Explain how 9×4 can help you find 9×8?
The Correct Answer and Explanation is :
To understand how calculating (9 \times 4) can help you find (9 \times 8), we can use the distributive property of multiplication. The distributive property states that (a \times (b + c) = a \times b + a \times c). This property allows us to break down complex multiplication into simpler parts.
First, let’s calculate (9 \times 4):
[
9 \times 4 = 36
]
Now, we can express (9 \times 8) in a way that includes (9 \times 4):
[
9 \times 8 = 9 \times (4 + 4) = 9 \times 4 + 9 \times 4
]
Here, we are breaking (8) into (4 + 4). This allows us to use the value we already calculated, (9 \times 4 = 36).
Now, substituting back into the equation:
[
9 \times 8 = 9 \times 4 + 9 \times 4 = 36 + 36
]
Now we can perform the addition:
[
36 + 36 = 72
]
Therefore, (9 \times 8 = 72).
This approach is effective because it demonstrates how previously calculated values can simplify our calculations. By recognizing patterns in multiplication, such as doubling, we can quickly derive larger products. Knowing (9 \times 4) not only aids in calculating (9 \times 8) but also shows the importance of the distributive property in arithmetic. This method can be particularly useful for mental math, allowing us to perform calculations without extensive memorization or complex computations. Thus, using smaller, manageable products, we can effectively tackle larger multiplication problems with confidence.