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In mathematical calculations, division is a fundamental operation that distributes a number into equal parts. Consider the exercise \((45 \div 10) \cdot 2\). Division is performed before multiplication according to the order of operations. To carry out the division, you divide the dividend (45) by the divisor (10). This calculation results in 4.5.

Understanding division:

• Dividend: The number you want to divide. Here, it's 45.
• Divisor: The number by which you divide. In this case, it's 10.
• Quotient: The result of the division, which is 4.5 for our example.

The division process can be thought of as finding out how many times the divisor fits into the dividend. Hence, 10 goes into 45 a total of 4.5 times, meaning, if you share 45 units into groups of 10, you get 4.5 groups.

Multiplication is a process of repeated addition. In the context of the exercise \((45 \div 10) \cdot 2\), after obtaining the result from the division, we multiply it by two. Our division result was 4.5. So, multiplying 4.5 by 2 gives us the product 9.

Key aspects of multiplication:

• Factors: The numbers being multiplied together (4.5 and 2).
• Product: The result of multiplying factors (here it's 9).

With multiplication, you can see it as adding the number 4.5, two times. Thus, \(4.5 \times 2\) indicates two sets of 4.5, which sum up to 9. Multiplication enhances understanding of scaling numbers efficiently without adding every single time.

Breaking down a problem using a step-by-step solution helps clarify and organize the process of solving it. This approach ensures you tackle each operation in the correct sequence, enhancing accuracy and understanding.

Steps for solving \((45 \div 10) \cdot 2\) include:

• Step 1: Perform Division. Calculate \(45 \div 10\) to find 4.5.
• Step 2: Perform Multiplication. Multiply the result 4.5 by 2 to get 9.

Such a clear step-by-step guide not only facilitates learning but also helps avoid common mistakes often encountered with operations. It's critical to adhere to the order of operations—sometimes abbreviated as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). By following these structured steps, you arrive at the correct solution, reducing confusion and improving problem-solving skills.