Problem 8 - Prealgebra

Question

Add the decimals. \(18.7+7\)

Step-by-Step Solution

Answer

The result of the addition is 25.7.

Step 1: Write the Problem

Write down the addition problem aligning the decimal points: \[18.7 + 7.0\]

Step 2: Align Decimal Points

Notice that there is no decimal point in 7, but we can write it as 7.0 to make sure the decimal points are aligned for both numbers:\[\begin{array}{c@{}c@{}c@{}c} & 18.7 \+ & 7.0 \\hline\end{array}\]

Step 3: Add Column by Column

Start adding from the right-most column (tenths place), move to the left: 1. Tenths: 7 + 0 = 7. 2. Units: 8 + 7 = 15. Place 5 in the units place and carry over 1. 3. Tens: 1 + 1 (carried over) = 2.

Step 4: Write the Result

Write the completed sum, aligning the decimal points correctly:\[\begin{array}{c@{}c@{}c@{}c} & 18.7 \+ & 7.0 \\hline & 25.7 \\end{array}\]

Key Concepts

Aligning Decimal Points

When dealing with decimal addition, one of the most important steps is aligning decimal points. This ensures precise calculation and avoids any confusion about place values. It's essential to align numbers in vertical format so that each digit lines up with its counterpart. For instance, if you have the numbers 18.7 and 7, you can write 7 as 7.0. Adding a zero after the decimal point clarifies the number's tenths place even if it wasn't shown originally.

• Aligning the decimal points guarantees accuracy in calculations.
• It helps ensure that the digits in the same place value columns are added together.
• Using zeros can clarify positions, making sure that every column lines up correctly.

This simple adjustment can prevent mistakes and bring more clarity to your work, especially in more complex problems.

Columnar Addition

Columnar addition means adding the numbers column by column, starting from the right-most side, which is often the tenths or hundredths position in decimals. This method is similar to adding whole numbers and helps manage any carry-over digits easily. Electing a straightforward approach makes complex sums appear simpler.
Let's break it down using our example:

• Start with the tenths column: Here, 7 (from 18.7) plus 0 (from 7.0) equals 7. Write the sum directly below.
• Move to the units column: 8 plus 7 equals 15. Place the 5 below, while you must remember to carry over the 1 to the next column.
• A final step is to add numbers in the tens column, don't forget your carryover. Add the carried-over 1 with the existing 1 to make 2.

Following these neatly executed steps will ensure precision and help foster an easy path to learning how to sum decimals.

Carrying Over in Addition

Carrying over is a crucial aspect of columnar addition. It happens when the sum of digits in a column exceeds 9. In our example, while adding the units' column, 8 plus 7 results in 15. However, only the 5 can fit into the units' space, so we need to "carry over" the 1 as an extra digit to the next column on the left.
Here's how carrying over works:

• Write down the digit from 0 to 9 that results from your addition.
• Transfer the additional value (10 and above) to the next column on the left as a carryover.
• You’ll then add this carryover number to your subsequent column's digits.

This process ensures that every piece of the sum is accounted for and properly placed, maintaining the result's accuracy. Mastering the carry-over method in decimal addition will make your math calculations quicker and error-free.