Verified Answer :

  • Multiply the non-zero digits of the numbers.
  • Append a zero to the product to account for the factor of 10.
  • Resulting products:
  • \(3 \times 80 = 240\)
  • \(8 \times 80 = 640\)
  • \(7 \times 50 = 350\)
  • \(4 \times 90 = 360\)
  • \(4 \times 20 = 80\)
  • \(5 \times 70 = 350\)
  • Final answers: \(\boxed{240, 640, 350, 360, 80, 350}\)

Explanation

  1. Problem Analysis

The objective is to calculate six specific products involving a single-digit integer and a multiple of ten. These are: \(3 \times 80\), \(8 \times 80\), \(7 \times 50\), \(4 \times 90\), \(4 \times 20\), and \(5 \times 70\). All these products can be computed by multiplying the single-digit integer with the digit in the tens place of the other number and then appending a zero to the result.

  1. Method for Multiplication

To multiply a number by a multiple of 10, we can use the associative property of multiplication. For instance, to calculate \(a \times (b \times 10)\), we can compute \((a \times b) \times 10\). This allows us to perform the single-digit multiplication first and then multiply by 10 by simply shifting the digits to the left and placing a zero in the ones position.

  1. Step-by-Step Calculation

Using the established method, we calculate each product:

  • \(3 \times 80 = 3 \times 8 \times 10 = 24 \times 10 = 240\)
  • \(8 \times 80 = 8 \times 8 \times 10 = 64 \times 10 = 640\)
  • \(7 \times 50 = 7 \times 5 \times 10 = 35 \times 10 = 350\)
  • \(4 \times 90 = 4 \times 9 \times 10 = 36 \times 10 = 360\)
  • \(4 \times 20 = 4 \times 2 \times 10 = 8 \times 10 = 80\)
  • \(5 \times 70 = 5 \times 7 \times 10 = 35 \times 10 = 350\)
  1. Conclusion

The products of the requested operations are:
\(3 \times 80 = 240\)
\(8 \times 80 = 640\)
\(7 \times 50 = 350\)
\(4 \times 90 = 360\)
\(4 \times 20 = 80\)
\(5 \times 70 = 350\)
These calculations demonstrate how breaking down a multiplication problem into simpler parts allows for quick and accurate mental math.

Examples

This method is very useful in everyday life, especially when shopping. Imagine you are buying 8 items that cost \$80 each. Instead of struggling with the math, you can quickly think of @@MATH_TOKEN_27@@ and simply add a zero to find that the total is \$640. This mental strategy helps you estimate budgets and make faster decisions while shopping or planning finances.

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