Problem 25 - Fundamentals of Mathematics

Question

Determine the missing factor(s). \(20=4\) ______.

Step-by-Step Solution

Answer

The missing factor is 5.

Step 1: Understand the Equation

We are given the equation \(20 = 4 \times ?\). We need to find the missing factor that, when multiplied by 4, equals 20.

Step 2: Isolate the Missing Factor

In mathematics, when solving for a missing factor in a multiplication equation, you can divide the result by the known factor. The equation \(20 = 4 \times ?\) can be rewritten as \(? = \frac{20}{4}\).

Step 3: Perform the Division

Calculate \(\frac{20}{4}\) by dividing 20 by 4. This gives us \(5\).

Step 4: Substitute and Verify

Substitute 5 back into the equation: \(20 = 4 \times 5\). Multiply to verify: \(4 \times 5 = 20\). The equation is true, confirming that the solution is correct.

Key Concepts

Understanding a Multiplication Equation

A multiplication equation involves multiplying two or more numbers to achieve a product. In our exercise, the equation is set up as follows:

• Known factor: 4
• Unknown factor: marked as a question mark (\(?\))
• Product: 20

Your task is to find the missing factor that, when multiplied with 4, results in 20. To do this effectively, consider multiplication operations as repeated addition. Here, you are looking for how many times 4 needs to be added together to reach 20. Though it might seem simple, understanding this equation is the first step in determining the missing factor.

Finding the Missing Factor Through Division

Solving a multiplication equation with an unknown factor involves creative use of division. Imagine the equation rewritten to solve for the unknown factor:\[20 = 4 \times ?\]When you need to isolate the unknown factor, division becomes a powerful tool. By dividing the result (20) by the known factor (4), you will uncover the missing factor. This looks like:\[? = \frac{20}{4}\]Performing the division here is straightforward:

• Divide 20 by 4.
• The quotient is 5.

This quotient is the missing factor you have been looking for. It signifies the number that, when multiplied by 4, gives you the product of 20.

Verification of the Solution

Verifying your solution is crucial in mathematics to ensure accuracy. The process involves substituting the found factor back into the original multiplication equation. Thus, plug 5 into the equation:\[20 = 4 \times 5\]You then perform the multiplication:

• Multiply 4 by 5, which equals 20.

The product equals the initial equation result, confirming that our solution is correct. Verification not only reassures us of the solution's correctness but also strengthens understanding of the relation between multiplication and division. By completing this reverse step, you develop a deeper appreciation and confidence in solving similar exercises in the future.