Worked Example 1
Distributive Property
Rewrite 4(2x − 3) without parentheses.
- 1Multiply each term inside by 4.
- 24 × 2x = 8x and 4 × (−3) = −12
Answer: 8x − 12
Florida Grade 6 Math · Algebraic Reasoning
MA.6.AR.1.4: Equivalent Expressions
What this Grade 6 benchmark means, worked examples, common mistakes, and a free printable worksheet.
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What Is Benchmark MA.6.AR.1.4?
Students use the associative, commutative, and distributive properties to write equivalent expressions with integer coefficients. For example, 5(3x + 1) = 15x + 5, and 2x + 3x = 5x.
Equivalent expressions have the same value for every value of the variable. Like terms (such as 3x and 5x) can be combined; unlike terms (such as 3x and 5) cannot.
Official benchmarkApply the properties of operations to generate equivalent algebraic expressions with integer coefficients.
On the FAST test: part of the Grade 6 reporting category Algebraic Reasoning, which is about 25–36% of the test.
Worked Examples
Worked Example 2
Combining Like Terms
Simplify 3x + 7 + 5x − 2.
- 1Reorder (commutative property): 3x + 5x + 7 − 2
- 2Combine like terms: 3x + 5x = 8x and 7 − 2 = 5
Answer: 8x + 5
Common Mistakes to Watch For
Distributing to only the first term
Wrong:4(2x − 3) = 8x − 3
Multiply every term by 4: 4(2x − 3) = 8x − 12.
Combining unlike terms
Wrong:3x + 5 = 8x
3x and 5 are not like terms, so 3x + 5 can't be combined.
Helpful Math Tip
Test two expressions by substituting the same number, like x = 2, into both. If they give different values, they are not equivalent.
Related Grade 6 Skills
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