Question

Ms. Chin asked her students to use the properties of multiplication to rewrite the expression (-5){-2/7}[{4/11}(-9}. The table below shows the properties that each of four students used to rewrite the expression. Expressions Generated by Students Student Properties used to rewrite the expression Mitul Commutative property Stacy Associative property Tom Associative property and then the commutative property Walt Commutative property and then the associative property How many of the students created an expression that was equivalent to the original? one two three four

Answer 1

4Explanation:

Answer 2

Four

Explanation:

We have the expression
`(-5)((-2)/(7))((4)/(11))(-9)`.

Now, four different students have applied different properties to rewrite the expression above.

1. Mitul used commutative property i.e. ab = ba

So,
`[(-5)((-2)/(7))][((4)/(11))(-9)]` =
`[((-2)/(7))(-5)][(-9)((4)/(11))]`.

2. Stacy used associative property i.e. a(bc) = (ab)c

Then,
`-5[(-2)/(7)((4)/(11)* -9)]` =
`-5[((-2)/(7)* (4)/(11))(-9)]`

3. Tom used associative property followed by commutative property

Thus,
`-5[(-2)/(7)((4)/(11)* -9)]` =
`-5[((-2)/(7)* (4)/(11))(-9)]` =
`-5[((4)/(11)* (-2)/(7))(-9)]`

4. Walt used commutative property followed by associative property

So,
`[(-5)((-2)/(7))][((4)/(11))(-9)]` =
`[((-2)/(7))(-5)][(-9)((4)/(11))]` =
`((-2)/(7))[(-5* -9)((4)/(11))]` =
`((-2)/(7))[(-5)(-9* (4)/(11))]`.

Hence, we see that all the four students have rewritten the expressions equivalent to the original expression.