Verified Answer :

  • Decompose \(3579\) into \(3000 + 500 + 70 + 9\).
  • Multiply each term by \(8\) to get \(24000\), \(4000\), \(560\), and \(72\).
  • Add the products together: \(24000 + 4000 + 560 + 72 = 28632\).
  • The final product is \(\boxed{28632}\).

Explanation

  1. Decomposition of the Number

To find the product of \(3579\) and \(8\), we can decompose the larger number into its place value components: thousands, hundreds, tens, and ones. This approach allows us to multiply each component individually and then sum the results. The number \(3579\) can be written as \(3000 + 500 + 70 + 9\). We need to calculate \(8 \times (3000 + 500 + 70 + 9)\).

  1. Applying the Distributive Property

Now, we distribute the multiplication by \(8\) across each term of the sum:
\(3000 \times 8 = 24000\)
\(500 \times 8 = 4000\)
\(70 \times 8 = 560\)
\(9 \times 8 = 72\)

  1. Final Calculation and Summation

Finally, we sum these products to obtain the result:
\(24000 + 4000 + 560 + 72\)
First, add the thousands: \(24000 + 4000 = 28000\).
Next, add the remaining terms: \(28000 + 560 + 72 = 28560 + 72 = 28632\).
Therefore, the product is \(28632\).

  1. Final Answer

The product of \(3579\) and \(8\) is \(\boxed{28632}\).

Examples

Multiplication is a fundamental skill used daily, such as when calculating total costs. For example, if you are buying 8 items that each cost \$3,579, you need to perform the operation \(3579 \times 8\) to find the total expenditure of \(\$28,632\). Mastering this process ensures you can manage budgets and plan purchases accurately.

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