Problem 61 - Algebra 1: Concepts and Skills

Question

ADDING DECIMALS Add. $$ 1.0008+10.15 $$

Step-by-Step Solution

Answer

The sum of 1.0008 and 10.15 is 11.1508.

Step 1: Align the Decimals

First, write the numbers so that the decimal points line up vertically. This gives: \ \[ 10.1500 \ +1.0008 \ \] Fill any extra spaces with 0.

Step 2: Add the decimals

Perform the addition column by column from right to left. Remember to carry forward any '1' if a column adds up to 10 or more. The result of the addition becomes: \[ 11.1508 \ \] No column adds up to 10 or more, so no carrying is needed.

Step 3: Writing the Final Answer

The answer to the addition problem is the same as the result obtained from step 2, so the final result is: \(11.1508\)

Key Concepts

Aligning Decimal Points

Mastering the addition of decimals begins with the proper alignment of decimal points. When you write down the numbers, it's crucial to ensure that the decimal points are directly above or below each other. This alignment allows you to clearly see which place values correspond and need to be added together.

Imagine stacking coins of different values—pennies, dimes, and dollars—one atop the other. Each coin's value must be aligned with others of the same value for a correct count. Similarly, aligning the decimal points guarantees that units, tenths, hundredths, and so on, are all in the correct position for addition.

Decimal Addition

Once your decimal points are aligned, you can proceed with decimal addition, much like you would with whole numbers. You start adding from the furthest right column and move leftward, column by column. If all numbers are aligned correctly, you simply add the numbers in the same place value.

Consider using a placeholder, such as a zero, if one number has fewer decimal places than the other. This balances the numbers and ensures that each numeral is added to the correct corresponding place value. If you're calculating money, think of it as adding cents to cents and dollars to dollars; the same principles apply!

Carrying Over in Addition

Carrying over is a step in addition you encounter when the sum of a column exceeds the base number of our numbering system, which is 10. When this happens, you keep the rightmost digit of the sum in the current column and carry over the remaining value to the next left column.

However, in our example with the numbers 1.0008 and 10.15, carrying over isn't necessary because no column's sum exceeds 9. This makes the addition straightforward, but the understanding of carrying over is essential for more complex operations where columns do exceed the base number, ensuring that all sums are accurately calculated.