10 \\
4. & \ 13 - k \\
5. & \ q + 72 \\
6. & \ 11 + m \\
7. & \ r - 97 \\
8. & \ 61d \\
9. & \ 39 + f \\
10. & \ j + 23 \\
11. & \ \frac{12}{c} \\
12. & \ 85y \\
13. & \ w - 58 \\
14. & \ b - 58 \\
15. & \ z + 46 \\
16. & \ \frac{h}{31} \\
17. & \ n + 49 \\
18. & \ \frac{S}{42} \\
19. & \ 40t \\
20. & \ c + 23
\end{aligned}
}