digit multiplication problem that efficiently uses…

Mathematics Questions

Can you create a 2-digit by 3-digit multiplication problem that efficiently uses Half-Ten facts, and then solve it using that strategy?

Short Answer

To multiply 56 by 362 using the Half-Tens method, first double 56 to get 112, then multiply 112 by 362 to yield 40544. Finally, divide 40544 by 2 to obtain the result of 20272.

Step-by-Step Solution

Step 1: Double the First Number

Begin by doubling the two-digit number you want to multiply, which in this case is 56. Perform the calculation:

  • 56 √ó 2 = 112

This step prepares us for the next multiplication involving the three-digit number.

Step 2: Multiply the Doubled Number with the Second Number

Now, take the result from the first step (112) and multiply it by the three-digit number (362). Execute the multiplication:

  • 112 √ó 362 = 40544

This step will help us get the product needed before the final adjustment.

Step 3: Divide by 2 for the Final Result

The last step is to take the product from the previous multiplication (40544) and divide it by 2. This gives you the final

  • 40544 √∑ 2 = 20272

Therefore, using the Half-Tens method, we find that 56 √ó 362 equals 20272, confirming the result.

Related Concepts

Two-digit number

A number that has exactly two digits, ranging from 10 to 99.

Three-digit number

A number that has exactly three digits, ranging from 100 to 999.

Half-tens method

A calculation technique that involves doubling a two-digit number, multiplying it by a three-digit number, and then dividing by 2 to simplify multiplication.

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