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Chapter 1: Problem 452

Simplify. $$ \frac{6}{11}-\frac{s}{11} $$

Short Answer

Expert verified
\(\frac{6 - s}{11}\)

Step by step solution

01

Identify the common denominator

Notice that both fractions have the same denominator of 11. This means we can combine them directly.
02

Combine the numerators

Since the denominators are the same, we combine the numerators: \(\frac{6}{11} - \frac{s}{11} = \frac{6 - s}{11}\)
03

Write the simplified fraction

The expression simplifies to: \(\frac{6 - s}{11}\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Simplifying Fractions
Simplifying fractions is an essential skill in mathematics. To simplify a fraction, we need to reduce it to its simplest form by dividing the numerator and the denominator by their greatest common divisor (GCD). For instance, if we have the fraction $$\frac{12}{16}$$, we find the GCD of 12 and 16, which is 4. Then, we divide both the numerator (12) and the denominator (16) by 4 to get the simplified fraction $$\frac{3}{4}$$. Simplifying fractions makes calculations easier and results more comprehensible.
Remember:
  • The simplified fraction must have the smallest possible numerator and denominator.
  • Simplifying does not change the value of the fraction, it only makes it easier to work with.
Common Denominator
A common denominator is necessary when adding or subtracting fractions. The denominator is the bottom part of a fraction, and finding a common one simplifies operations. If two fractions have the same denominator, you can directly add or subtract the numerators. If they don't, you need to find the least common denominator (LCD) before you proceed.
For example, to subtract $$\frac{3}{4}$$ from $$\frac{5}{6}$$, follow these steps:
  1. Determine the least common denominator of 4 and 6. The smallest number both 4 and 6 divide into without a remainder is 12.
  2. Convert each fraction to have this common denominator:
    • $$\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$$
    • $$\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}$$
  3. Now we can subtract them easily: $$\frac{10}{12} - \frac{9}{12} = \frac{1}{12}$$
Practicing with common denominators makes fraction operations smoother and clearer.
Subtracting Fractions
Subtracting fractions involves a few straightforward steps, especially if the fractions share a common denominator. Here's how you can solve such problems easily:
  1. First, ensure both fractions have the same denominator. If not, find a common one (as explained above).
  2. Next, subtract the numerators while keeping the denominator unchanged.
  3. Finally, simplify the resulting fraction if possible.
Let's revisit our initial example: $$\frac{6}{11} - \frac{s}{11}$$. Notice both fractions have the same denominator (11). This means we can directly subtract the numerators:
$$\frac{6 - s}{11}$$. The fraction is already in its simplest form, so that's our final answer.
To sum up:
  • Keep the denominator the same.
  • Subtract the numerators.
  • Check for simplification and simplify if necessary.
Mastering these steps ensures you can handle more complex fractions with confidence.

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