Question

identify all expressions equivalent to the given expressions. 2/3 • 9 ÷ 3 - 1 ANWSER: 6 ÷ 2 - 1 + 2 3 • 2/3 -12/3 • 9 ÷ 1

Answer 1

Simplify each expression and find if the simplified form is the same.

`2/3\cdot9/3-1`

This can also be writen as:

`=(2)/(3)\cdot9/3-1`

Multiply 2/3 by 9:

`=6/3-1`

divide 6 by 3:

`=2-1`

Substract 1 from 2:

`=1`

Now, check each option:

6 ÷ 2

Divide both numbers:

`(6)/(2)=3`

This is NOT equivalent to the given expression.

- 1 + 2

Add the numbers:

`-1+2=1`

This IS equivalent to the given expression.

3 • 2/3 -1

First, multiply 3 times 2/3:

`3\cdot(2)/(3)-1=2-1`

Then, add both numbers:

`2-1=1`

This IS equivalent to the given expression.

2/3 • 9 ÷ 1​

Perform the operations from left to right:

`\begin{gathered} (2)/(3)\cdot9/1=6/1 \\ =6 \end{gathered}`

This is NOT equivalent to the given expression.

Therefore, the expressions that are equivalent to the given one, are:

`\begin{gathered} -1+2 \\ 3\cdot2/3-1 \end{gathered}`