Problem 33 - Fundamentals of Mathematics

Question

For the following 18 problems, perform each subtraction. Use a calcula tor to cherk each result. $$ 142-85 $$

Step-by-Step Solution

Answer

The difference is 57.

Step 1: Understand the Problem

We need to subtract 85 from 142.

Step 2: Set Up the Subtraction

Align the numbers by place value: ``` 142 - 85 ```

Step 3: Subtract the Units

Start by subtracting the units: 2 - 5. Since 2 is less than 5, we need to borrow from the tens place.

Step 4: Borrowing from Tens Place

Borrow 1 from the tens place of 4, making it 3, and add 10 to the units place of 2, making it 12. Now perform 12 - 5 = 7.

Step 5: Subtract the Tens

Subtract the tens: 3 - 8. Since 3 is less than 8, borrow 1 from the hundreds place of 1, making it 0.

Step 6: Borrowing from Hundreds Place

Borrow 10 making the 3 equal to 13. Now, perform the subtraction: 13 - 8 = 5.

Step 7: Subtract the Hundreds

Now, subtract the hundreds place: 1 became a 0 when we borrowed so it's simply 0.

Step 8: Verify Result with a Calculator

Input 142 - 85 into a calculator to confirm the result is 57.

Key Concepts

Using a Calculator

Using calculators can be incredibly helpful when performing arithmetic operations like subtraction. They help ensure accuracy, especially when dealing with large numbers or complex problems. When subtracting numbers such as 142 - 85, a calculator can quickly provide the result, which is 57 in this case.

To use a calculator for subtraction:

• Enter the first number, 142.
• Press the subtraction button, usually marked with a "-" sign.
• Enter the second number, 85.
• Press the equals button, typically marked with a "=" sign.

The display will show 57, confirming your manual calculations. Calculators are also great tools for double-checking your work, making them invaluable for students learning subtraction.

Borrowing in Subtraction

Borrowing is a crucial concept in subtraction, especially when the digit in the top row is smaller than the digit directly below it. This technique allows you to subtract larger numbers by borrowing from the next left column.

In the example of 142 - 85:

• Look at the units: 2 minus 5. Since 2 is smaller, you need to borrow from the tens column.
• Reduce the number in the tens place (4) by 1, making it 3.
• Add 10 to the units place: 2 becomes 12.
• Carry out the subtraction: 12 - 5 equals 7.

Borrowing ensures you can always subtract a larger number from a smaller number by redistributing values from higher place values.

Step-by-Step Subtraction

Performing subtraction using a step-by-step approach is an excellent way to ensure you understand how the process works. Following each step carefully helps build confidence and accuracy.
When subtracting 85 from 142, these are the steps:

• Align the numbers by their respective place values.
• Begin with the rightmost column. If necessary, borrow from the upper place value to handle larger bottom digits like 2 and 5.
• Subtract the tens: In this case, after borrowing, you subtract 8 from 13.
• Finally, subtract the hundreds. If the column was left with a zero, you simply write down zero.
• Combine the results from each column for the final answer: 57.

Repeat these steps whenever you face a subtraction problem to improve your precision and capability.

Checking Subtraction Results

After completing a subtraction, it's essential to verify the result for accuracy. Double-checking can catch any potential errors in calculation before finalizing a solution.
Here’s how to check your subtraction result of 142 - 85:

• Add the result to the smaller original number. In this case, add 57 to 85.
• Calculate: 57 + 85 equals 142.
• Check that the sum equals the original larger number, 142.

If both are equal, your subtraction work is correct. Incorporating this verification step into your math routine helps reinforce your understanding and boosts your confidence in your math skills.