Let's solve the expression step by step:

Given expression:  
\[
-14 \frac{3}{8} - 1 \frac{5}{7} + \frac{5}{7}
\]

### Step 1: Convert mixed numbers to improper fractions

1. **Convert** \( -14 \frac{3}{8} \) to an improper fraction:
   \[
   -14 \frac{3}{8} = -\left(\frac{14 \times 8 + 3}{8}\right) = -\frac{112 + 3}{8} = -\frac{115}{8}
   \]

2. **Convert** \( -1 \frac{5}{7} \) to an improper fraction:
   \[
   -1 \frac{5}{7} = -\left(\frac{1 \times 7 + 5}{7}\right) = -\frac{7 + 5}{7} = -\frac{12}{7}
   \]

3. **The fraction** \( \frac{5}{7} \) is already an improper fraction.

### Step 2: Combine the fractions

The expression is now:
\[
-\frac{115}{8} - \frac{12}{7} + \frac{5}{7}
\]

### Step 3: Combine the fractions with common denominators

First, combine the fractions with the same denominator:
\[
-\frac{12}{7} + \frac{5}{7} = -\frac{12 - 5}{7} = -\frac{7}{7} = -1
\]

Now the expression is:
\[
-\frac{115}{8} - 1
\]

### Step 4: Combine these results

Convert \( -1 \) into a fraction with the same denominator as \( \frac{115}{8} \):
\[
-\frac{115}{8} - \frac{8}{8} = -\frac{115 + 8}{8} = -\frac{123}{8}
\]

So, the final result is:
\[
-\frac{123}{8}
\]

This improper fraction can also be written as a mixed number:
\[
-15 \frac{3}{8}
\]

The final answer is:
\[
-15 \frac{3}{8}
\]

Would you like more details on any of these steps or have any questions?

---

Here are 5 related questions to consider:

1. How do you convert a mixed number to an improper fraction?
2. What is the process of finding a common denominator for adding or subtracting fractions?
3. How can improper fractions be simplified or converted back to mixed numbers?
4. What is the importance of handling negative signs correctly in fraction operations?
5. How do you add or subtract fractions with unlike denominators?

**Tip:** Always check if fractions can be simplified further before finalizing your answer!

Learn how to solve the expression involving mixed numbers and fractions: -14 3/8 - 1 5/7 + 5/7 step-by-step. This problem covers converting mixed numbers to improper fractions, adding and subtracting fractions with unlike denominators. Suitable for 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