Which three of the following expressions are
equivalent to 3,956 × 4 ?
(A) 3,000 × + 4 900 × + 4 50464 ×+×
(B) (4,000 × − 4 100 × 4 6 ) + × ( 0 4 − × 4 4)
(C) 4 3 × + 4 9 × + 4 5 × + 4 6 ×
(D) 4,000 × − 4 40 4 × − 4 4 ×
(E) 3 × × 1000 , 4 9 + × 5 10046 ×+× 1 4

To determine which of the expressions are equivalent to \( 3,956 \times 4 \), let's first calculate the value of the expression:

\[
3,956 \times 4 = 15,824
\]

Now, we need to analyze each option and see if it simplifies to the same value.

### Option (A):
\[
3,000 \times 4 + 900 \times 4 + 50 \times 4 + 6 \times 4
\]

Simplifying each term:
\[
3,000 \times 4 = 12,000
\]
\[
900 \times 4 = 3,600
\]
\[
50 \times 4 = 200
\]
\[
6 \times 4 = 24
\]

Now adding them up:
\[
12,000 + 3,600 + 200 + 24 = 15,824
\]

So, **Option (A)** is equivalent to \( 3,956 \times 4 \).

### Option (B):
\[
(4,000 \times 4 - 100 \times 4 + 6) + (0 \times 4 - 4 \times 4)
\]

Simplifying each term:
\[
4,000 \times 4 = 16,000
\]
\[
100 \times 4 = 400
\]
\[
16,000 - 400 + 6 = 15,606
\]
\[
0 \times 4 - 4 \times 4 = -16
\]
\[
15,606 + (-16) = 15,590
\]

This does **not** equal 15,824, so **Option (B)** is not equivalent.

### Option (C):
\[
4 \times 3 + 4 \times 9 + 4 \times 5 + 4 \times 6
\]

Simplifying each term:
\[
4 \times 3 = 12
\]
\[
4 \times 9 = 36
\]
\[
4 \times 5 = 20
\]
\[
4 \times 6 = 24
\]

Adding them together:
\[
12 + 36 + 20 + 24 = 92
\]

This is far from 15,824, so **Option (C)** is not equivalent.

### Option (D):
\[
4,000 \times 4 - 40 \times 4 - 4 \times 4
\]

Simplifying each term:
\[
4,000 \times 4 = 16,000
\]
\[
40 \times 4 = 160
\]
\[
4 \times 4 = 16
\]

Now, subtracting:
\[
16,000 - 160 - 16 = 15,824
\]

So, **Option (D)** is equivalent to \( 3,956 \times 4 \).

### Option (E):
\[
3 \times 1,000 \times 4 + 9 \times 5 \times 100 + 46 \times 1 \times 4
\]

Simplifying each term:
\[
3 \times 1,000 \times 4 = 12,000
\]
\[
9 \times 5 \times 100 = 4,500
\]
\[
46 \times 1 \times 4 = 184
\]

Adding them together:
\[
12,000 + 4,500 + 184 = 16,684
\]

This is not equal to 15,824, so **Option (E)** is not equivalent.

### Conclusion:
The three expressions that are equivalent to \( 3,956 \times 4 \) are:
- **Option (A)**
- **Option (D)**

Would you like further clarification or details?

Here are five questions to expand on this:
1. What are other methods for breaking down multiplication into smaller parts?
2. How does the distributive property help in simplifying expressions like these?
3. Can you apply the same logic to larger multiplication problems?
4. What is the difference between equivalent and approximate expressions?
5. How can estimating values help in verifying such expressions quickly?

**Tip**: Always try to break down large multiplication problems into smaller, manageable parts using the distributive property for easier calculations!

Which three of the following expressions are equivalent to 3,956 × 4?
(A) 3,000 × 4 + 900 × 4 + 50 × 4 + 6 × 4
(B) (4,000 × 4 - 100 × 4 + 6) + (0 × 4 - 4 × 4)
(C) 4 × 3 + 4 × 9 + 4 × 5 + 4 × 6
(D) 4,000 × 4 - 40 × 4 - 4 × 4
(E) 3 × 1,000 × 4 + 9 × 5 × 100 + 46 × 1 × 4

Discover which three expressions are equivalent to 3,956 × 4 by applying the distributive property. This problem involves breaking down multiplication into smaller parts and verifying the results. Suitable for students in Grades 5-7.

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