What is another way to solve 4 x 9?
The Correct Answer and Explanation is:
To solve (4 \times 9) in a different way, you can break it down using the distributive property. This property allows you to break a multiplication problem into smaller, more manageable parts. Here’s how you can do it:
Step-by-Step Explanation:
- Use the Distributive Property: The distributive property states that (a(b + c) = ab + ac). In this case, you can rewrite 9 as (5 + 4). Therefore, instead of multiplying (4 \times 9), you can multiply (4) by (5) and (4) by (4), then add the results together: [
4 \times 9 = 4 \times (5 + 4)
]
Applying the distributive property:
[
4 \times 9 = (4 \times 5) + (4 \times 4)
] - Multiply the Numbers: Now, perform the individual multiplications:
[
4 \times 5 = 20
]
[
4 \times 4 = 16
] - Add the Results: After multiplying, add the two products together:
[
20 + 16 = 36
]
So, (4 \times 9 = 36), which is the correct answer.
Why This Works:
The distributive property is useful because it simplifies multiplication by breaking it down into smaller steps that are easier to perform mentally. In this example, instead of memorizing (4 \times 9), you used smaller, more familiar multiplications (like (4 \times 5) and (4 \times 4)) to reach the same result.
This method is especially helpful when you are working with larger numbers or when you need to do mental math without a calculator. By breaking down complex multiplication into simpler parts, you can often solve problems more quickly and with less effort.
In summary, using the distributive property provides an alternative way to approach multiplication that can enhance your understanding of the concept and make calculations more manageable.