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The question asks which of the following uses properties of operations to help find \(27 \times 14\):

A. \(20 + 7 + 10 + 4\)

B. \(20 \times 7 \times 10 \times 4\)

C. \(27 + 14\)

D. \((20 + 7) \times (10 + 4)\)

To find \(27 \times 14\) using the properties of operations (specifically the distributive property), we break down the numbers into parts that are easier to multiply, then combine the results. Let's check each option:

A. \(20 + 7 + 10 + 4\): This option only adds the numbers, not relevant to the multiplication problem.

B. \(20 \times 7 \times 10 \times 4\): This option multiplies several numbers together, but not in a way that simplifies \(27 \times 14\).

C. \(27 + 14\): This option simply adds the two numbers, not relevant to the multiplication problem.

D. \((20 + 7) \times (10 + 4)\): This option applies the distributive property correctly, as \(27 = 20 + 7\) and \(14 = 10 + 4\). It shows how to break down the multiplication into smaller parts:
\[
(20 + 7) \times (10 + 4) = 20 \times 10 + 20 \times 4 + 7 \times 10 + 7 \times 4
\]
This distributes the multiplication over addition correctly.

Therefore, the correct answer is:

**D. \((20 + 7) \times (10 + 4)\)**

Would you like any details or have any questions? Here are some related questions you might find interesting:

1. How does the distributive property work in multiplication?
2. Can you provide another example of using the distributive property to simplify multiplication?
3. What are the associative and commutative properties of multiplication?
4. How can breaking down numbers help in mental math?
5. What is the difference between breaking down numbers for addition and multiplication?

**Tip:** When solving multiplication problems, breaking down larger numbers into smaller parts using properties like the distributive property can make calculations easier and more intuitive.

Which of the following uses properties of operations to help find 27 × 14?

Learn how to use the distributive property to simplify multiplication problems like 27 × 14. Break down numbers into smaller parts and distribute multiplication over addition. Suitable for Grade 4-6 students.

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