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.

$2/3\cdot9\div3-1$

This can also be writen as:

$=\frac{2}{3}\cdot9\div3-1$

Multiply 2/3 by 9:

$=6\div3-1$

divide 6 by 3:

$=2-1$

Substract 1 from 2:

$=1$

Now, check each option:

6 ÷ 2

Divide both numbers:

$\frac{6}{2}=3$

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:

$3\cdot\frac{2}{3}-1=2-1$

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:

$\begin{gathered} \frac{2}{3}\cdot9\div1=6\div1 \\ =6 \end{gathered}$

This is NOT equivalent to the given expression.

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

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