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Distributive Method:

Table Method:

[tex]\[

\begin{array}{|l|l|l|}

\hline

x & \multicolumn{2}{|c|}{\begin{array}{l} 40 \\ 5 \end{array}} \\

\hline

\multirow[t]{4}{*}{500 + 40 +} & 20000 & 2500 \\

\hline

& 1600 & 200 \\

\hline

& 280 & 35 \\

\hline

& \multicolumn{2}{|c|}{24615} \\

\hline

\end{array}

\][/tex]

Expanded Notation:

[tex]\[

\begin{aligned}

& 547 \times 45 \\

= & (500+40+7) \times (40+5) \\

= & 20000 + 2500 + 1600 + 200 + 280 + 35 \\

= & 20000 + 2000 + 1000 + 500 + 600 + 200 + 200 + 80 + 30 + 5 \\

= & 20000 + 3000 + 1500 + 110 + 5 \\

= & 20000 + 3000 + 1000 + 500 + 100 + 10 + 5 \\

= & 20000 + 4000 + 600 + 10 + 5 \\

= & 24615

\end{aligned}

\][/tex]

1. Multiply the following using both methods:
a. [tex]578 \times 25[/tex]

Answer :

We will calculate the product of [tex]$$578 \times 25$$[/tex] using two different methods: the distributive method and the table method.

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1. Distributive Method

Break [tex]$$578$$[/tex] into its expanded form:
[tex]$$578 = 500 + 70 + 8.$$[/tex]

Then, multiply each part by [tex]$$25$$[/tex]:

- For the first part:
[tex]$$500 \times 25 = 12500.$$[/tex]

- For the second part:
[tex]$$70 \times 25 = 1750.$$[/tex]

- For the third part:
[tex]$$8 \times 25 = 200.$$[/tex]

Now, sum the three products:
[tex]$$12500 + 1750 + 200 = 14450.$$[/tex]

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2. Table Method

Alternatively, we can break [tex]$$25$$[/tex] into:
[tex]$$25 = 20 + 5.$$[/tex]

Now, we multiply [tex]$$578$$[/tex] by each part separately:

- Multiplying [tex]$$578$$[/tex] by [tex]$$20$$[/tex]:
[tex]$$578 \times 20 = 11560.$$[/tex]

- Multiplying [tex]$$578$$[/tex] by [tex]$$5$$[/tex]:
[tex]$$578 \times 5 = 2890.$$[/tex]

The sum of these products gives:
[tex]$$11560 + 2890 = 14450.$$[/tex]

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Final Answer:
Both methods lead to the same product. Therefore,
[tex]$$578 \times 25 = 14450.$$[/tex]

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