Problem 35 - Prealgebra

Question

Subtract. $$25-21$$

Step-by-Step Solution

Answer

The result of subtracting 21 from 25 is 4.

Step 1: Identify the Operation

The exercise requires us to subtract two numbers: 25 and 21. Subtraction is the process of finding the difference between two numbers.

Step 2: Set Up the Subtraction Problem

We place the larger number (25) on top and the smaller number (21) below it, aligning the digits by place value. It should look like this:\[\begin{array}{c} 25 \-21\end{array}\]

Step 3: Perform the Subtraction

Subtract the digits in each column starting from the rightmost column. In the ones column, we have 5 - 1, which equals 4. In the tens column, we have 2 - 2, which equals 0. \[\begin{array}{c} 25 \-21 \\hline 04 \\end{array}\]

Step 4: Interpret the Result

The final result of the subtraction is 4. Double check to ensure no borrowing was needed and that the operation was carried out correctly.

Key Concepts

Place Value

Understanding place value is essential in subtraction. Place value refers to the digit's position in a number, determining its value. Let's look at the number 25. It has two digits:

• The **2** in 25 is in the tens place. It is worth 20.
• The **5** is in the ones place and is worth 5.

When aligning numbers to subtract, you must line them up according to their place values. This ensures that you subtract each digit from the correct column. For example, in the subtraction of 21 from 25:

• Ensure that the tens are aligned (2 and 2) and the ones are aligned (5 and 1).

Doing this accurately helps maintain the integrity of the calculation, leading to a correct outcome.

Subtraction Steps

Subtraction involves several clear steps to determine the difference between two numbers.
Here's how you can subtract 21 from 25:

• **Step 1:** Identify the numbers to subtract: 25 minus 21.
• **Step 2:** Place 25 on top and 21 below, aligning digits by place value.
• **Step 3:** Start from the rightmost column, the ones column - subtract 1 from 5, which gives 4.
• **Step 4:** Move to the next column, the tens - subtract 2 from 2, which equals 0.
• **Conclusion:** Write down your result. After finishing both steps, you get 04, which simplifies to 4.

Each step should follow a logical sequence to ensure no errors and is clear for double-checking.

Borrowing in Subtraction

Borrowing, also known as regrouping, is a method used when the number you are subtracting from (minuend) is smaller than the number you are subtracting (subtrahend) within a column.
In our example, 25 - 21, no borrowing is needed. Here’s a preview of when borrowing would be necessary:

• **For example:** Consider subtracting 37 from 45.
• If the ones digit of the top number is smaller than the bottom number, you borrow 1 from the tens place.
• This increases the value of the ones place in the minuend so you can subtract properly.

Borrowing ensures the subtraction process can continue smoothly even when digits aren't large enough in one place value column. Practice makes perfect, so try out more examples to understand borrowing deeply!