Problem 11 - Prealgebra

Question

Add the decimals. \(4.76+2.1\)

Step-by-Step Solution

Answer

The sum of 4.76 and 2.1 is 6.86.

Step 1: Align the Decimal Points

First, write down the numbers with the decimal points aligned. This ensures that you add the digits in the correct place values.\[\begin{array}{c} 4.76 \+ 2.10 \\hline\end{array}\]

Step 2: Add the Hundredths Place

Add the digits in the hundredths place. Here, it's 6 (from 4.76) plus 0 (from 2.10). \[6 + 0 = 6\]Place this below the line in the hundredths column.

Step 3: Add the Tenths Place

Add the digits in the tenths place, which are 7 (from 4.76) and 1 (from 2.10).\[7 + 1 = 8\]Write 8 below the line in the tenths column.

Step 4: Add the Units Place

Now, add the digits in the units place. That's 4 (from 4.76) plus 2 (from 2.10).\[4 + 2 = 6\]Write 6 below the line in the units column.

Step 5: Write Down the Result

Combine all the digits you have added in each column to find the sum of the decimal numbers.\[\begin{array}{c} 4.76 \+ 2.10 \\hline 6.86\end{array}\]

Key Concepts

Aligning Decimal Points

When adding decimals, maintaining proper alignment is essential. Begin by lining up the decimal points of the numbers you want to add. This alignment ensures each digit is placed in its correct column.
This way, every number can be correctly placed in their respective value categories: units, tenths, hundredths, etc.
Using vertical alignment allows you to perform operations with precision, as it mimics addition of whole numbers where columns represent specific values.

Place Value

Place value is the concept where the position of a digit in a number determines its value. Each digit in a decimal number has a specific place value:

• The digit to the left of the decimal point is the units place, representing whole numbers or 'ones.'
• The digit immediately to the right of the decimal represents the tenths place, equal to one-tenth of a unit.
• The next digit after the tenths is the hundredths place, which is one-hundredth of a unit.

Understanding place value helps in systematically carrying out arithmetic operations by ensuring that you’re adding digits of the same magnitude together.

Adding Decimals Step-by-Step

Let's break down adding decimals through a clear, step-by-step process.
Start by aligning the decimals. Write the numbers one below the other so the decimal points are in a vertical line.
Next, work from right to left. Begin with the smallest place value, which is furthest to the right:

• Add digits in the hundredths place: 6 (from 4.76) + 0 (from 2.10) = 6.
• Add digits in the tenths place: 7 (from 4.76) + 1 (from 2.10) = 8.
• Finally, add the digits in the units place: 4 (from 4.76) + 2 (from 2.10) = 6.

After you add each place value, combine all the digits to get the final sum, ensuring decimals are correctly placed in the result: 6.86. Following these steps guarantees accuracy in your decimal addition.