Problem 59 - Algebra 1: Concepts and Skills

Question

ADDING DECIMALS Add. $$ 16.8+7.1 $$

Step-by-Step Solution

Answer

The sum of 16.8 and 7.1 is 23.9

Step 1: Write Down the Numbers

First things first, jot down the numbers carefully one below the other aligning the decimal points. It looks like this: \[16.8\] \[+ \quad 7.1\]

Step 2: Add the Parts Separately

Now start the addition process from right to left, just like in basic math. Add the numbers after the decimal point first then the numbers before the decimal point. \[ 16.8\] \[+ \quad7.1\] \[--------\] \[23.9\]

Step 3: Write the Final Answer

After adding up, we just ensure that the answer got the correct decimal point. So, the final answer is 23.9

Key Concepts

Understanding Decimal Points

Decimals are an essential part of mathematics, especially when dealing with non-whole numbers. A decimal point is a dot that separates the whole number part from the fractional part of a number. It is essential that during addition, subtraction, or any operation involving decimals, you align decimal points to ensure accuracy. Here’s how decimal points work in the number 16.8:

• The number '16' is the whole number.
• The number '8' after the decimal point represents the fractional part, or tenths, in this case.

Align the decimal points when stacking numerical values vertically for clear computation, ensuring all fractional parts are correctly placed.

Performing Addition With Decimals

Adding decimals is similar to adding whole numbers; the main focus should be on decimal alignment. Start by placing one number under another, ensuring the decimal points meet. This alignment guarantees that each digit is in its correct column, whether units, tenths, hundredths, etc. Consider the first step:

• Align '16.8' over '7.1' precisely by the decimal point.

You now add each column starting from the rightmost digit, just as with whole numbers. This careful organization helps maintain the integrity of your arithmetic procedure.

Basic Math Techniques

Basic math techniques come into play when practicing addition, especially with decimals. Remember to always add from the rightmost side moving left. This rule applies to both whole numbers and numbers involving decimal points. Let’s break it down:

• 8 (tenths of 16.8) + 1 (tenths of 7.1) equals 9 tenths.
• 6 (of 16) and 7 (of 7) result in 13, with the carryover adjusted appropriately.

This systematic method of handling carryovers ensures your results are accurate and logical.

Step-by-Step Solution Approach

Following a step-by-step solution can aid greatly in understanding and solving decimal addition tasks. Breaking down the procedure into smaller, manageable steps helps in internalizing the method. Here are the crucial steps:

• Write Down the Numbers: Align numbers vertically by decimal points.
• Add the Parts Separately: Begin with the smallest place value (tenths, hundredths, etc.).
• Finalize the Answer: Re-check alignment to ensure accuracy of the result.

For example, as demonstrated with 16.8 + 7.1, approach each step diligently to achieve the final sum of 23.9, verifying that the decimal remains in its proper location throughout your calculations.