Problem 29 - Fundamentals of Mathematics

Question

For the following problems, perform the subtractions. You may chedk each difference with a calculator. $$ \begin{array}{r} 14 \\ -\quad 6 \\ \hline \end{array} $$

Step-by-Step Solution

Answer

The result of the subtraction \(14 - 6\) is 8.

Step 1: Identify the problem

We are given the subtraction problem \(14 - 6\). Our task is to find the difference between the two numbers.

Step 2: Perform the subtraction

Subtract 6 from 14. Start with the units: \(4 - 6\) is not possible directly, so borrow 1 from the tens. Now we have \(14 - 6\) in units, which equals 8. Thus, the difference is 8.

Step 3: Verify the result with addition

To confirm the result, add the difference back to the subtracted number (6) to see if you get the original number (14). Calculate: \(8 + 6 = 14\). This confirms our subtraction is correct.

Step 4: Alternative verification using a calculator

Re-input the subtraction \(14 - 6\) into a calculator. The calculator should also show the result as 8, verifying our manual calculation.

Key Concepts

Borrowing in Subtraction

When performing subtraction, especially with larger numbers, you might encounter a situation where you cannot subtract a smaller digit from a larger one, particularly in the units place. This requires a technique known as borrowing. Borrowing is a process used when the digit in the subtrahend is larger than the digit directly above it in the minuend. Imagine you're trying to subtract 6 from 4 in the number 14. You cannot directly do it because 4 is less than 6. Here's where borrowing is used:

• Look to the left of the digit in the minuend you need to subtract from (in this case, 1 from 14).
• Borrow 1 from this digit, turning the 1 (in the tens place) into a 0, and adding 10 to the units digit.
• Now you have 14 in the units place, which allows you to perform the subtraction: 14 - 6 = 8.

This method ensures that each digit is appropriately managed so you can subtract without issues.

Manual Verification

Once you have performed the subtraction, it’s a good practice to manually verify your result. Manual verification often involves using addition to confirm your subtraction outcome. Let's see how you can do this:

• Take the result of your subtraction (often called the difference). Here we've found the difference to be 8.
• Add the difference back to the number you subtracted (the subtrahend). So, we calculate: 8 + 6.
• If your result matches the original number you started with, your subtraction is correct. In this case, 8 + 6 equals 14, which matches our original minuend.

This method helps reinforce the understanding by confirming the accuracy of your calculation.

Calculator Verification

Another way to verify your subtraction work is through calculator verification. This is especially helpful in double-checking your work and can provide peace of mind when verifying manual calculations. Here's how you can use a calculator to check your subtraction:

• Enter the subtraction equation into the calculator exactly as it appears: 14 - 6.
• Observe the result shown on the calculator screen.
• If the calculator confirms your manual result (which is 8 in this case), your subtraction has been verified as accurate.

Calculator verification is a trusted and straightforward method, especially convenient when you need quick verification.