Problem 301 - Prealgebra

Question

In the following exercises, simplify. $$6,251+4,749$$

Step-by-Step Solution

Answer

11,000

Step 1: Set Up the Problem

Write down the numbers for the addition problem. We need to add 6,251 and 4,749.

Step 2: Add the Units Place

Add the digits in the units place: \[1 + 9 = 10\] Write down 0 and carry over 1 to the next place.

Step 3: Add the Tens Place

Add the digits in the tens place along with the carried over 1: \[5 + 4 + 1 = 10\] Write down 0 and carry over 1 to the next place.

Step 4: Add the Hundreds Place

Add the digits in the hundreds place along with the carried over 1: \[2 + 7 + 1 = 10\] Write down 0 and carry over 1 to the next place.

Step 5: Add the Thousands Place

Add the digits in the thousands place along with the carried over 1: \[6 + 4 + 1 = 11\] Write down 11 as there are no more places to carry over.

Step 6: Combine the Results

Write down the final result, combining all the digits: \[6,251 + 4,749 = 11,000\]

Key Concepts

carry over method

Understanding the carry-over method is essential in addition, especially with large numbers. When adding digits in each place value and the sum exceeds 9, the excess digit is carried over to the next higher place.
For example, if we are adding 1 and 9 in the units place and get 10, we write down 0 and carry over 1 to the tens place. This process repeats for each place:

• Start from the units place and move left.
• If sum exceeds 9, carry over the extra value to the next place.

With practice, the carry-over method helps simplify multi-digit addition and ensures you get the correct result.

place value

Place value helps us understand the value of each digit in a number, depending on its position. In the number 6,251:

• 1 is in the units place, so its value is 1.
• 5 is in the tens place, so its value is 50.
• 2 is in the hundreds place, so its value is 200.
• 6 is in the thousands place, so its value is 6,000.

While adding 6,251 and 4,749, each digit aligns with its respective place. This alignment ensures we add units to units, tens to tens, hundreds to hundreds, and thousands to thousands. Understanding place value makes it easier to manage numbers and reduces mistakes in calculations.

basic operations

Understanding basic operations like addition is foundational in prealgebra. Addition combines two numbers to get a total sum. The given problem, 6,251 + 4,749, involves addition of two four-digit numbers. We followed these steps:

• Line up numbers by place value.
• Start adding from the rightmost digit (units place).
• Use the carry-over method if needed.
• Progress to the next column towards the left.

By mastering basic operations, we set the stage for more complex math concepts. Consistent practice with such exercises builds confidence and aids in faster calculations.