Properties of Operations Points of Confusion

Properties of Operations (Differentiating). Points of Confusion

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Many students have trouble discriminating between commutative and associative properties.

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Copy these notes.

• Order changes --> Commutative

• Grouping Changes --> Associative

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 $6\cdot5=5\cdot6$  (Type the letter A, B, C or D.)

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 $\left(vw\right)x=v\left(wx\right)$  (Type the letter A, B, C or D.)

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 $\left(xy\right)z=\left(yx\right)z$  (Type the letter A, B, C or D.)

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 $7\cdot\left(4\cdot12\right)=\left(7\cdot4\right)\cdot12$  (Type the letter A, B, C or D.)

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 $s+\left(t+u\right)=s+\left(u+t\right)$  (Type the letter A, B, C or D.)

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 $6+\left(9+11\right)=\left(6+9\right)+11$  (Type the letter A, B, C or D.)

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 $v+w=w+v$  (Type the letter A, B, C or D.)

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 $6\cdot\left(3\cdot5\right)=6\cdot\left(5\cdot3\right)$ (Type the letter A, B, C or D.) 

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 $s+\left(t+u\right)=\left(s+t\right)+u$  (Type the letter A, B, C or D.)

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 $10+\left(2+7\right)=10+\left(7+2\right)$  (Type the letter A, B, C or D.)

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 $pq=qp$  (Type the letter A, B, C or D.)

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 $\left(g+h\right)+j=\left(h+g\right)+j$  (Type the letter A, B, C or D.)

Many students confuse Identity and Inverse Properties

Here's the idea!

• Identity - keep the number's identity

--> ^{add 0 (additive identity)}

--> ^{multiply by 1 (multiplicative identity)}

• Inverse Properties - undo something

--> ^{add the opposite (additive inverse)}

--> ^{multiply by the reciprocal (multiplicative inverse)}

Shortcut Notes:

• Identity is add 0 or multiply by 1

• Inverse is add the opposite or multiply by the reciprocal

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 $\left(\frac{1}{y}\right)\cdot y=1$  (Type the letter F, G, H or I)

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 $p=0+p$  (Type the letter F, G, H or I)

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 $2=2\cdot1$  (Type the letter F, G, H or I)

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 $\left(-g\right)+g=0$  (Type the letter F, G, H or I)

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 $\left(\frac{y}{h}\right)\left(\frac{h}{y}\right)=1$  (Type the letter F, G, H or I)

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 $\left(\frac{7}{3}\right)\left(\frac{3}{7}\right)=1$  (Type the letter F, G, H or I)

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 $0=8+\left(-8\right)$  (Type the letter F, G, H or I)

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 $12=12+0$  (Type the letter F, G, H or I)

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 $h\cdot1=h$  (Type the letter F, G, H or I)

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 $\left(-\frac{6}{5}\right)+\frac{6}{5}=0$  (Type the letter F, G, H or I)

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 $\frac{8}{3}\cdot\frac{3}{8}=1$  (Type the letter F, G, H or I)

Now you are ready to practice all of the properties.