Algebraic expressions worksheet for converting phrases into expressions and expressions into phrases.

Let’s go step by step to solve each problem.

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Part 1: Write an expression for each phrase.

We’ll use a variable (like *x* or *y*) to represent “a number” unless the problem gives us a specific letter.

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1) Six less than a number

“Less than” means we subtract, but note: “six less than a number” means we start with the number and take away six.

So if the number is *x*, then:
→ x - 6

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2) The sum of 10 times a number and two

“Sum” means addition.
“10 times a number” = 10*x*
Then add 2 →
→ 10x + 2

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3) The quotient of 20 divided by y, increased by seven

“Quotient” means division → 20 ÷ y = 20/y
“Increased by seven” means add 7 →
→ 20/y + 7

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4) The product of 4 and a number, divided by 2

“Product” means multiplication → 4 × x = 4x
Then divide that by 2 →
→ (4x)/2
This can be simplified to 2x, but since the question says “write an expression,” either is acceptable. We’ll leave it as (4x)/2 to match the wording exactly — though simplifying is also correct. Let’s write both versions in mind, but for final answer, we’ll use the unsimplified form to reflect the phrase literally.

Actually, let’s check: “The product of 4 and a number, divided by 2” — this could mean (4×number)÷2, which is indeed (4x)/2. But often in math, we simplify. Since the instruction doesn’t say “simplify,” we can write it as is. However, most teachers expect simplified form. Let me think... In middle school algebra, they usually accept either, but prefer simplified. I’ll go with 2x because it’s simpler and equivalent.

Wait — let’s read again: “The product of 4 and a number, divided by 2”. That’s clearly (4 * x) / 2 = 2x. So yes, 2x is fine.

But to be safe, let’s see what the original phrase implies. It doesn’t say “then divide the result by 2” — it says “divided by 2” after “the product”, so yes, it’s (product) ÷ 2.

I think 2x is best.

Actually, let’s hold off and do all first, then decide.

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5) The difference of ten and six, multiplied by a number

“Difference of ten and six” = 10 - 6 = 4
Then multiply by a number → 4 × x = 4x

Note: If it said “the difference of a number and six”, it would be x - 6, but here it’s “ten and six”, so fixed numbers.

So → 4x

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Now Part 2: Write a phrase for each expression.

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6) 2x - 6

This means: two times a number, minus six.
Or: six less than twice a number.

Both are correct. Let’s pick one clear version:
→ Six less than twice a number

(Alternatively: “Two times a number minus six” — also good.)

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7) 5(6 + x)

This is 5 multiplied by the quantity (6 plus x).
So:
→ Five times the sum of six and a number

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8) (2 + x) - 8

First, 2 plus a number, then subtract 8.
→ The sum of two and a number, decreased by eight

Or: “Eight less than the sum of two and a number”

Either works. Let’s use:
→ The sum of two and a number, minus eight

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9) (2 + x)/5

This is the sum of 2 and x, all divided by 5.
→ The sum of two and a number, divided by five

Or: “One-fifth of the sum of two and a number”

We’ll go with:
→ The quotient of the sum of two and a number and five

But simpler:
→ The sum of two and a number, divided by five

Yes.

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10) 20/x + 7

This is 20 divided by x, then add 7.
→ Twenty divided by a number, increased by seven

Which matches #3 backwards! Good.

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Now let’s compile final answers carefully.

Double-checking:

1) Six less than a number → x - 6 ✔
2) Sum of 10 times a number and two → 10x + 2 ✔
3) Quotient of 20 divided by y, increased by seven → 20/y + 7 ✔
4) Product of 4 and a number, divided by 2 → (4x)/2 or 2x → I think 2x is better and standard. Let’s confirm: if you have “product of 4 and x” = 4x, then “divided by 2” = 4x/2 = 2x. Yes. So 2x
5) Difference of ten and six, multiplied by a number → (10-6)*x = 4x ✔

6) 2x - 6 → “Six less than twice a number” ✔
7) 5(6+x) → “Five times the sum of six and a number” ✔
8) (2+x)-8 → “The sum of two and a number, minus eight” ✔
9) (2+x)/5 → “The sum of two and a number, divided by five” ✔
10) 20/x + 7 → “Twenty divided by a number, increased by seven” ✔

All look good.

Final Answer:

1) x - 6
2) 10x + 2
3) 20/y + 7
4) 2x
5) 4x
6) Six less than twice a number
7) Five times the sum of six and a number
8) The sum of two and a number, minus eight
9) The sum of two and a number, divided by five
10) Twenty divided by a number, increased by seven