Algebraic Expression Word Problems Practice Test

Translate costs, rates, measurements, percentages, and verbal relationships into correct expressions.

Algebraic Expression Word Problems Practice Test

20 word problems on writing, evaluating, and simplifying algebraic expressions.

Instant feedback · Worked explanations

After the test · modeling studio

A word problem becomes manageable when the story is separated into quantities, relationships, and operations

Algebraic-expression word problems usually do not ask you to solve for an unknown. They ask you to build the mathematical rule that represents the situation. That means deciding what changes, what stays fixed, how quantities are related, and which operation connects them.

Fixed + variable costRatesPercentGeometry AgesAveragesRepeated quantitiesParentheses

Story anatomy

Mark the fixed quantity, the changing quantity, and the relationship before writing symbols

A service charges a $25 fixed fee plus $8 for each of n items.

Fixed$25 appears once

Variablen counts the items

Relationship$8 is multiplied by n

Expression: 25 + 8n. The fixed fee is not multiplied by n because it is charged only once.

Phrase switchboard

Translate complete phrases into operations

7 more than x

x + 7

5 less than y

y − 5

three times the sum of x and 4

3(x + 4)

half the difference of a and 6

(a − 6)/2

15% of p

0.15p

Words such as “sum” and “difference” often signal that an entire grouped quantity must be multiplied or divided.

Word-order trap

“Less than” reverses the visible order of the quantities

4 less than x

x − 4

not 4 − x

The phrase tells you that the final amount is four below x. A quick verbal check helps: if x were 10, “4 less than 10” should be 6.

Use a simple test value whenever verbal subtraction feels ambiguous.

Unit checkpoint

Units can tell you whether an expression makes sense before you calculate anything

Each term in an addition must represent the same kind of quantity, and multiplication should produce the expected unit.

Rate60 miles/hour

Timet hours

Operation60 · t

Distance60t miles

Fixed + variable cost

Separate the one-time part from the per-unit part

Fixed charge $18 setup fee

Changing charge $2.75 per item × n items

C = 18 + 2.75n

The fixed $18 appears once. Only the per-item charge changes with n.

Rate model route

Rate word problems become expressions by tracking “per” as multiplication by a count or time

Rate72 kilometers per hour

Durationt hours

Distance expression72t kilometers

A rate already contains a division in its unit. Multiplying by the matching count or time removes that denominator conceptually.

Percent translation

Turn a percentage into a multiplier before attaching it to the original quantity

Discount amount

20% of p
= 0.20p

Price after discount

p − 0.20p
= 0.80p

“20% off” and “20% of” are related but not identical questions: one asks for the reduction, the other may ask for the remaining amount.

Geometry blueprint

Translate the measurements first, then apply the geometry formula

If a rectangle has length 3x + 2 and width x + 4, the same dimensions can generate different expressions depending on what the question asks.

Perimeter: P = 2(3x + 2) + 2(x + 4)

P = 8x + 12

Area: A = (3x + 2)(x + 4)

Perimeter and area model different quantities.

Parentheses trigger

Words that name an entire sum or difference often require grouping

Multiply a whole sum

“three times the sum of x and 4”
→ 3(x + 4)

Divide a whole difference

“half the difference of a and 6”
→ (a − 6)/2

Modeling error detective

Four expressions that fail because they misread the story, not because the arithmetic is difficult

“5 less than x” → 5 − x x − 5

The amount is five below x, so x is the starting quantity.

$12 fixed fee + $3 per item → 12n + 3n 12 + 3n

The fixed fee is charged once; only the per-item part depends on n.

“25% of p” → 25p 0.25p

25% = 25/100 = 0.25.

“twice the sum of x and 7” → 2x + 7 2(x + 7)

The word “sum” names the whole quantity that is doubled.

Use the score diagnostically

A missed word problem usually reveals a translation error before it reveals an algebra error

Classify the misunderstanding so the next practice attempt targets the correct modeling skill.

Quantity rolesFixed, variable, rate, total, or repeated amount.

Language orderLess than, more than, difference, quotient.

GroupingA whole sum or difference needed parentheses.

Model meaningUnits, percent interpretation, perimeter vs area.