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Question 519311: Instructions are to simplify each expression and tell which property you used:
Ex. 6 x 23, teacher did example as =6(20+3) and indicates "distribute".
Ex. 13 x 12, teacher did example as =12 x 13 and indicates "commutative".
Is there any particular reason she didn't do the second example as =13(10+2) (distributive) or the first example as =23 x 6 (commutative)?
Can you just chose either randomly depending on what's convenient for mental math or is there an absolute answer?
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! The Distributive Property allows you to multiply a sum by multiplying each addend separately and then summing. So,
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6*23 = 6(20+3) = 120 + 18 = 138
or
6*23 = (3+3)*(23) = 69+69 = 138
or
6*23 = (3+3)*(20+3) = 60 +9 +60 +9 = 138
etc.
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The Commutative Property holds that if you change the order of operands, you do not change the result. So,
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13*12 = 12*13
13*12 = 156
12*13 = 156
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As you can see, the order did not matter.
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The reason she didn't show the second example at 13*(10+2) is that 13*(10+2) would illustrate the Distributive Property, not the Commutative Property.
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Of course, it is true that 13*12=13*(10+2), applying the Distributive Property. Similarly, 6*23 can be shown as 23*6, which would illustrate the Commutative Property, not the Distributive Property.
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No, you do not pick randomly. You choose the property to apply that makes your work easier to do. As you said, the "mental math". Oftentimes, you will use several properties to solve a single problem.
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