**Which of the following expressions are equivalent to \[-5\cdot \dfrac{1}4\cdot 3 \]?**

Choose all answers that apply:

Choose all answers that apply:

(Choice A)   

\[-\dfrac{5}4\cdot 3\]

A

\[-\dfrac{5}4\cdot 3\]

(Choice B)   

\[3\cdot(-5)\cdot \dfrac{1}4 \]

B

\[3\cdot(-5)\cdot \dfrac{1}4 \]

(Choice C)   

None of the above

C

None of the above

Let's evaluate the given expression and then compare it with the options.

### Given Expression:
\[-5 \cdot \dfrac{1}{4} \cdot 3\]

### Step 1: Multiply \(-5\) and \(\dfrac{1}{4}\)
\[
-5 \cdot \dfrac{1}{4} = -\dfrac{5}{4}
\]

### Step 2: Multiply the result by 3
\[
-\dfrac{5}{4} \cdot 3 = -\dfrac{15}{4}
\]

So, the expression simplifies to \(-\dfrac{15}{4}\).

Now, let's evaluate each option:

### Option A:
\[-\dfrac{5}{4} \cdot 3\]

Multiply:
\[
-\dfrac{5}{4} \cdot 3 = -\dfrac{15}{4}
\]
This is equivalent to the given expression.

### Option B:
\[3 \cdot (-5) \cdot \dfrac{1}{4}\]

Multiply \(3\) and \(-5\) first:
\[
3 \cdot (-5) = -15
\]

Now multiply:
\[
-15 \cdot \dfrac{1}{4} = -\dfrac{15}{4}
\]
This is also equivalent to the given expression.

### Option C: 
"None of the above"

This option is incorrect since both Options A and B are equivalent to \(-5 \cdot \dfrac{1}{4} \cdot 3\).

### Conclusion:
Both Option A and Option B are correct.

**Answer:** Both Option A and Option B are correct.

Would you like more details or have any questions?

Here are 5 related questions you might find helpful:

1. How do you multiply fractions and whole numbers?
2. What are the properties of multiplication involving negative numbers?
3. How can you simplify complex fractions?
4. Why is the order of multiplication important?
5. How do you determine if two expressions are equivalent?

**Tip:** When multiplying fractions and whole numbers, you can multiply the numerators and denominators directly to simplify the process.

Explore equivalent expressions in mathematics: -5 multiplied by one-fourth multiplied by 3. Understand how to determine equivalence and solve similar problems. Suitable for students in Grades 6-8.

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