Testinar Grade 6 math

The Distributive Property with Common Factors

Students will build Grade 6 mastery of the distributive property with common factors using models, equations, and test-style reasoning.

CH02-05 The Number System

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

Which expression is equivalent to \(18+24\) using the distributive property?
1. \(6(3+4)\)
2. \(6(3+24)\)
3. \(2(9+24)\)
4. \(3(6+8)\)
Factor \(12+20\) using the distributive property.
1. \(4(3+5)\)
2. \(2(6+10)\)
3. \(3(4+20)\)
4. \(5(2+4)\)
Which shows \(15+10\) factored using the GCF?
1. \(3(5+10)\)
2. \(5(3+2)\)
3. \(2(8+5)\)
4. \(10(2+1)\)
What is the GCF of \(21\) and \(28\)?
1. \(2\)
2. \(4\)
3. \(7\)
4. \(14\)
Which expression is equivalent to \(30+45\)?
1. \(5(6+9)\)
2. \(15(2+3)\)
3. \(3(10+15)\)
4. \(6(5+7.5)\)
Expand \(7(4+6)\).
1. \(28+42\)
2. \(28+6\)
3. \(4+42\)
4. \(11 \times 7\)
Which two expressions are equivalent?
1. \(8(5+3)\) and \(40+24\)
2. \(8(5+3)\) and \(8 + 8\)
3. \(8(5+3)\) and \(45+24\)
4. \(8(5+3)\) and \(40+3\)
Expand \(6(2+9)\).
1. \(12+54\)
2. \(12+9\)
3. \(6+18\)
4. \(66\)

Teacher and parent reference

Answer key and explanations

A. \(6(3+4)\)
Peek for the biggest factor both sums share evenly: that's \(6\). Pull it out softly: \(18+24=6\cdot3+6\cdot4=6(3+4)\)---the distributive property read backward.
A. \(4(3+5)\)
The GCF of \(12\) and \(20\) is \(4\). So \(12+20 = 4(3+5)\). Choice B uses GCF \(2\), which is correct but not the greatest common factor. Choice A uses the greatest common factor.
B. \(5(3+2)\)
GCF of \(15\) and \(10\) is \(5\). Thus \(15+10=5(3+2)\). Choice A uses factor \(3\) (not the greatest); Choice C uses \(2\) (not a common factor of both); Choice D uses \(10\) but yields \(30\), not \(25\).
C. \(7\)
Factors of \(21\): \(1, 3, 7, 21\). Factors of \(28\): \(1, 2, 4, 7, 14, 28\). Common factors: \(1, 7\). The GCF is \(7\).
B. \(15(2+3)\)
GCF of \(30\) and \(45\) is \(15\). So \(30+45 = 15(2+3)\). Choice A uses GCF \(5\), which works but is not the greatest. Choice B is correct.
A. \(28+42\)
Using the distributive property: \(7(4+6) = 7 \cdot 4 + 7 \cdot 6 = 28 + 42 = 70\).
A. \(8(5+3)\) and \(40+24\)
\(8(5+3) = 8 \cdot 5 + 8 \cdot 3 = 40 + 24\). Choice B gives \(8+8=16\), so it is not equivalent.
A. \(12+54\)
Distributive property: \(6(2+9) = 6 \cdot 2 + 6 \cdot 9 = 12 + 54 = 66\). Choice A shows the expanded form before simplifying.