Problem 38 - Prealgebra

Question

Add. $$10,456.78+156.85$$

Step-by-Step Solution

Answer

The sum is $10,613.63$.

Step 1: Aligning Decimal Points

To add the numbers $10,456.78$ and $156.85$, start by aligning them vertically by their decimal points. It is important to ensure that both the integer and decimal parts line up correctly.

Step 2: Adding the Decimal Parts

Add the decimal parts together: $0.78 + 0.85 = 1.63$. Write down the $0.63$ under the decimal line and carry over the $1$ to the whole number part.

Step 3: Adding Whole Numbers with Carry Over

Add the whole numbers together, including the carry over: $10,456 + 156 = 10,612$, then add the carry over of $1$ to get $10,613$.

Step 4: Writing the Final Result

Combine the results from adding the whole numbers and the decimal parts. The final result is $10,613.63$.

Key Concepts

Aligning Decimal Points

When dealing with decimal addition, aligning decimal points is a crucial first step. This involves arranging the numbers so that the decimal points are directly above each other. This ensures that the digits of the same place value, such as the tenths or hundredths, line up, making it easier to add them accurately.

To align decimal points, do the following:

• Write each number with the decimal point in a vertical line.
• Add zeros if necessary to ensure each number has the same number of decimal places, this helps with easy addition.
• Once aligned, you can clearly see which digits belong to the same decimal places, much like adding whole numbers.

Aligning the decimals simplifies the process and guarantees precision as we move on to the next steps.

Carry Over in Addition

In decimal addition, just like with whole numbers, you may encounter a situation where you need to carry over a digit. This typically occurs when the sum of digits in a column exceeds 9.

For example, while adding the decimal parts, you might find:

• Adding 0.78 and 0.85 gives you 1.63.
• The 1 represents a whole unit, so it's carried over to the next place, the whole numbers column.
• The "0.63" is written under the decimal part.

Carry-over helps maintain the correct value in each decimal place, allowing you to seamlessly continue with the addition of the whole numbers.

Adding Whole Numbers

Adding whole numbers in decimal addition is very similar to regular addition. After dealing with the decimal parts, you often have a whole number that might need a carry-over addition at this stage.

In our example:

• You first add the whole numbers: 10,456 and 156, disregarding any decimals.
• This gives a total of 10,612.
• However, because of the previous decimal addition, you must add the carry-over of 1 from the decimal section.
• The new total becomes 10,613.

Integrating the carry-over ensures accuracy and lets you confidently combine this with the decimal response for the final answer.