Problem 35 - Prealgebra

Question

Add. $$10,000+150$$

Step-by-Step Solution

Answer

The sum is 10,150.

Step 1: Understand the Problem

We need to add two numbers together: \(10,000\) and \(150\). This involves performing basic addition.

Step 2: Align the Numbers

Write the two numbers, \(10,000\) and \(150\), aligning their digits according to place value, so the units digits are in one column, the tens in another, etc.``` 10,000+ 150```

Step 3: Add the Numbers from Right to Left

Start adding the digits from the rightmost column (units) towards the left. Sum each column:- Units: \(0 + 0 = 0\)- Tens: \(0 + 5 = 5\)- Hundreds: \(0 + 1 = 1\)- Thousands: \(0\) (from \(10,000\), as there is no thousands digit in \(150\))- Ten-thousands: \(1\) (from \(10,000\), as there is no ten-thousands digit in \(150\))Place each result into the correct position in the sum.

Step 4: Write the Result

Combine the results from each step to find the total sum.The total sum is \(10,150\).

Key Concepts

Place Value

Understanding place value is essential in arithmetic. Place value refers to the value of a digit depending on its position within a number. This helps us correctly align numbers when performing operations like addition or subtraction.
Each digit in a number has a specific position:

• Units (Ones)
• Tens
• Hundreds
• Thousands
• Ten-thousands

For example, in the number 10,000, the '1' is in the ten-thousands position, which means it represents 10,000. Similarly, in 150, the '1' is in the hundreds position, representing 100.
When adding two numbers, it is crucial that these positions are aligned to ensure each digit adds properly with its corresponding value.

Basic Addition

Basic addition involves simple arithmetic where numbers are added together to produce a sum. It's an operation that accumulates quantities and is one of the fundamental operations in mathematics.
When performing basic addition, especially with larger numbers, it's critical to keep some rules in mind:

• Work from the smallest unit up to the largest. Start with the units (ones) column.
• If any column sums to ten or more, carry over the extra to the next column.

Practicing basic addition helps improve numerical fluency, enabling quicker calculations in everyday scenarios.

Column Addition

Column addition is a method used to add larger numbers systematically by stacking them according to their place values. This technique helps in visualizing the calculation and minimizes errors.
The process involves:

• Aligning the numbers vertically, ensuring the digits are in the correct columns.
• Adding the numbers column by column, starting from the rightmost one (units).
• Carrying over when sums reach ten or more.

For instance, when adding 10,000 and 150, arrange them vertically: ``` 10,000 + 150```
Begin by adding the units column, then tens, and so on. If you have a carry, make sure to move it to the next higher column. This helps in achieving an accurate sum efficiently.