Question

identify all expressions equivalent to \\(\frac{3}{4}\cdot 8\div 2 - 1\\).
\\(\square\\) \\(6\div 3\\)
\\(\square\\) \\(-1 + 3\\)
\\(\square\\) \\(4\cdot \frac{3}{4} - 1\\)
\\(\square\\) \\(\frac{3}{4}\cdot 8\div 1\\)
what do we know?

what are we looking for?

show steps/draw a picture:

explain your solution/how you found your answer:

Explanation:

Step1: Calculate the original expression

First, we calculate the value of the given expression $\frac{3}{4} \cdot 8 \div 2 - 1$.
We follow the order of operations (PEMDAS/BODMAS).
First, multiply $\frac{3}{4}$ and $8$: $\frac{3}{4} \cdot 8 = \frac{3 \times 8}{4} = \frac{24}{4} = 6$.
Then, divide the result by $2$: $6 \div 2 = 3$.
Finally, subtract $1$: $3 - 1 = 2$.
So the value of the original expression is $2$.

Step2: Calculate each option

• Option 1: $6 \div 3 = 2$. This is equal to the value of the original expression.
• Option 2: $-1 + 3 = 2$. This is equal to the value of the original expression.
• Option 3: $4 \cdot \frac{3}{4} - 1$. First, multiply $4$ and $\frac{3}{4}$: $4 \cdot \frac{3}{4} = 3$. Then subtract $1$: $3 - 1 = 2$. This is equal to the value of the original expression.
• Option 4: $\frac{3}{4} \cdot 8 \div 1$. First, multiply $\frac{3}{4}$ and $8$: $\frac{3}{4} \cdot 8 = 6$. Then divide by $1$: $6 \div 1 = 6$. This is not equal to the value of the original expression.

Answer:

The equivalent expressions are:

• $6 \div 3$
• $-1 + 3$
• $4 \cdot \frac{3}{4} - 1$