Algebra Practice

Algebraic Expressions with Decimals Practice Test

Combine decimal coefficients, distribute accurately, evaluate expressions, and model everyday situations.

Algebraic Expressions with Decimals Practice Test

20 varied questions on decimal coefficients and algebraic expressions.

Instant feedback · Worked explanations
After the test · decimal lab

Decimal coefficients behave like ordinary coefficients — precision and place value are the extra layer

In algebraic expressions with decimals, the algebraic structure does not change. Like terms still require identical variable parts, distribution still reaches every term, and substitution still follows order of operations. What changes is the numerical bookkeeping: decimal places, signs, exact values, and rounding must stay under control.

Signed decimalsLike termsDistributionEvaluation Equivalent formsPlace valueRoundingModels
Place-value rail

Decimal coefficient arithmetic is safest when place values are mentally aligned

Trailing zeros can be added without changing value, making the decimal structure easier to compare.

Term 12.75x
Term 2−0.80x
Term 3+1.05x
Coefficients2.75−0.80+1.05
Result3.00x = 3x
Adding trailing zeros changes notation, not value: 0.8 = 0.80 and 3.0 = 3.00.
Decimal coefficient board

Combine decimal coefficients only after confirming that the terms are actually like terms

Same variable identity

4.6y
−1.25y
+0.65y
4.6 − 1.25 + 0.65 = 4.00 → 4y

Different variable identity

4.6y
−1.25y²
+0.65
Keep all three terms separate.
Decimal distribution bench

A decimal factor distributes to every term just like an integer factor

0.4(5x − 7.5)
2x − 3
0.4·5x = 2x
0.4·(−7.5) = −3

Do the multiplication term by term. If the decimal multiplication is awkward, rewrite a terminating decimal as a fraction temporarily, such as 0.4 = 2/5.

Distribution errors are algebra errors; misplaced decimal points are arithmetic errors. Check both separately.
Signed-decimal substitution

Negative decimal inputs need parentheses before powers are evaluated

For x = −1.5, evaluate 2.4x² − 0.6 without losing the sign or the exponent structure.

Expression2.4x² − 0.6
Substitute2.4(−1.5)² − 0.6
Compute2.4(2.25) − 0.6
Result4.8
Decimal–fraction bridge

Terminating decimals can be rewritten as fractions when that makes algebra easier

Decimal0.375x
↔
Fraction3/8x
↔
Percent coefficient37.5%x

These forms represent the same numerical coefficient. Choose the notation that makes the next step shortest and clearest.

Precision checkpoint

Do not round an intermediate decimal unless the problem actually asks you to

Exact terminating result

1.25(2.4x)
= 3.00x
= 3x
No rounding is needed.

Nonterminating decimal

1 ÷ 3 = 0.3333…
Keep 1/3 exactly unless a rounding instruction is given.
Equivalent decimal forms

Decimal expressions can move between expanded, factored, and fractional forms

Factored decimal 0.5(6x + 4)
Expanded decimal 3x + 2
Fraction factor 1/2(6x + 4)

All three forms are equivalent because 0.5 = 1/2 and distribution produces the same expanded expression.

Perimeter model length = 2.5x + 1.2
width = 1.5x + 0.8
Cost model fixed fee = $7.50
unit rate = $2.25n
Decimal expressions in context

Decimal coefficients often represent measured quantities, prices, or rates

In applied expressions, the decimal coefficient has meaning, so units and interpretation should survive simplification.

P = 2(2.5x + 1.2) + 2(1.5x + 0.8)
P = 5x + 2.4 + 3x + 1.6
P = 8x + 4
Cost model: C = 7.50 + 2.25n
Decimal error radar

Four mistakes that look small but change the algebraic value

2.4x + 0.6x = 3.0x² 2.4x + 0.6x = 3x

Combining like terms changes the coefficient, not the exponent.

0.3(x + 5) = 0.3x + 5 0.3(x + 5) = 0.3x + 1.5

The decimal factor multiplies every term inside the parentheses.

4.25x − 0.8x = 4.17x 4.25x − 0.80x = 3.45x

Align the decimal places before subtracting the coefficients.

For x = −1.2, x² = −1.44 (−1.2)² = 1.44

A negative substituted value must be grouped before applying the exponent.

Use the score diagnostically

Separate decimal-arithmetic errors from algebraic-structure errors

That distinction tells you whether to review place value or the algebraic rule itself.

Place valueAlign decimal points and preserve signs.
Algebraic structureLike terms, powers, constants, variables.
Distribution & evaluationDecimal factors and signed inputs.
Precision & modelsRounding, units, cost and measurement meaning.