Writing Algebraic Expressions Worksheets - Math Monks - Free Printable

Problem: Writing Algebraic Expressions

The task involves translating phrases into algebraic expressions and vice versa. Let's solve each part step by step.

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#### Part 1: Write an expression for each phrase

1. Six less than a number
- Phrase: "Six less than a number"
- Expression: If the number is represented by \( x \), then six less than the number is:
\[
x - 6
\]

2. The sum of 10 times a number and two
- Phrase: "The sum of 10 times a number and two"
- Expression: If the number is \( x \), then 10 times the number is \( 10x \). Adding two to this gives:
\[
10x + 2
\]

3. The quotient of 20 divided by \( y \), increased by seven
- Phrase: "The quotient of 20 divided by \( y \), increased by seven"
- Expression: The quotient of 20 divided by \( y \) is \( \frac{20}{y} \). Increasing this by seven gives:
\[
\frac{20}{y} + 7
\]

4. The product of 4 and a number, divided by 2
- Phrase: "The product of 4 and a number, divided by 2"
- Expression: If the number is \( x \), then the product of 4 and the number is \( 4x \). Dividing this by 2 gives:
\[
\frac{4x}{2} = 2x
\]

5. The difference of ten and six, multiplied by a number
- Phrase: "The difference of ten and six, multiplied by a number"
- Expression: The difference of ten and six is \( 10 - 6 = 4 \). Multiplying this by a number \( x \) gives:
\[
4x
\]

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#### Part 2: Write a phrase for each expression

6. \( 2x - 6 \)
- Expression: \( 2x - 6 \)
- Phrase: "Twice a number, decreased by six"

7. \( 5(6 + x) \)
- Expression: \( 5(6 + x) \)
- Phrase: "Five times the sum of six and a number"

8. \( (2 + x) - 8 \)
- Expression: \( (2 + x) - 8 \)
- Phrase: "Two plus a number, decreased by eight"

9. \( \frac{2 + x}{5} \)
- Expression: \( \frac{2 + x}{5} \)
- Phrase: "The quotient of the sum of two and a number, divided by five"

10. \( \frac{20}{x} + 7 \)
- Expression: \( \frac{20}{x} + 7 \)
- Phrase: "The quotient of twenty divided by a number, increased by seven"

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Final Answers:

1. \( x - 6 \)
2. \( 10x + 2 \)
3. \( \frac{20}{y} + 7 \)
4. \( 2x \)
5. \( 4x \)

6. "Twice a number, decreased by six"
7. "Five times the sum of six and a number"
8. "Two plus a number, decreased by eight"
9. "The quotient of the sum of two and a number, divided by five"
10. "The quotient of twenty divided by a number, increased by seven"

\boxed{
\begin{aligned}
&1. \, x - 6 \\
&2. \, 10x + 2 \\
&3. \, \frac{20}{y} + 7 \\
&4. \, 2x \\
&5. \, 4x \\
&6. \, \text{"Twice a number, decreased by six"} \\
&7. \, \text{"Five times the sum of six and a number"} \\
&8. \, \text{"Two plus a number, decreased by eight"} \\
&9. \, \text{"The quotient of the sum of two and a number, divided by five"} \\
&10. \, \text{"The quotient of twenty divided by a number, increased by seven"}
\end{aligned}
}