Answer :
Let's solve the problem step by step by multiplying [tex]$578$[/tex] by [tex]$25$[/tex] using two different methods.
--------------------------------------------------
Method 1: Distributive Method
We start by breaking down [tex]$578$[/tex] into parts:
[tex]$$
578 = 500 + 70 + 8.
$$[/tex]
Then, we use the distributive property to get:
[tex]$$
578 \times 25 = (500 + 70 + 8) \times 25 = 500 \times 25 + 70 \times 25 + 8 \times 25.
$$[/tex]
Now, calculate each product:
[tex]\[
\begin{aligned}
500 \times 25 &= 12500, \\
70 \times 25 &= 1750, \\
8 \times 25 &= 200.
\end{aligned}
\][/tex]
Finally, add these results together:
[tex]$$
12500 + 1750 + 200 = 14450.
$$[/tex]
--------------------------------------------------
Method 2: Foble Method
In this method, we break down [tex]$25$[/tex] into two convenient numbers:
[tex]$$
25 = 20 + 5.
$$[/tex]
Then, we rewrite the multiplication as follows:
[tex]$$
578 \times 25 = 578 \times (20 + 5) = 578 \times 20 + 578 \times 5.
$$[/tex]
Now, compute each term:
[tex]\[
\begin{aligned}
578 \times 20 &= 11560, \\
578 \times 5 &= 2890.
\end{aligned}
\][/tex]
Adding these two products gives:
[tex]$$
11560 + 2890 = 14450.
$$[/tex]
--------------------------------------------------
Conclusion
Both methods yield the same result:
[tex]$$
578 \times 25 = 14450.
$$[/tex]
Thus, the final answer is [tex]$\boxed{14450}$[/tex].
--------------------------------------------------
Method 1: Distributive Method
We start by breaking down [tex]$578$[/tex] into parts:
[tex]$$
578 = 500 + 70 + 8.
$$[/tex]
Then, we use the distributive property to get:
[tex]$$
578 \times 25 = (500 + 70 + 8) \times 25 = 500 \times 25 + 70 \times 25 + 8 \times 25.
$$[/tex]
Now, calculate each product:
[tex]\[
\begin{aligned}
500 \times 25 &= 12500, \\
70 \times 25 &= 1750, \\
8 \times 25 &= 200.
\end{aligned}
\][/tex]
Finally, add these results together:
[tex]$$
12500 + 1750 + 200 = 14450.
$$[/tex]
--------------------------------------------------
Method 2: Foble Method
In this method, we break down [tex]$25$[/tex] into two convenient numbers:
[tex]$$
25 = 20 + 5.
$$[/tex]
Then, we rewrite the multiplication as follows:
[tex]$$
578 \times 25 = 578 \times (20 + 5) = 578 \times 20 + 578 \times 5.
$$[/tex]
Now, compute each term:
[tex]\[
\begin{aligned}
578 \times 20 &= 11560, \\
578 \times 5 &= 2890.
\end{aligned}
\][/tex]
Adding these two products gives:
[tex]$$
11560 + 2890 = 14450.
$$[/tex]
--------------------------------------------------
Conclusion
Both methods yield the same result:
[tex]$$
578 \times 25 = 14450.
$$[/tex]
Thus, the final answer is [tex]$\boxed{14450}$[/tex].
