Problem 31 - Fundamentals of Mathematics

Question

For the following problems, perform the subtractions. You may chedk each difference with a calculator. $$ \begin{array}{r} 56 \\ -12 \end{array} $$

Step-by-Step Solution

Answer

The difference is 44.

Step 1: Understand the Problem

We are given the subtraction problem where we need to subtract 12 from 56. This can be written in mathematical notation as \(56 - 12\).

Step 2: Subtract the Units

First, look at the units digit: 6 (from 56) minus 2 (from 12). Calculate \(6 - 2 = 4\). The units digits of our difference is 4.

Step 3: Subtract the Tens

Then, subtract the tens: 5 (from 56) minus 1 (from 12). Calculate \(5 - 1 = 4\). The tens digit of our difference is 4.

Step 4: Combine the Results

Combine the results from each digit place. The units are 4 and the tens are 4, giving us a total difference of 44.

Step 5: Verify with a Calculator

Use a calculator to verify the subtraction: input \(56 - 12\). You should obtain the result 44, confirming our calculations.

Key Concepts

Understanding Units Digit Subtraction

When you're dealing with subtraction problems, it's crucial to handle the units digit correctly. This is the digit in the ones place of a number. Let’s break down the process:

• Look at the units digit of each number you're subtracting. In our example, these digits are 6 (from 56) and 2 (from 12).
• Subtract the smaller units digit from the larger units digit: calculate \(6 - 2\).
• The subtraction here is simple: \(6 - 2 = 4\), giving you the units digit of the answer.

Always begin subtraction from the units digit to ensure accuracy, especially if borrowing is needed. In this example, borrowing isn't required, so the operation is straightforward.

Breaking Down Tens Digit Subtraction

The tens digit plays a key role in determining the result of a subtraction problem. In our problem, the tens digits are 5 (from 56) and 1 (from 12). Here's how you subtract them:

• Identify the tens digit in both numbers: 5 for 56 and 1 for 12.
• Subtract the tens digits: calculate \(5 - 1\).
• Perform the subtraction to get \(5 - 1 = 4\), representing the tens digit in your answer.

Once you've found both the units and tens digits, you can combine them to form the full answer. For 56 minus 12, the final result is 44, with both digits being 4.

Steps to Verify Subtraction with a Calculator

After manually performing a subtraction, it's always a good idea to double-check your work with a calculator. This ensures accuracy and boosts your confidence in your mathematical skills.

• Enter the subtraction problem into the calculator. For our case, input \(56 - 12\).
• Press the equals button to calculate the result.
• The calculator should display the result: 44.

If the calculator confirms your manual subtraction result, you've done it correctly! If the numbers don't match, revisit each step: check both your units and tens digit subtraction to spot any errors.