Let's solve the expression step by step:

Given expression:  
\[
\frac{4}{23} + \frac{7}{3} - \frac{94}{3}
\]

1. **Convert all fractions to have a common denominator**:

   - The common denominator for the fractions \(\frac{7}{3}\) and \(\frac{94}{3}\) is already \(3\).
   - The fraction \(\frac{4}{23}\) has a different denominator.

2. **Find the Least Common Denominator (LCD)**:

   - The LCD for \(23\) and \(3\) is \(69\).

3. **Convert each fraction to have the denominator \(69\)**:

   - Convert \(\frac{4}{23}\):
   \[
   \frac{4}{23} = \frac{4 \times 3}{23 \times 3} = \frac{12}{69}
   \]

   - Convert \(\frac{7}{3}\):
   \[
   \frac{7}{3} = \frac{7 \times 23}{3 \times 23} = \frac{161}{69}
   \]

   - Convert \(\frac{94}{3}\):
   \[
   \frac{94}{3} = \frac{94 \times 23}{3 \times 23} = \frac{2162}{69}
   \]

4. **Combine all fractions**:

   \[
   \frac{12}{69} + \frac{161}{69} - \frac{2162}{69}
   \]

   \[
   = \frac{12 + 161 - 2162}{69}
   \]

   \[
   = \frac{173 - 2162}{69}
   \]

   \[
   = \frac{-1989}{69}
   \]

5. **Simplify the fraction**:

   \[
   \frac{-1989}{69} = -29
   \]

So, the final result is:
\[
\frac{4}{23} + \frac{7}{3} - \frac{94}{3} = -29
\]

### Do you want more details or have any questions?

Here are some related questions for further exploration:

1. How do you find the least common denominator (LCD) of multiple fractions?
2. What are the steps to convert a fraction to have a specific denominator?
3. How can you simplify a fraction after combining like terms?
4. What are some strategies for dealing with negative numbers in fraction operations?
5. How do you interpret a negative result in real-world applications?

**Tip:** Always double-check your arithmetic when combining fractions, especially when negative numbers are involved!

Explore how to add and subtract fractions with a step-by-step solution for 4/23 + 7/3 - 94/3. This problem involves fractions with different denominators and covers arithmetic operations and simplification. Suitable 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