Basic Algebra Worksheets - Free Printable

The task involves generating algebraic expressions based on verbal descriptions. Below, I will explain the solution for each problem step by step.

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Problem 1: "4 more than \( a \)"

- Verbal Description: "4 more than \( a \)"
- Mathematical Interpretation: Add 4 to \( a \).
- Expression: \( a + 4 \)
- Alternative Form: \( 4 + a \) (since addition is commutative)

Answer: \( a + 4 \) or \( 4 + a \)

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Problem 2: "double \( b \)"

- Verbal Description: "double \( b \)"
- Mathematical Interpretation: Multiply \( b \) by 2.
- Expression: \( 2b \)
- Alternative Form: \( b \times 2 \)

Answer: \( 2b \) or \( b \times 2 \)

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Problem 3: "10 less than \( c \)"

- Verbal Description: "10 less than \( c \)"
- Mathematical Interpretation: Subtract 10 from \( c \).
- Expression: \( c - 10 \)

Answer: \( c - 10 \)

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Problem 4: "a half of \( d \)"

- Verbal Description: "a half of \( d \)"
- Mathematical Interpretation: Divide \( d \) by 2.
- Expression: \( \frac{d}{2} \)
- Alternative Form: \( \frac{1}{2}d \)

Answer: \( \frac{d}{2} \) or \( \frac{1}{2}d \)

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Problem 5: "8 more than \( e \)"

- Verbal Description: "8 more than \( e \)"
- Mathematical Interpretation: Add 8 to \( e \).
- Expression: \( e + 8 \)

Answer: \( e + 8 \)

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Problem 6: "9 subtract \( f \)"

- Verbal Description: "9 subtract \( f \)"
- Mathematical Interpretation: Subtract \( f \) from 9.
- Expression: \( 9 - f \)

Answer: \( 9 - f \)

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Problem 7: "4 lots of \( g \)"

- Verbal Description: "4 lots of \( g \)"
- Mathematical Interpretation: Multiply \( g \) by 4.
- Expression: \( 4g \)

Answer: \( 4g \)

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Problem 8: "7 subtract \( h \)"

- Verbal Description: "7 subtract \( h \)"
- Mathematical Interpretation: Subtract \( h \) from 7.
- Expression: \( 7 - h \)

Answer: \( 7 - h \)

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Problem 9: "14 less than \( i \)"

- Verbal Description: "14 less than \( i \)"
- Mathematical Interpretation: Subtract 14 from \( i \).
- Expression: \( i - 14 \)

Answer: \( i - 14 \)

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Problem 10: "multiply \( j \) by 4"

- Verbal Description: "multiply \( j \) by 4"
- Mathematical Interpretation: Multiply \( j \) by 4.
- Expression: \( 4j \)

Answer: \( 4j \)

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Problem 11: "divide \( k \) by 3"

- Verbal Description: "divide \( k \) by 3"
- Mathematical Interpretation: Divide \( k \) by 3.
- Expression: \( \frac{k}{3} \)
- Alternative Form: \( k \div 3 \)

Answer: \( \frac{k}{3} \) or \( k \div 3 \)

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Problem 12: "double \( l \) and add 2"

- Verbal Description: "double \( l \) and add 2"
- Mathematical Interpretation: First, multiply \( l \) by 2, then add 2.
- Expression: \( 2l + 2 \)

Answer: \( 2l + 2 \)

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Problem 13: "halve \( m \) and then subtract 3"

- Verbal Description: "halve \( m \) and then subtract 3"
- Mathematical Interpretation: First, divide \( m \) by 2, then subtract 3.
- Expression: \( \frac{m}{2} - 3 \)
- Alternative Form: \( \frac{1}{2}m - 3 \)

Answer: \( \frac{m}{2} - 3 \) or \( \frac{1}{2}m - 3 \)

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Problem 14: "double \( n \) and then add 5"

- Verbal Description: "double \( n \) and then add 5"
- Mathematical Interpretation: First, multiply \( n \) by 2, then add 5.
- Expression: \( 2n + 5 \)

Answer: \( 2n + 5 \)

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Problem 15: "double \( o \) and then subtract 3"

- Verbal Description: "double \( o \) and then subtract 3"
- Mathematical Interpretation: First, multiply \( o \) by 2, then subtract 3.
- Expression: \( 2o - 3 \)

Answer: \( 2o - 3 \)

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Problem 16: "halve \( p \) and then add 6"

- Verbal Description: "halve \( p \) and then add 6"
- Mathematical Interpretation: First, divide \( p \) by 2, then add 6.
- Expression: \( \frac{p}{2} + 6 \)
- Alternative Form: \( \frac{1}{2}p + 6 \)

Answer: \( \frac{p}{2} + 6 \) or \( \frac{1}{2}p + 6 \)

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Problem 17: "subtract \( q \) from 10"

- Verbal Description: "subtract \( q \) from 10"
- Mathematical Interpretation: Subtract \( q \) from 10.
- Expression: \( 10 - q \)

Answer: \( 10 - q \)

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Problem 18: "subtract 10 from \( q \)"

- Verbal Description: "subtract 10 from \( q \)"
- Mathematical Interpretation: Subtract 10 from \( q \).
- Expression: \( q - 10 \)

Answer: \( q - 10 \)

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Problem 19: "multiply \( r \) by 8 then add 1"

- Verbal Description: "multiply \( r \) by 8 then add 1"
- Mathematical Interpretation: First, multiply \( r \) by 8, then add 1.
- Expression: \( 8r + 1 \)

Answer: \( 8r + 1 \)

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Problem 20: "divide \( s \) by 5 and then subtract 4"

- Verbal Description: "divide \( s \) by 5 and then subtract 4"
- Mathematical Interpretation: First, divide \( s \) by 5, then subtract 4.
- Expression: \( \frac{s}{5} - 4 \)
- Alternative Form: \( s \div 5 - 4 \)

Answer: \( \frac{s}{5} - 4 \) or \( s \div 5 - 4 \)

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Problem 21: "multiply \( t \) by 4 and then subtract 6"

- Verbal Description: "multiply \( t \) by 4 and then subtract 6"
- Mathematical Interpretation: First, multiply \( t \) by 4, then subtract 6.
- Expression: \( 4t - 6 \)

Answer: \( 4t - 6 \)

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Problem 22: "add 2 to \( u \) and then double it"

- Verbal Description: "add 2 to \( u \) and then double it"
- Mathematical Interpretation: First, add 2 to \( u \), then multiply the result by 2.
- Expression: \( 2(u + 2) \)
- Simplified Form: \( 2u + 4 \)

Answer: \( 2(u + 2) \) or \( 2u + 4 \)

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Problem 23: "subtract 3 from \( v \) and then multiply by 2"

- Verbal Description: "subtract 3 from \( v \) and then multiply by 2"
- Mathematical Interpretation: First, subtract 3 from \( v \), then multiply the result by 2.
- Expression: \( 2(v - 3) \)
- Simplified Form: \( 2v - 6 \)

Answer: \( 2(v - 3) \) or \( 2v - 6 \)

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Problem 24: "multiply \( w \) by 6 and then subtract 9"

- Verbal Description: "multiply \( w \) by 6 and then subtract 9"
- Mathematical Interpretation: First, multiply \( w \) by 6, then subtract 9.
- Expression: \( 6w - 9 \)

Answer: \( 6w - 9 \)

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Final Answer

\[
\boxed{
\begin{array}{ll}
1) & a + 4 \text{ or } 4 + a \\
2) & 2b \text{ or } b \times 2 \\
3) & c - 10 \\
4) & \frac{d}{2} \text{ or } \frac{1}{2}d \\
5) & e + 8 \\
6) & 9 - f \\
7) & 4g \\
8) & 7 - h \\
9) & i - 14 \\
10) & 4j \\
11) & \frac{k}{3} \text{ or } k \div 3 \\
12) & 2l + 2 \\
13) & \frac{m}{2} - 3 \text{ or } \frac{1}{2}m - 3 \\
14) & 2n + 5 \\
15) & 2o - 3 \\
16) & \frac{p}{2} + 6 \text{ or } \frac{1}{2}p + 6 \\
17) & 10 - q \\
18) & q - 10 \\
19) & 8r + 1 \\
20) & \frac{s}{5} - 4 \text{ or } s \div 5 - 4 \\
21) & 4t - 6 \\
22) & 2(u + 2) \text{ or } 2u + 4 \\
23) & 2(v - 3) \text{ or } 2v - 6 \\
24) & 6w - 9 \\
\end{array}
}
\]