Problem 76 - Algebra 1: Concepts and Skills

Question

Add. Write the answer as a decimal. (Skills Review pp. 759, 767) $$0.06+\frac{1}{8}$$

Step-by-Step Solution

Answer

The sum of 0.06 and \(\frac{1}{8}\) is 0.185.

Step 1: Convert Fraction to Decimal

The fraction is given as \(\frac{1}{8}\). Since 1 divided by 8 equals 0.125, the decimal equivalent of the fraction is 0.125.

Step 2: Add the Two Numbers

Now, add the decimal number 0.06 to the decimal equivalent of the fraction we just found, which is 0.125. Therefore, 0.06 + 0.125 = 0.185.

Key Concepts

Converting Fractions to Decimals

Understanding how to convert fractions to decimals is a fundamental skill that lays the foundation for many mathematical operations. A fraction represents a part of a whole, where the numerator is the top number indicating how many parts you have, and the denominator is the bottom number indicating into how many parts the whole is divided. To convert a fraction to a decimal, you simply divide the numerator by the denominator.

For instance, to convert the fraction \(\frac{1}{8}\) to a decimal, we divide 1 by 8. The division results in 0.125, which is the decimal form of the fraction \(\frac{1}{8}\). It's essential to ensure that the division is done accurately to obtain a precise decimal representation.

A calculator can be handy for this step, but understanding the process is crucial for developing strong arithmetic skills. Always remember when converting fractions that may result in a repeating decimal, it's important to round to the necessary degree of accuracy.

Decimal Addition

Once you have all numbers involved in an operation represented as decimals, adding them together is the next step. Decimal addition follows the same principles as adding whole numbers, with the key focus on aligning the decimal points. This means writing the numbers vertically with their decimal points lined up, one under the other, and then proceeding to add the values as you would do with whole numbers.

For example, when adding 0.06 and 0.125, place them one above the other, ensuring the decimal points are in a vertical line. Then add the two numbers together, starting from the rightmost digits, and carry over if necessary:

• \(.06\)
• \(+ .125\)
• \(-------\)
• \(.185\)

Remember to include any zeros necessary to fill in empty decimal places to maintain alignment. The result of this sum is the decimal 0.185.

Arithmetic Skills

Arithmetic skills encompass a range of mathematical techniques, from basic operations like addition and subtraction to more complex concepts such as fractions and decimals. Strong arithmetic skills allow you to perform calculations accurately and efficiently. These skills are built through practice and by understanding the why behind each step.

When approaching problems that require converting between fractions and decimals or performing decimal addition, remember to:

• Understand the value of each digit in a decimal.
• Use precise alignment of numbers to ensure accurate calculations.
• Practice the conversion of fractions to decimals to become fluent in recognizing common fractions and their decimal equivalents.

Building proficiency in these areas through exercises, such as the addition of fractions and decimals, prepares you for more complex mathematical tasks and real-world applications such as financial calculations and scientific measurements. Patience and practice are key—as with any skill, repetition and practical application lead to mastery.