Writing Algebraic Expressions worksheet for practicing converting phrases to algebraic expressions and vice versa.

Let's solve each problem step by step.

---

Part 1: Write an expression for each phrase

We need to translate each verbal phrase into an algebraic expression. Let’s use x as the variable for "a number" unless otherwise specified.

---

1) Six less than a number
- "Six less than" means subtract 6 from the number.
- So, if the number is $ x $, then:
$$
x - 6
$$

✔ Answer: $ x - 6 $

---

2) The sum of 10 times a number and two
- "10 times a number" = $ 10x $
- "The sum of ... and two" means add 2:
$$
10x + 2
$$

✔ Answer: $ 10x + 2 $

---

3) The quotient of 20 divided by y, increased by seven
- "Quotient of 20 divided by y" = $ \frac{20}{y} $
- "Increased by seven" means add 7:
$$
\frac{20}{y} + 7
$$

✔ Answer: $ \frac{20}{y} + 7 $

---

4) The product of 4 and a number, divided by 2
- "Product of 4 and a number" = $ 4x $
- "Divided by 2" = $ \frac{4x}{2} $ or simplified: $ 2x $

But since we're writing the expression as described, we can leave it as:
$$
\frac{4x}{2}
$$

Alternatively, simplified: $ 2x $. But unless asked to simplify, we can write the direct translation.

✔ Answer: $ \frac{4x}{2} $ or $ 2x $

> (Both are correct; $ 2x $ is simpler.)

---

5) The difference of ten and six, multiplied by a number
- "Difference of ten and six" = $ 10 - 6 = 4 $
- "Multiplied by a number" = $ 4 \times x = 4x $

✔ Answer: $ 4x $

---

Part 2: Write a phrase for each expression

Now, we interpret each algebraic expression in words.

---

6) $ 2x - 6 $
- $ 2x $: "Two times a number"
- Minus 6: "six less than"
- So: Six less than two times a number

✔ Phrase: *Six less than two times a number*

---

7) $ 5(6 + x) $
- $ 6 + x $: "the sum of six and a number"
- Multiplied by 5: "five times the sum of six and a number"

✔ Phrase: *Five times the sum of six and a number*

---

8) $ (2 + x) - 8 $
- $ 2 + x $: "the sum of two and a number"
- Minus 8: "eight less than that sum"
- So: Eight less than the sum of two and a number

✔ Phrase: *Eight less than the sum of two and a number*

---

9) $ \frac{2 + x}{5} $
- $ 2 + x $: "the sum of two and a number"
- Divided by 5: "divided by five"
- So: The quotient of the sum of two and a number, divided by five

✔ Phrase: *The quotient of the sum of two and a number, divided by five*

---

10) $ \frac{20}{x} + 7 $
- $ \frac{20}{x} $: "the quotient of twenty divided by a number"
- Plus 7: "increased by seven"
- So: Seven more than the quotient of twenty divided by a number

✔ Phrase: *Seven more than the quotient of twenty divided by a number*

---

✔ Final Answers:

#### Write an expression for each phrase:
1) $ x - 6 $
2) $ 10x + 2 $
3) $ \frac{20}{y} + 7 $
4) $ \frac{4x}{2} $ or $ 2x $
5) $ 4x $

#### Write a phrase for each expression:
6) Six less than two times a number
7) Five times the sum of six and a number
8) Eight less than the sum of two and a number
9) The quotient of the sum of two and a number, divided by five
10) Seven more than the quotient of twenty divided by a number

---

Let me know if you'd like this formatted for printing or want explanations for any specific one!