Problem 202 - Prealgebra

Question

In the following exercises, simplify. $$ 305-262 $$

Step-by-Step Solution

Answer

The simplified form of \(305 - 262\) is \(43\).

Step 1: Identify the numbers

Observe the subtraction: \(305 - 262\). We need to simplify this expression by subtracting the second number from the first.

Step 2: Subtract the two numbers

Perform the subtraction: \(305 - 262 = 43\).

Key Concepts

Simplifying Expressions

In mathematics, simplifying expressions is a key process. It involves reducing a complex expression into its simplest form. Simplifying can mean performing arithmetic operations or combining like terms. For example, in the expression \(305 - 262\), we simplify it by performing the subtraction to end up with a single number, in this case, \(43\).

Simplifying helps solve problems more easily and gives a clear, concise result. When you see an expression that can be simplified, always look for the operations you should perform first. In subtraction, as in this example, we subtract the smaller number from the larger number directly.

Remember, the goal of simplification is to make the expression as simple as possible. This usually involves performing basic arithmetic operations like addition, subtraction, multiplication, or division.

Subtraction Step-by-Step

Subtraction is a fundamental operation in arithmetic. It allows us to find the difference between two numbers. Let's walk through the subtraction process step by step using the example \(305 - 262\):

• First, align the numbers vertically by their place values (hundreds, tens, and ones).
• Starting from the rightmost digit (ones place), subtract each pair of digits. If the top digit is smaller, you may need to borrow from the next left digit.
• For \(305 - 262\), begin with 5 - 2 = 3 in the ones place.
• Next, move to the tens place: 0 - 6, here you need to borrow. From the hundreds place, borrow 1, making it 10 - 6 = 4.
• Finally, move to the hundreds place: 2 - 2 = 0.

Putting it all together, you get \(43\) as the result. This step-by-step approach ensures accuracy.

Elementary Arithmetic

Elementary arithmetic covers basic mathematical operations including addition, subtraction, multiplication, and division. These operations form the foundation for all other math concepts. Understanding them is essential to progress in math.

Subtraction is one of the first arithmetic skills learned in elementary school. It helps in understanding the concept of taking away or finding the difference between quantities.

Proper command over subtraction also sets the stage for more complex operations like working with negative numbers or solving algebraic equations later on.

• Always remember to line up numbers by their place values when subtracting.
• Subtract each digit from right to left.
• Borrow from the next digit if necessary.
• Verify your result by adding the subtraction result to the smaller number; you should get the larger number.

Practice regularly to become more confident and efficient in performing these essential operations.