Problem 10 - Algebra A Combined Function

Question

Add or subtract as indicated. $$ 2.31+6.4 $$

Step-by-Step Solution

Answer

The sum is 8.71.

Step 1: Align the Numbers

To add the numbers, align them by their decimal points. Make sure that each digit is in the correct column:\[\begin{array}{r} 2.31 \+ 6.40 \\hline\end{array}\]

Step 2: Add the Hundredths Place

Add the digits in the hundredths place. Since there is a 0 in the hundredths place of 6.4, simply bring down the 1:\[\begin{array}{r} 2.31 \+ 6.40 \\hline \,\,\,\,\,\,\,\,\,\,1 \\end{array}\]

Step 3: Add the Tenths Place

Add the tenths place next, which is 3 + 4 = 7:\[\begin{array}{r} 2.31 \+ 6.40 \\hline \,\,\,\,7 1 \\end{array}\]

Step 4: Add the Units Place

Add the digits in the units place, 2 + 6 = 8. Write the result to the left of the previously computed digits:\[\begin{array}{r} 2.31 \+ 6.40 \\hline 8.71 \\end{array}\]

Step 5: Final Result

The sum of 2.31 and 6.4 is 8.71.

Key Concepts

Aligning Decimal Points

Aligning decimal points is crucial when adding decimals. Begin by writing the numbers vertically. Align them so their decimal points are directly above each other. This ensures each digit is placed in the correct column according to its place value.
When you align decimals, you essentially are lining up numbers based on where they stand in hundreds, tens, units, tenths, or hundredths columns.

• Write the numbers so that the decimal points form a straight line.
• Don't worry if your numbers have different lengths after the decimal. Just make sure the points line up.
• Fill in empty spaces with zeros to help visualize the addition. This does not change the value but aids in correct addition.

Aligned decimals allow you to add each column separately, ensuring you handle each part of the number accurately.

Addition of Decimals

Adding decimals is similar to adding whole numbers; you just need to pay attention to their place values. After aligning your numbers by their decimal points:

• Start adding from the rightmost column, moving towards the left.
• If there's a missing digit in a column due to different decimal lengths, treat it as zero.
• Make sure to carry over numbers when the sum of a column exceeds 9, just like in whole number addition.

By ensuring each column is correctly added, including carrying over from one column to another if necessary, you can achieve the correct sum. The process flows smoothly if alignment is done right.

Place Value in Addition

Understanding place value is key to performing accurate decimal addition. Each digit in a number holds a specific value based on its position:

• The units place holds whole numbers.
• The tenths and hundredths come after the decimal point.
• Inaccurate addition results without respecting these positions.

When adding decimals, consider each digit's place value. For instance, numbers in the tenths place should only be added to other tenths place numbers.
Respecting place value helps avoid errors and contributes to an accurate and precise addition process. Always write the addition result aligned with its place values to verify accuracy.