Problem 1 - Beginning and Intermediate Algebra

Question

Add or subtract, as indicated. $$\frac{8}{11}-\frac{3}{11}$$

Step-by-Step Solution

Answer

The short answer to the question, 'Add or subtract, as indicated: \(\frac{8}{11} - \frac{3}{11}\)' is \(\frac{5}{11}\).

Step 1: Identify the common denominator

Both fractions have the same denominator, which is 11. This means we can directly subtract the numerators.

Step 2: Subtract the numerators

Subtract the numerator of the second fraction from the numerator of the first fraction: \(8 - 3 = 5\)

Step 3: Write the result

Now we have the result of the subtraction: \(\frac{5}{11}\) So, \(\frac{8}{11} - \frac{3}{11} = \frac{5}{11}\).

Key Concepts

Understanding a Common Denominator

When dealing with fractions, a common denominator is vital for addition and subtraction. A common denominator refers to the same bottom number shared between two or more fractions. In this case, both fractions have a denominator of 11, making it simple to subtract.

Using a common denominator allows fractions to be directly compared or combined.

• If the denominators were different, you would need to find a least common multiple to achieve the same denominator for each fraction.
• Without a common denominator, direct subtraction is not possible because you're comparing different parts of a whole.

By ensuring the denominators match, we can accurately perform operations such as subtraction.

Focusing on Numerators

The numerators—the top numbers of fractions—are your main focus when you perform subtraction with a common denominator. Here, you are subtracting 3 from 8.

Think of the numerators as specific parts of a whole that are being compared.

• The operation becomes straightforward: simply subtract the second fraction’s numerator from the first one.
• This means we perform the subtraction \(8 - 3 = 5\).

Now, the result is the numerator of the new fraction. The denominator remains the same, in this case, 11. This action combines the parts of the fractions efficiently.

Step By Step Solution Breakdown

Breaking down problems into steps can drastically simplify the process of solving them. Let's recap the steps for subtracting these fractions:

1. **Identify the Common Denominator:** This is already given as both fractions have 11 as their denominators.
2. **Subtract the Numerators:** Using simple arithmetic, subtract 3 from 8, resulting in 5.
3. **Write Down the Result:** The new fraction becomes \(\frac{5}{11}\).

By methodically following these steps, fractions are made less daunting. Always look to break down processes into digestible steps, ensuring each part of the problem is understood before proceeding.