This answer key gives complete worked solutions for the algebraic expressions worksheet. Each solution shows the substitution or the property that was used, and every final answer is in bold so students can check their own work quickly.
Grade 6Common Core: 6.EE.A.2 · 6.EE.A.3 · 6.EE.A.4
Problem 1: Parts of an Expression
- The terms are \(7x\), \(4y\), and \(9\): 3 terms
- The coefficient of \(x\) is \(7\)
- The coefficient of \(y\) is \(4\)
- The term with no variable is \(9\)
Problem 2: Writing Simple Expressions
- \(n\) plus 8: \(n + 8\)
- \(y\) minus 6: \(y – 6\)
- 5 times \(m\): \(5m\)
- \(k\) over 4: \(\frac{k}{4}\)
Problem 3: Writing Longer Expressions
- Sum first, then double: \(2(x + 7)\)
- \(3a\), then subtract 2: \(3a – 2\)
- 20 divided by \(p\): \(\frac{20}{p}\)
- The product is \(4t\); 9 less than it is \(4t – 9\)
Problem 4: Evaluating Expressions
- \(6 + 9 = \) \(15\)
- \(4\times 6 = \) \(24\)
- \(30: 6 = \) \(5\)
- \(3\times 6 – 5 = 18 – 5 = \) \(13\)
Problem 5: Exponents and Formulas
- \(7^2 = \) \(49\)
- \(5\times 4^2 – 10 = 5\times 16 – 10 = 80 – 10 = \) \(70\)
- \(V = 5^3 = 125\). Answer: \(125\text{ ft}^3\)
- \(A = 6\times (\frac{1}{2})^2 = 6\times \frac{1}{4} = \frac{6}{4} = \) \(\frac{3}{2}\text{ in}^2\), or 1.5 square inches
Problem 6: Distributive Property
- \(3\times x + 3\times 5 = \) \(3x + 15\)
- \(4\times 2y + 4\times 1 = \) \(8y + 4\)
- The greatest common factor of \(6\) and \(9\) is \(3\): \(3(2x + 3)\)
- The greatest common factor of \(10\) and \(15\) is \(5\): \(5(2 + 3m)\)
Problem 7: Combining Like Terms
- \(7 + 3 = 10\): \(10a\)
- \(9 – 4 = 5\): \(5b\)
- \(2x + 6x = 8x\) and \(5 + 1 = 6\): \(8x + 6\)
- \(3y + y + 2y = 6y\), so the result is \(6y + 4\)
Problem 8: Dog Walking Pay
Pay for \(h\) hours is \(12h\), plus the $5 tip: \(12h + 5\).
When \(h = 6\): \(12\times 6 + 5 = 72 + 5 = 77\).
Total pay: \(12h + 5\); $77
Problem 9: Flower Bed Area
Area is width times length: \(4(x + 6)\). By the distributive property, \(4(x + 6) = 4x + 24\).
Check with \(x = 3\): \(4(3 + 6) = 4\times 9 = 36\), and \(4(3) + 24 = 12 + 24 = 36\). Both give \(36\).
Equivalent expressions: \(4(x + 6)\) and \(4x + 24\)
Problem 10: Gift Box
- \(V = 8^3 = 8\times 8\times 8 = 512\). Answer: \(512\text{ in}^3\)
- \(A = 6\times 8^2 = 6\times 64 = 384\). Answer: \(384\text{ in}^2\)
- Cost \(= 384\times \$0.02 = \$7.68\). Answer: \(\$7.68\)
See every chapter on the Grade 6 math page.