Problem 26 - Fundamentals of Mathematics

Question

For the following problems, perform the subtractions. You may chedk each difference with a calculator. $$ \begin{array}{r} 15 \\ -8 \\ \hline \end{array} $$

Step-by-Step Solution

Answer

The difference is 7.

Step 1: Understand the Problem

We need to subtract 8 from 15. In other words, we are calculating the difference between 15 and 8.

Step 2: Set Up the Subtraction

Write the numbers stacked such that the larger number (15) is on top, and align the smaller number (8) beneath it by the units place.

Step 3: Subtract the Units

Starting from the rightmost digit, subtract the number on the bottom (8) from the number on the top (15). Since 15 - 8 = 7, write 7 below the line.

Step 4: Write the Result

The answer from the subtraction is 7. Therefore, the difference between 15 and 8 is 7.

Key Concepts

step-by-step subtraction

In basic subtraction, learning to solve problems one step at a time is crucial. It helps in understanding the process and ensures accuracy. To perform step-by-step subtraction:

• Understand the Problem: First, figure out the numbers involved in the subtraction—here, it's 15 minus 8.


• Set Up the Subtraction: Arrange the numbers vertically with the bigger number on top (15) and the smaller number directly below it without changing the columns.


• Subtract Units: Start from the rightmost digit. Subtract the bottom number from the top number. Here, from 15, remove 8 to get 7.


• Write the Result: After subtracting, write down the result. Thus, the answer is 7.

Step-by-step subtraction is helpful as it allows you to focus on each part of the process, reducing mistakes and building confidence.

checking subtraction with a calculator

After performing subtraction manually, you can verify your solution using a calculator. Checking your work with a calculator ensures that your manual calculations are accurate and provides a quick method to confirm your result. To check your subtraction with a calculator:

• Enter the number from which you are subtracting. In this case, key in 15.


• Press the minus (-) key, often represented with a dash on the calculator.


• Enter the number to subtract, 8 in this scenario.


• Press the equals (=) key to see the result.


• Compare the calculator result with your handwritten answer, which should also be 7.

Using a calculator for checking is a reliable way to catch any mistakes made during manual calculations and to reinforce learning by seeing how the process leads to the same outcome.

subtracting single-digit numbers

Subtracting single-digit numbers is one of the first arithmetic skills learned and is foundational for understanding more complex math concepts. This process is not only simple but reinforces basic arithmetic rules. Here's a quick guide to subtracting single-digit numbers:

• Identify the Highest Number: Always start from the number with the highest value if subtracting numbers within the same digit range.


• Use Counting Back: If you find subtraction challenging, use the counting back method. For example, from 15, count back 8 steps to arrive at 7.


• Conceptualize with Objects: For visual learners, using fingers or small objects can help. Start with 15 objects and remove 8 to physically see that there are 7 remaining.

Mastering these steps builds confidence and makes it easier to apply subtraction skills in various situations, such as mentally calculating change or determining reduced amounts in practical scenarios.