https://file.aiquickdraw.com/mathbot/file/1728934971584uiuhelgl.jpg

The problem shown in the image is:

\[
\frac{5}{6} - \frac{6}{5} - \frac{5}{9}
\]

To solve this, we need to subtract these fractions. Here's a step-by-step breakdown:

### Step 1: Find the least common denominator (LCD)
We have three fractions: \(\frac{5}{6}\), \(\frac{6}{5}\), and \(\frac{5}{9}\). To subtract them, we need a common denominator.

- The denominators are 6, 5, and 9.
- The least common denominator (LCD) of 6, 5, and 9 is 90.

### Step 2: Rewrite each fraction with the LCD of 90
- \(\frac{5}{6}\) becomes \(\frac{5 \times 15}{6 \times 15} = \frac{75}{90}\)
- \(\frac{6}{5}\) becomes \(\frac{6 \times 18}{5 \times 18} = \frac{108}{90}\)
- \(\frac{5}{9}\) becomes \(\frac{5 \times 10}{9 \times 10} = \frac{50}{90}\)

### Step 3: Perform the subtraction
Now subtract the fractions:

\[
\frac{75}{90} - \frac{108}{90} - \frac{50}{90}
\]

First, subtract \(\frac{75}{90} - \frac{108}{90}\):

\[
\frac{75 - 108}{90} = \frac{-33}{90}
\]

Now subtract \(\frac{-33}{90} - \frac{50}{90}\):

\[
\frac{-33 - 50}{90} = \frac{-83}{90}
\]

### Step 4: Simplify the fraction
The fraction \(\frac{-83}{90}\) is already in its simplest form because 83 and 90 have no common factors other than 1.

Thus, the final answer is:

\[
\boxed{\frac{-83}{90}}
\]

---

Would you like any further explanation or have any questions about this solution?

Here are 5 additional questions to explore:
1. How do you find the least common denominator for multiple fractions?
2. How would the problem change if it involved addition instead of subtraction?
3. What would happen if one of the fractions was a mixed number?
4. Can you show an example where the final result is a whole number?
5. How would you approach a similar problem involving improper fractions?

**Tip:** Always check if your fractions can be simplified before performing operations; this can make calculations easier!

Evaluate 5/6 - 6/5 - 5/9 and write the answer in simplest form.

Learn how to solve the subtraction of fractions problem: 5/6 - 6/5 - 5/9. This detailed solution includes finding the least common denominator (LCD) and performing the subtraction in simplified form, ideal for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation