To begin, let's explore the multiplication of a two-digit number and a non-decimal with one decimal to achieve the product of 50. This article aims to delve into the mathematics behind such multiplication and provide insights into the various combinations that result in 50.

Introduction to Two-Digit Multiplication

Multiplication of numbers is a fundamental mathematical operation that combines two numbers to produce a product. When dealing with two-digit numbers, we are referring to numbers between 10 and 99. In our exploration, we need to combine a two-digit number (between 10 and 99) with another number containing one decimal place but not a whole number, to achieve the product of 50.

Understanding the Problem

The problem requires that the product of a two-digit number and a decimal number (which has only one decimal place) is 50. It's important to note that the non-decimal must be within the range of 10 to 99. The decimal number cannot be a whole number, which means it must be a number that has a single digit after the decimal point (e.g., 2.0, 25.0, etc.).

Exploring Possible Combinations

Let's examine the possible combinations that can multiply to 50.

Combination 1: 20 x 2.5

Here, we have a two-digit number, 20, and a decimal number 2.5. Performing the multiplication:

20 x 2.5  50

This is a valid solution as both 20 and 2.5 meet the criteria, and the product is 50.

Combination 2: 50 x 1.0

This would be a trivial case, but in our context, 1.0 is not a valid non-decimal number as it has no fractional part. Thus, we exclude this combination.

Combination 3: 25 x 2.0

Here, we have a two-digit number, 25, and a decimal number 2.0. However, 2.0 is a whole number, so we exclude this as well.

Combination 4: 10 x 5.0

This is another valid solution where 10 is a two-digit number and 5.0 is a decimal number. Performing the multiplication:

10 x 5.0  50

Conclusion

In conclusion, the valid combinations that meet the given criteria and multiply to 50 are 20 x 2.5 and 10 x 5.0. These combinations demonstrate the versatility and complexity of multiplying two-digit numbers with decimals to achieve a specific product.

Understanding these concepts is crucial for students and professionals alike, as it helps in problem-solving and mathematical reasoning. Teachers and educational content providers can use these examples to illustrate the principles of multiplication and decimals to a wider audience.