Problem 78 - Algebra 1: Concepts and Skills

Question

Add. Write the answer as a decimal. (Skills Review pp. 759, 767) $$\frac{3}{5}+0.4$$

Step-by-Step Solution

Answer

The sum is 1.0

Step 1 - Convert Fraction To Decimal

To convert a fraction to a decimal, we divide the numerator by the denominator. So, to convert \( \frac{3}{5} \) to a decimal, divide 3 by 5 which is 0.6.

Step 2 - Add The Decimal Numbers

The given decimals are 0.6 (from the converted fraction) and 0.4. Add both numbers to get a result.

Step 3 - Write the Final Result

After obtaining the sum of the two decimals, write down the final result.

Key Concepts

Fraction to Decimal Conversion

When dealing with addition between a fraction and a decimal, the first important step is to convert the fraction into a decimal. This makes it easier to add because you're working with the same number format.

To convert a fraction like \( \frac{3}{5} \) to a decimal, you simply divide the numerator by the denominator.

• **Numerator**: This is the top number in a fraction, which represents how many parts of the whole you have.
• **Denominator**: This is the bottom number in a fraction, which shows into how many parts the whole is divided.

In this case, you divide 3 by 5, which equals 0.6.

This conversion step is crucial when combining different number types, as working with decimals simplifies the arithmetic process.

Numerator and Denominator

Understanding the numerator and the denominator is essential when working with fractions.

The numerator is the top number in a fraction and it tells you how many parts we are talking about. For instance, in the fraction \( \frac{3}{5} \), the numerator is 3. This means we have 3 parts out of a total that is defined by the denominator.

Then, the denominator is the bottom number and it indicates the total number of equal parts into which the whole is divided. In \( \frac{3}{5} \), the denominator is 5, meaning the whole is divided into 5 equal parts.

Why are these terms important? Because understanding them will make operations like fraction to decimal conversion smoother. When you know that converting involves dividing these two numbers, it simplifies your work, making it less daunting to handle mixed types of numbers.

Adding Decimals

Once you have all your numbers in decimal form, the task becomes straightforward. Adding decimals is similar to regular addition, with a focus on aligning the decimal points.

• Ensure all numbers have their decimal points aligned vertically.
• Start adding from the rightmost digit (usually the smallest place value).

Take this exercise as an example; you have the decimal 0.6 from the fraction \( \frac{3}{5} \) and the decimal 0.4. By aligning the decimal points, you can swiftly add them together: \[0.6 + 0.4 = 1.0\]

Notice how aligning the decimal points made the addition effortless, as you focus on one digit at a time starting from the rightmost side.