Problem 61 - Fundamentals of Mathematics

Question

Subtract 63 from 92 .

Step-by-Step Solution

Answer

The result of subtracting 63 from 92 is 29.

Step 1: Understand the Problem

The problem is asking us to subtract one number from another. We have two numbers: 92 and 63, and we need to find the difference between them.

Step 2: Set Up the Subtraction

We write the larger number, 92, above the smaller number, 63, aligning them by their place value:\[\begin{array}{c} \phantom{0}9\phantom{0}2 \- \phantom{0}6\phantom{0}3\end{array}\]

Step 3: Perform Subtraction in the Units Column

Focus first on the units column (rightmost digits). We subtract 3 from 2. Since 2 is smaller than 3, we need to borrow from the tens column.

Step 4: Borrow from the Tens Column

Borrowing means taking 1 from the next column (tens column), thus turning 2 into 12. The tens column is reduced by 1, turning 9 into 8.\[\begin{array}{c} 8\phantom{0}12 \- \phantom{0}6\phantom{0}3\end{array}\]

Step 5: Subtract After Borrowing

Now, subtract 3 from 12 in the units column, getting 9. So, we write 9 in the result for the units column.

Step 6: Subtract in the Tens Column

Now, move to the tens column. Subtract 6 from 8, which equals 2. Place the 2 in the tens column of our answer.

Step 7: Compile the Results

Combine the results of the subtraction from both columns into one number: 29. This means 92 - 63 = 29.

Key Concepts

Borrowing in Subtraction

When subtracting, sometimes the number in a particular column is smaller than the number being subtracted. This is where borrowing comes in handy. Let's take the problem of subtracting 63 from 92 for example. In this case, the number 2 in the units column of 92 is smaller than the 3 in the units column of 63. To solve the subtraction problem, you need to borrow.

Borrowing involves taking a value from the next highest column to increase the number you need to subtract from. In our example, we borrow 10 from the tens column to add to the units column. This changes the 2 units in the original number to 12.

The action of borrowing does not increase the total value of the number as a whole; it just rearranges the quantities in each column, making subtraction possible. Remember, borrowing is essential whenever a digit in one column is too small to subtract directly from a larger digit below it.

Place Value Alignment

Place value alignment is crucial when setting up a subtraction problem. It ensures that numbers are properly positioned, so each digit is subtracted from the correct column. Let's consider the subtraction problem: 92 minus 63.

First, write the larger number above the smaller one. Align the numbers by their place values, so each column represents the same unit (such as tens or ones). In our example, make sure the 2 is aligned above the 3, and the 9 is above the 6.

Proper alignment looks like this:

• 9 above 6 in the tens column
• 2 above 3 in the ones column

This visual arrangement is key to performing subtraction accurately. When place values are misaligned, it leads to incorrect calculations and results. Always double-check your alignment before you begin subtracting.

Step-by-Step Subtraction

The step-by-step methodical approach helps simplify subtraction problems and ensure accuracy. Let's break down how you solve 92 minus 63 using this technique.

Begin with aligning the numbers, as previously mentioned. Start with the rightmost units column and check if borrowing is necessary. If a digit is less than the one directly beneath it, perform borrowing. In our example, you borrow 10 from the tens column, changing 2 to 12.

Subtract the two digits in the units column. Here, 12 minus 3 equals 9. Write this result in the units place of the answer.

Next, move to the tens column. Subtract the top digit from the bottom digit, resulting in 8 minus 6 or 2. Write 2 in the tens place of the answer. Lastly, compile your results for the final answer, 29.

• Check units column: borrow if needed, then subtract
• Move to tens column: subtract directly
• Combine results for the final answer

Following this structured approach ensures clarity and accuracy with subtraction problems.