Problem 91 - Fundamentals of Mathematics

Question

For the following problems, replace the [U+2610] with the whole number that will make the subtraction true. $$ \begin{array}{r} 21 \\ -\square \\ \hline 14 \end{array} $$

Step-by-Step Solution

Answer

The missing number is 7.

Step 1: Understand the Problem

We need to find a whole number that when subtracted from 21 gives us 14. This can be represented by the equation: \( 21 - x = 14 \) where \( x \) is the missing number (\( \square \)).

Step 2: Set Up the Equation

The subtraction equation given by the problem is \( 21 - x = 14 \). Here, \( x \) represents the number we need to find to complete the subtraction.

Step 3: Solve the Equation

To find the value of \( x \), we can rearrange the equation: \( x = 21 - 14 \).

Step 4: Calculate the Difference

Perform the subtraction: \( 21 - 14 = 7 \).

Step 5: Verify the Solution

To ensure the solution is correct, substitute \( x = 7 \) back into the original subtraction to check: \( 21 - 7 = 14 \). Since this statement is true, \( x = 7 \) is indeed the solution.

Key Concepts

Understanding Whole Numbers

Whole numbers are the basic building blocks of mathematics. They are non-negative numbers starting from zero and include all the positive integers. This means whole numbers are:

• 0, 1, 2, 3, and so on.
• Whole numbers do not include fractions, decimals, or negative numbers.
• They are often used in everyday counting and simple arithmetic operations like addition, subtraction, multiplication, and division.

The concept of whole numbers is fundamental to understanding more complex mathematical topics. In subtraction, whole numbers help maintain simplicity, avoiding potential complexities that arise with fractions or negative numbers. For instance, when subtracting two whole numbers, the result could still be a whole number or zero. In our example, subtracting one whole number from another lets us practice this important operation neatly.

Basics of Equation Solving

Equation solving is a crucial skill in mathematics education. It's a process where we find the unknown value that makes an equation true. When solving equations, particularly with subtraction, we follow several steps:

• Identify the variable, which stands for the unknown number. In our problem, it is represented by \( x \).
• Set up the equation using the information given in the problem, such as \( 21 - x = 14 \).
• Rearrange the equation to isolate the variable on one side, like \( x = 21 - 14 \).
• Solve the resulting equation to find the value of the variable.

In practice, solving equations helps understand the concept of balancing both sides and transferring numbers or variables across the equals sign to maintain the equation's validity. The step-by-step approach ensures accuracy and helps verify if the solution makes sense when substituted back.

Importance of Mathematics Education

Mathematics education plays a vital role in developing logical reasoning and problem-solving skills. Understanding concepts such as subtraction with whole numbers and solving equations are part of this foundation. It allows learners:

• To think critically and approach problems methodically.
• To apply concepts like subtraction in daily life situations, making decisions involving numbers easier and more informed.
• To build a base for advanced mathematical studies, fostering confidence in exploring further mathematical disciplines.

A firm grasp of these concepts paves the way for future learning, from algebra to calculus. Adopting interactive and problem-based learning, as seen in the exercise, cultivates interest and better retention of mathematical principles.