2.6: Exercise 2
 Page ID
 13972
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State the property or indicate that no property is applicable.

\(5+x=x+5\)

\(7(a2)=7a7(2)\)

\(5(x\cdot 2)=(5x)(2)\)

\((y+2)+4=4+(y+2)\)

\(6\cdot (t\cdot 2)=(6\cdot t)\cdot (6\cdot 2)\)

\(w5=5w\)

\(xy=yx\)

\(a\div \pi=\pi \div a\)

\((4.7)+[(6.5)+(\sqrt{2})]=[(4.7)+(6.5)]+(\sqrt{2})\)

\(x4=4x\)

Factor \(12x+18\)

Factor \(24x^2+12x\)
The solutions follow:
Keep them covered up till you have worked out each of the problems above.

\(5+x=x+5\)
Solution:
\(5+x=x+5\) illustrates the commutative property of addition. The terms commuted to each other’s position. 
\(7(a2)=7a7(2)\)
Solution:
\(7(a2)=7a7(2)\) illustrates the distributive property of multiplication over addition. 
\(5(x\cdot 2)=(5x)(2)\)
Solution:
\(5(x\cdot 2)=(5x)(2)\) illustrates the associative property of multiplication. 
\((y+2)+4=4+(y+2)\)
Solution:
\((y+2)+4=4+(y+2)\) illustrates the commutative property of addition. \((y+2)\) and 4 have commuted to each other’s position. \(y\) remains grouped with 2.N regrouping took place.

\(6\cdot (t\cdot 2)=(6\cdot t)\cdot (6\cdot 2)\)
Solution:
\(6\cdot (t\cdot 2)=(6t)\cdot (6\cdot 2)\) does not illustrate any of the mentioned properties. You cannot distribute multiplication over multiplication. 
\(w5=5w\)
Solution:
\(w5=5w\) does not illustrate any of the mentioned properties. Subtraction is not commutative.
We shall learn later that \(w5=w+(5)=(5)+w\) because addition is commutative. 
\(xy=yx\)
Solution:
\(xy=yx\) illustrates the commutative property of multiplication. The terms commuted to each other’s position. 
\(a\div \pi=\pi \div a\)
Solution:
\(a\div \pi=\pi \div a\) does not illustrate any of the mentioned properties. Division is not commutative. 
\((4.7)+[(6.5)+(\sqrt{2})]=[(4.7)+(6.5)]+(\sqrt{2})\)
Solution:
\((4.7)+[(6.5)+(\sqrt{2})]=[(4.7)+(6.5)]+(\sqrt{2})\) illustrates the associative property of addition. \(6.5\) is associated (grouped) with \(\sqrt{2}\) on the left and \(4.7\) on the right. 
\(x4=4x\)
Solution:
\(x4=4x\) does not illustrate any of the mentioned properties. Subtraction is not commutative. 
Factor \(12x+18\)
Solution:
\(\begin{array}{rcl lll} 12x+18&=&(3)(4)x+(3)(6)\\ &=&3(4x+6)\\ \end{array}\)A quick check: \(3(4x+6)=3(4x)+3(6)=12x+18\)Gthe result grees wiht the iginal statement.

Factor \(24x^2+12x\)
Solution:
\(\begin{array}{rcl lll} 24x^2+12x&=&2(12)x\ x+1(12)x\\ &=&12x(2x+1)\\ \end{array}\)
Note the \(1\) besides the \(12\).A quick check: \(12x(2x+1)=12x(2x)+12x(1)=24x^2+12x\)